Documentation of branch “master” at 1af9c554

coq · Jan 11, 2025 · a9c933c · a9c933c
1 parent 0176178
commit a9c933c
Show file tree

Hide file tree

Showing 246 changed files with 1,189 additions and 1,189 deletions.
diff --git a/master/refman/.doctrees/addendum/extraction.doctree b/master/refman/.doctrees/addendum/extraction.doctree
diff --git a/master/refman/.doctrees/addendum/generalized-rewriting.doctree b/master/refman/.doctrees/addendum/generalized-rewriting.doctree
diff --git a/master/refman/.doctrees/addendum/implicit-coercions.doctree b/master/refman/.doctrees/addendum/implicit-coercions.doctree
diff --git a/master/refman/.doctrees/addendum/micromega.doctree b/master/refman/.doctrees/addendum/micromega.doctree
diff --git a/master/refman/.doctrees/addendum/miscellaneous-extensions.doctree b/master/refman/.doctrees/addendum/miscellaneous-extensions.doctree
diff --git a/master/refman/.doctrees/addendum/program.doctree b/master/refman/.doctrees/addendum/program.doctree
diff --git a/master/refman/.doctrees/addendum/rewrite-rules.doctree b/master/refman/.doctrees/addendum/rewrite-rules.doctree
diff --git a/master/refman/.doctrees/addendum/ring.doctree b/master/refman/.doctrees/addendum/ring.doctree
diff --git a/master/refman/.doctrees/addendum/sprop.doctree b/master/refman/.doctrees/addendum/sprop.doctree
diff --git a/master/refman/.doctrees/addendum/type-classes.doctree b/master/refman/.doctrees/addendum/type-classes.doctree
diff --git a/master/refman/.doctrees/addendum/universe-polymorphism.doctree b/master/refman/.doctrees/addendum/universe-polymorphism.doctree
diff --git a/master/refman/.doctrees/changes.doctree b/master/refman/.doctrees/changes.doctree
diff --git a/master/refman/.doctrees/environment.pickle b/master/refman/.doctrees/environment.pickle
diff --git a/master/refman/.doctrees/language/cic.doctree b/master/refman/.doctrees/language/cic.doctree
diff --git a/master/refman/.doctrees/language/coq-library.doctree b/master/refman/.doctrees/language/coq-library.doctree
diff --git a/master/refman/.doctrees/language/core/assumptions.doctree b/master/refman/.doctrees/language/core/assumptions.doctree
diff --git a/master/refman/.doctrees/language/core/basic.doctree b/master/refman/.doctrees/language/core/basic.doctree
diff --git a/master/refman/.doctrees/language/core/coinductive.doctree b/master/refman/.doctrees/language/core/coinductive.doctree
diff --git a/master/refman/.doctrees/language/core/conversion.doctree b/master/refman/.doctrees/language/core/conversion.doctree
diff --git a/master/refman/.doctrees/language/core/inductive.doctree b/master/refman/.doctrees/language/core/inductive.doctree
diff --git a/master/refman/.doctrees/language/core/modules.doctree b/master/refman/.doctrees/language/core/modules.doctree
diff --git a/master/refman/.doctrees/language/core/primitive.doctree b/master/refman/.doctrees/language/core/primitive.doctree
diff --git a/master/refman/.doctrees/language/core/records.doctree b/master/refman/.doctrees/language/core/records.doctree
diff --git a/master/refman/.doctrees/language/core/sections.doctree b/master/refman/.doctrees/language/core/sections.doctree
diff --git a/master/refman/.doctrees/language/core/variants.doctree b/master/refman/.doctrees/language/core/variants.doctree
diff --git a/master/refman/.doctrees/language/extensions/arguments-command.doctree b/master/refman/.doctrees/language/extensions/arguments-command.doctree
diff --git a/master/refman/.doctrees/language/extensions/canonical.doctree b/master/refman/.doctrees/language/extensions/canonical.doctree
diff --git a/master/refman/.doctrees/language/extensions/evars.doctree b/master/refman/.doctrees/language/extensions/evars.doctree
diff --git a/master/refman/.doctrees/language/extensions/implicit-arguments.doctree b/master/refman/.doctrees/language/extensions/implicit-arguments.doctree
diff --git a/master/refman/.doctrees/language/extensions/match.doctree b/master/refman/.doctrees/language/extensions/match.doctree
diff --git a/master/refman/.doctrees/practical-tools/coq-commands.doctree b/master/refman/.doctrees/practical-tools/coq-commands.doctree
diff --git a/master/refman/.doctrees/practical-tools/coqide.doctree b/master/refman/.doctrees/practical-tools/coqide.doctree
diff --git a/master/refman/.doctrees/proof-engine/ltac.doctree b/master/refman/.doctrees/proof-engine/ltac.doctree
diff --git a/master/refman/.doctrees/proof-engine/ltac2.doctree b/master/refman/.doctrees/proof-engine/ltac2.doctree
diff --git a/master/refman/.doctrees/proof-engine/ssreflect-proof-language.doctree b/master/refman/.doctrees/proof-engine/ssreflect-proof-language.doctree
diff --git a/master/refman/.doctrees/proof-engine/tactics.doctree b/master/refman/.doctrees/proof-engine/tactics.doctree
diff --git a/master/refman/.doctrees/proof-engine/vernacular-commands.doctree b/master/refman/.doctrees/proof-engine/vernacular-commands.doctree
diff --git a/master/refman/.doctrees/proofs/automatic-tactics/auto.doctree b/master/refman/.doctrees/proofs/automatic-tactics/auto.doctree
diff --git a/master/refman/.doctrees/proofs/automatic-tactics/logic.doctree b/master/refman/.doctrees/proofs/automatic-tactics/logic.doctree
diff --git a/master/refman/.doctrees/proofs/writing-proofs/equality.doctree b/master/refman/.doctrees/proofs/writing-proofs/equality.doctree
diff --git a/master/refman/.doctrees/proofs/writing-proofs/proof-mode.doctree b/master/refman/.doctrees/proofs/writing-proofs/proof-mode.doctree
diff --git a/master/refman/.doctrees/proofs/writing-proofs/reasoning-inductives.doctree b/master/refman/.doctrees/proofs/writing-proofs/reasoning-inductives.doctree
diff --git a/master/refman/.doctrees/user-extensions/syntax-extensions.doctree b/master/refman/.doctrees/user-extensions/syntax-extensions.doctree
diff --git a/master/refman/.doctrees/using/libraries/funind.doctree b/master/refman/.doctrees/using/libraries/funind.doctree
diff --git a/master/refman/.doctrees/using/libraries/writing.doctree b/master/refman/.doctrees/using/libraries/writing.doctree
diff --git a/master/refman/proof-engine/ltac.html b/master/refman/proof-engine/ltac.html
@@ -4286,42 +4286,42 @@ <h3>Profiling <code class="docutils literal notranslate"><span class="pre">L</sp
 </span></dt><dd><span>No more goals.
 </span></dd>
 <dt><span></span><span class="coqdoc-keyword">Show</span><span> </span><span class="coqdoc-keyword">Ltac</span><span> </span><span class="coqdoc-var">Profile</span><span>.</span><span>
-</span></dt><dd><span>total time:      1.944s
+</span></dt><dd><span>total time:      0.933s
 
