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This commit is contained in:
Thomas Baruchel 2023-12-04 06:34:07 +01:00
parent 06acb4fd7e
commit 24c29ad273
1 changed files with 3 additions and 11 deletions
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14
src/mapping.v
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@ -348,20 +348,12 @@ Proof.
(* second case in split *) (* second case in split *)
rewrite H0. rewrite H0.
(*
apply FinFun.bInjective_bSurjective in H3.
apply FinFun.bSurjective_bBijective in H3. destruct H3 as [g].
destruct H3.
*)
assert (forall s, (forall y, In y s -> y < length base) assert (forall s, (forall y, In y s -> y < length base)
-> map (nth_error base) s -> map (nth_error base) s
= map (nth_error (map (fun e => nth (g e) base x) (seq 0 (length base)))) (map f s)). = map (nth_error (map (fun e => nth (g e) base x) (seq 0 (length base)))) (map f s)).
intro s. rewrite map_map. induction s; intro K. reflexivity. intro s. rewrite map_map. induction s; intro K. reflexivity.
simpl. rewrite IHs. simpl. rewrite IHs.
assert (forall q p, p < q -> nth p (seq 0 q) 0 = p). assert (forall q p, p < q -> nth p (seq 0 q) 0 = p).
intro q. induction q; intro p'; intro J4. intro q. induction q; intro p'; intro J4.
apply Nat.nlt_0_r in J4. contradiction. apply Nat.nlt_0_r in J4. contradiction.
@ -378,7 +370,6 @@ Proof.
with (Some ((fun e => nth (g e) base x) with (Some ((fun e => nth (g e) base x)
(nth (f a) (seq 0 (length base)) 0))). (nth (f a) (seq 0 (length base)) 0))).
assert (forall m n f' g', assert (forall m n f' g',
FinFun.bFun m f' -> FinFun.bFun m g' FinFun.bFun m f' -> FinFun.bFun m g'
-> (forall x : nat, x < m -> g' (f' x) = x /\ f' (g' x) = x) -> (forall x : nat, x < m -> g' (f' x) = x /\ f' (g' x) = x)
@ -389,9 +380,10 @@ Proof.
rewrite H6. apply H5 in N. destruct N. rewrite H8. reflexivity. rewrite H6. apply H5 in N. destruct N. rewrite H8. reflexivity.
apply H2. assumption. rewrite H6. apply H5 in N. destruct N. apply H2. assumption. rewrite H6. apply H5 in N. destruct N.
rewrite H7.
rewrite nth_error_nth' with (d := x). symmetry. rewrite map_nth_error with (d := f a). reflexivity.
rewrite nth_error_nth' with (d := 0). rewrite H6. reflexivity.