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Simple lemma about appending permutations #2989

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Jul 10, 2023
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Simple lemma about appending permutations #2989

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6 changes: 6 additions & 0 deletions ulib/FStar.Seq.Properties.fst
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Original file line number Diff line number Diff line change
Expand Up @@ -189,6 +189,12 @@ let lemma_swap_permutes_aux #_ s i j x =
end
#pop-options

let append_permutations #a s1 s2 s1' s2' =
(
lemma_append_count s1 s2;
lemma_append_count s1' s2'
)

let lemma_swap_permutes #a s i j
= FStar.Classical.forall_intro
#a
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5 changes: 5 additions & 0 deletions ulib/FStar.Seq.Properties.fsti
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Expand Up @@ -196,6 +196,11 @@ val lemma_swap_permutes_aux: #a:eqtype -> s:seq a -> i:nat{i<length s} -> j:nat{

type permutation (a:eqtype) (s1:seq a) (s2:seq a) =
(forall i. count i s1 = count i s2)

val append_permutations: #a:eqtype -> s1:seq a -> s2:seq a -> s1':seq a -> s2':seq a -> Lemma
(requires permutation a s1 s1' /\ permutation a s2 s2')
(ensures permutation a (append s1 s2) (append s1' s2'))

val lemma_swap_permutes (#a:eqtype) (s:seq a) (i:nat{i<length s}) (j:nat{i <= j && j<length s})
: Lemma (permutation a s (swap s i j))

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