  tactic                                      local  total   calls       max
 ───────────────────────────────────────────┴──────┴──────┴───────┴─────────┘
-─tac --------------------------------------   0.1% 100.0%       1    1.944s
-─&lt;Corelib.Init.Tauto.with_uniform_flags&gt; --   0.0%  94.3%      26    0.114s
-─&lt;Corelib.Init.Tauto.tauto_gen&gt; -----------   0.0%  94.3%      26    0.114s
-─&lt;Corelib.Init.Tauto.tauto_intuitionistic&gt;    0.0%  94.2%      26    0.114s
-─t_tauto_intuit ---------------------------   0.1%  94.1%      26    0.114s
-─&lt;Corelib.Init.Tauto.simplif&gt; -------------  60.2%  90.6%      26    0.112s
-─&lt;Corelib.Init.Tauto.is_conj&gt; -------------  22.8%  22.8%   28756    0.050s
-─lia --------------------------------------   0.1%   5.4%      28    0.069s
-─Zify.zify --------------------------------   3.8%   4.3%      54    0.068s
-─elim id ----------------------------------   4.1%   4.1%     650    0.000s
-─&lt;Corelib.Init.Tauto.axioms&gt; --------------   2.3%   3.5%       0    0.006s
+─tac --------------------------------------   0.1% 100.0%       1    0.933s
+─&lt;Corelib.Init.Tauto.with_uniform_flags&gt; --   0.0%  93.0%      26    0.059s
+─&lt;Corelib.Init.Tauto.tauto_gen&gt; -----------   0.0%  92.9%      26    0.059s
+─&lt;Corelib.Init.Tauto.tauto_intuitionistic&gt;    0.0%  92.9%      26    0.059s
+─t_tauto_intuit ---------------------------   0.1%  92.8%      26    0.059s
+─&lt;Corelib.Init.Tauto.simplif&gt; -------------  57.9%  89.2%      26    0.058s
+─&lt;Corelib.Init.Tauto.is_conj&gt; -------------  25.1%  25.1%   28756    0.025s
+─lia --------------------------------------   0.1%   6.7%      28    0.046s
+─Zify.zify --------------------------------   5.1%   5.6%      54    0.045s
+─&lt;Corelib.Init.Tauto.axioms&gt; --------------   2.3%   3.5%       0    0.002s
+─elim id ----------------------------------   2.9%   2.9%     650    0.000s
 
  tactic                                        local  total   calls       max
 ─────────────────────────────────────────────┴──────┴──────┴───────┴─────────┘
-─tac ----------------------------------------   0.1% 100.0%       1    1.944s
- ├─&lt;Corelib.Init.Tauto.with_uniform_flags&gt; --   0.0%  94.3%      26    0.114s
- │└&lt;Corelib.Init.Tauto.tauto_gen&gt; -----------   0.0%  94.3%      26    0.114s
- │└&lt;Corelib.Init.Tauto.tauto_intuitionistic&gt;    0.0%  94.2%      26    0.114s
- │└t_tauto_intuit ---------------------------   0.1%  94.1%      26    0.114s
- │ ├─&lt;Corelib.Init.Tauto.simplif&gt; -----------  60.2%  90.6%      26    0.112s
- │ │ ├─&lt;Corelib.Init.Tauto.is_conj&gt; ---------  22.8%  22.8%   28756    0.050s
- │ │ └─elim id ------------------------------   4.1%   4.1%     650    0.000s
- │ └─&lt;Corelib.Init.Tauto.axioms&gt; ------------   2.3%   3.5%       0    0.006s
- └─lia --------------------------------------   0.1%   5.4%      28    0.069s
-  └Zify.zify --------------------------------   3.8%   4.3%      54    0.068s
+─tac ----------------------------------------   0.1% 100.0%       1    0.933s
+ ├─&lt;Corelib.Init.Tauto.with_uniform_flags&gt; --   0.0%  93.0%      26    0.059s
+ │└&lt;Corelib.Init.Tauto.tauto_gen&gt; -----------   0.0%  92.9%      26    0.059s
+ │└&lt;Corelib.Init.Tauto.tauto_intuitionistic&gt;    0.0%  92.9%      26    0.059s
+ │└t_tauto_intuit ---------------------------   0.1%  92.8%      26    0.059s
+ │ ├─&lt;Corelib.Init.Tauto.simplif&gt; -----------  57.9%  89.2%      26    0.058s
+ │ │ ├─&lt;Corelib.Init.Tauto.is_conj&gt; ---------  25.1%  25.1%   28756    0.025s
+ │ │ └─elim id ------------------------------   2.9%   2.9%     650    0.000s
+ │ └─&lt;Corelib.Init.Tauto.axioms&gt; ------------   2.3%   3.5%       0    0.002s
+ └─lia --------------------------------------   0.1%   6.7%      28    0.046s
+  └Zify.zify --------------------------------   5.1%   5.6%      54    0.045s
 </span></dd>
 <dt><span></span><span class="coqdoc-keyword">Show</span><span> </span><span class="coqdoc-keyword">Ltac</span><span> </span><span class="coqdoc-var">Profile</span><span> &quot;lia&quot;.</span><span>
-</span></dt><dd><span>total time:      1.944s
+</span></dt><dd><span>total time:      0.933s
 
  tactic  local  total   calls       max
 ───────┴──────┴──────┴───────┴─────────┘
-─lia --   0.1%   5.4%      28    0.069s
+─lia --   0.1%   6.7%      28    0.046s
 
  tactic  local  total   calls       max
 ───────┴──────┴──────┴───────┴─────────┘

diff --git a/master/refman/proofs/writing-proofs/equality.html b/master/refman/proofs/writing-proofs/equality.html
@@ -2640,15 +2640,15 @@ <h3>Computing in a term: eval and Eval<a class="headerlink" href="#computing-in-
   True
 </span></dd>
 <dt><span></span><span class="coqdoc-keyword">Time</span><span> </span><span class="coqdoc-tactic">assert</span><span> (</span><span class="coqdoc-var">id</span><span> (</span><span class="coqdoc-var">fact</span><span> 8) = </span><span class="coqdoc-var">fact</span><span> 8) </span><span class="coqdoc-tactic">by</span><span> </span><span class="coqdoc-tactic">reflexivity</span><span>.</span><span>
-</span></dt><dd><span>Finished transaction in 0.074 secs (0.041u,0.032s) (successful)
+</span></dt><dd><span>Finished transaction in 0.051 secs (0.05u,0.001s) (successful)
 1 goal
 
   H : id (fact 8)</span><span> =</span><span> fact 8
   ============================
   True
 </span></dd>
 <dt><span></span><span class="coqdoc-keyword">Time</span><span> </span><span class="coqdoc-tactic">assert</span><span> (</span><span class="coqdoc-var">id</span><span> (</span><span class="coqdoc-var">fact</span><span> 9) = </span><span class="coqdoc-var">fact</span><span> 9) </span><span class="coqdoc-tactic">by</span><span> </span><span class="coqdoc-tactic">reflexivity</span><span>.</span><span>
-</span></dt><dd><span>Finished transaction in 0.692 secs (0.686u,0.005s) (successful)
+</span></dt><dd><span>Finished transaction in 0.33 secs (0.33u,0.s) (successful)
 1 goal
 
   H : id (fact 8)</span><span> =</span><span> fact 8
@@ -2676,7 +2676,7 @@ <h3>Computing in a term: eval and Eval<a class="headerlink" href="#computing-in-
 Timeout!
 </span></dd>
 <dt><span></span><span class="coqdoc-keyword">Time</span><span> </span><span class="coqdoc-tactic">assert</span><span> (</span><span class="coqdoc-var">id</span><span> (</span><span class="coqdoc-var">fact</span><span> 100) = </span><span class="coqdoc-var">fact</span><span> 100) </span><span class="coqdoc-tactic">by</span><span> </span><span class="coqdoc-var">with_strategy</span><span> -1 [</span><span class="coqdoc-var">id</span><span>] </span><span class="coqdoc-tactic">reflexivity</span><span>.</span><span>
-</span></dt><dd><span>Finished transaction in 0.001 secs (0.001u,0.s) (successful)
+</span></dt><dd><span>Finished transaction in 0. secs (0.u,0.s) (successful)
 1 goal
 
   H : id (fact 100)</span><span> =</span><span> fact 100
@@ -2711,7 +2711,7 @@ <h3>Computing in a term: eval and Eval<a class="headerlink" href="#computing-in-
   True
 </span></dd>
 <dt><span></span><span class="coqdoc-keyword">Time</span><span> </span><span class="coqdoc-tactic">assert</span><span> (</span><span class="coqdoc-var">id</span><span> (</span><span class="coqdoc-var">fact</span><span> 100) = </span><span class="coqdoc-var">fact</span><span> 100) </span><span class="coqdoc-tactic">by</span><span> </span><span class="coqdoc-var">with_strategy</span><span> -1 [</span><span class="coqdoc-var">id</span><span>] </span><span class="coqdoc-tactic">abstract</span><span> </span><span class="coqdoc-tactic">reflexivity</span><span>.</span><span>
-</span></dt><dd><span>Finished transaction in 0.002 secs (0.002u,0.s) (successful)
+</span></dt><dd><span>Finished transaction in 0.001 secs (0.001u,0.s) (successful)
 1 goal
 
   H : id (fact 100)</span><span> =</span><span> fact 100
@@ -2722,7 +2722,7 @@ <h3>Computing in a term: eval and Eval<a class="headerlink" href="#computing-in-
 </span></dt><dd><span>No more goals.
 </span></dd>
 <dt><span></span><span class="coqdoc-keyword">Time</span><span> </span><span class="coqdoc-keyword">Defined</span><span>.</span><span>
-</span></dt><dd><span>Finished transaction in 0.001 secs (0.001u,0.s) (successful)
+</span></dt><dd><span>Finished transaction in 0. secs (0.u,0.s) (successful)
 </span></dd>
 </dl>
 </div>

diff --git a/master/refman/searchindex.js b/master/refman/searchindex.js
diff --git a/master/stdlib/Stdlib.Arith.Arith_base.html b/master/stdlib/Stdlib.Arith.Arith_base.html
@@ -57,7 +57,7 @@ <h1 class="libtitle">Library Stdlib.Arith.Arith_base</h1>
 </div>
 
 <div class="doc">
-<a id="lab1"></a><h1 class="section"><span class="inlinecode"><span class="id" title="var">arith</span></span> hint database</h1>
+<a id="lab238"></a><h1 class="section"><span class="inlinecode"><span class="id" title="var">arith</span></span> hint database</h1>
 
 </div>
 <div class="code">
@@ -79,7 +79,7 @@ <h1 class="libtitle">Library Stdlib.Arith.Arith_base</h1>
 </div>
 
 <div class="doc">
-<a id="lab2"></a><h2 class="section"><span class="inlinecode"><span class="id" title="var">lt</span></span> and <span class="inlinecode"><span class="id" title="var">le</span></span></h2>
+<a id="lab239"></a><h2 class="section"><span class="inlinecode"><span class="id" title="var">lt</span></span> and <span class="inlinecode"><span class="id" title="var">le</span></span></h2>
 
 </div>
 <div class="code">

diff --git a/master/stdlib/Stdlib.Arith.EqNat.html b/master/stdlib/Stdlib.Arith.EqNat.html
@@ -55,7 +55,7 @@ <h1 class="libtitle">Library Stdlib.Arith.EqNat</h1>
 Equality on natural numbers 
 <div class="paragraph"> </div>
 
-<a id="lab18"></a><h1 class="section">Propositional equality</h1>
+<a id="lab237"></a><h1 class="section">Propositional equality</h1>
 
 </div>
 <div class="code">

diff --git a/master/stdlib/Stdlib.Arith.PeanoNat.html b/master/stdlib/Stdlib.Arith.PeanoNat.html
@@ -148,7 +148,7 @@ <h1 class="libtitle">Library Stdlib.Arith.PeanoNat</h1>
 </div>
 
 <div class="doc">
-<a id="lab3"></a><h2 class="section">Remaining constants not defined in Stdlib.Init.Nat</h2>
+<a id="lab222"></a><h2 class="section">Remaining constants not defined in Stdlib.Init.Nat</h2>
 
 <div class="paragraph"> </div>
 
@@ -166,7 +166,7 @@ <h1 class="libtitle">Library Stdlib.Arith.PeanoNat</h1>
 </div>
 
 <div class="doc">
-<a id="lab4"></a><h2 class="section">Basic specifications : pred add sub mul</h2>
+<a id="lab223"></a><h2 class="section">Basic specifications : pred add sub mul</h2>
 
 </div>
 <div class="code">
@@ -208,7 +208,7 @@ <h1 class="libtitle">Library Stdlib.Arith.PeanoNat</h1>
 </div>
 
 <div class="doc">
-<a id="lab5"></a><h2 class="section">Boolean comparisons</h2>
+<a id="lab224"></a><h2 class="section">Boolean comparisons</h2>
 
 </div>
 <div class="code">
@@ -240,7 +240,7 @@ <h1 class="libtitle">Library Stdlib.Arith.PeanoNat</h1>
 </div>
 
 <div class="doc">
-<a id="lab6"></a><h2 class="section">Decidability of equality over <span class="inlinecode"><span class="id" title="var">nat</span></span>.</h2>
+<a id="lab225"></a><h2 class="section">Decidability of equality over <span class="inlinecode"><span class="id" title="var">nat</span></span>.</h2>
 
 </div>
 <div class="code">
@@ -252,7 +252,7 @@ <h1 class="libtitle">Library Stdlib.Arith.PeanoNat</h1>
 </div>
 
 <div class="doc">
-<a id="lab7"></a><h2 class="section">Ternary comparison</h2>
+<a id="lab226"></a><h2 class="section">Ternary comparison</h2>
 
 <div class="paragraph"> </div>
 
@@ -281,7 +281,7 @@ <h1 class="libtitle">Library Stdlib.Arith.PeanoNat</h1>
 </div>
 
 <div class="doc">
-<a id="lab8"></a><h2 class="section">Minimum, maximum</h2>
+<a id="lab227"></a><h2 class="section">Minimum, maximum</h2>
 
 </div>
 <div class="code">
@@ -331,7 +331,7 @@ <h1 class="libtitle">Library Stdlib.Arith.PeanoNat</h1>
 </div>
 
 <div class="doc">
-<a id="lab9"></a><h2 class="section">Power</h2>
+<a id="lab228"></a><h2 class="section">Power</h2>
 
 </div>
 <div class="code">
@@ -349,7 +349,7 @@ <h1 class="libtitle">Library Stdlib.Arith.PeanoNat</h1>
 </div>
 
 <div class="doc">
-<a id="lab10"></a><h2 class="section">Square</h2>
+<a id="lab229"></a><h2 class="section">Square</h2>
 
 </div>
 <div class="code">
@@ -361,7 +361,7 @@ <h1 class="libtitle">Library Stdlib.Arith.PeanoNat</h1>
 </div>
 
 <div class="doc">
-<a id="lab11"></a><h2 class="section">Parity</h2>
+<a id="lab230"></a><h2 class="section">Parity</h2>
 
 </div>
 <div class="code">
@@ -405,7 +405,7 @@ <h1 class="libtitle">Library Stdlib.Arith.PeanoNat</h1>
 </div>
 
 <div class="doc">
-<a id="lab12"></a><h2 class="section">Division</h2>
+<a id="lab231"></a><h2 class="section">Division</h2>
 
 </div>
 <div class="code">
@@ -434,7 +434,7 @@ <h1 class="libtitle">Library Stdlib.Arith.PeanoNat</h1>
 </div>
 
 <div class="doc">
-<a id="lab13"></a><h2 class="section">Square root</h2>
+<a id="lab232"></a><h2 class="section">Square root</h2>
 
 </div>
 <div class="code">
@@ -458,7 +458,7 @@ <h1 class="libtitle">Library Stdlib.Arith.PeanoNat</h1>
 </div>
 
 <div class="doc">
-<a id="lab14"></a><h2 class="section">Logarithm</h2>
+<a id="lab233"></a><h2 class="section">Logarithm</h2>
 
 </div>
 <div class="code">
@@ -480,7 +480,7 @@ <h1 class="libtitle">Library Stdlib.Arith.PeanoNat</h1>
 </div>
 
 <div class="doc">
-<a id="lab15"></a><h2 class="section">Properties of <span class="inlinecode"><span class="id" title="var">iter</span></span></h2>
+<a id="lab234"></a><h2 class="section">Properties of <span class="inlinecode"><span class="id" title="var">iter</span></span></h2>
 
 </div>
 <div class="code">
@@ -532,7 +532,7 @@ <h1 class="libtitle">Library Stdlib.Arith.PeanoNat</h1>
 </div>
 
 <div class="doc">
-<a id="lab16"></a><h2 class="section">Gcd</h2>
+<a id="lab235"></a><h2 class="section">Gcd</h2>
 
 </div>
 <div class="code">
@@ -560,7 +560,7 @@ <h1 class="libtitle">Library Stdlib.Arith.PeanoNat</h1>
 </div>
 
 <div class="doc">
-<a id="lab17"></a><h2 class="section">Bitwise operations</h2>
+<a id="lab236"></a><h2 class="section">Bitwise operations</h2>
 
 </div>
 <div class="code">