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Completely fixed notation

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Niels
2017-08-08 17:00:30 +02:00
parent 92bc50d79f
commit 3cda0d9bf2
12 changed files with 96 additions and 100 deletions
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14
FiniteSets/fsets/length.v
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@@ -9,24 +9,22 @@ Section Length.
Context {A_deceq : DecidablePaths A}.
Context `{Univalence}.
Opaque isIn_b.
Definition length (x : FSetC A) : nat.
Proof.
simple refine (FSetC_ind A _ _ _ _ _ _ x ); simpl.
- exact 0.
- intros a y n.
pose (y' := FSetC_to_FSet y).
exact (if isIn_b a y' then n else (S n)).
- intros. rewrite transport_const. cbn.
simplify_isIn_b. simpl. reflexivity.
- intros. rewrite transport_const. cbn.
exact (if a ∈_d y' then n else (S n)).
- intros. rewrite transport_const. simpl.
simplify_isIn_b. reflexivity.
- intros. rewrite transport_const. simpl.
simplify_isIn_b.
destruct (dec (a = b)) as [Hab | Hab].
+ rewrite Hab. simplify_isIn_b. simpl. reflexivity.
+ rewrite Hab. simplify_isIn_b. reflexivity.
+ rewrite ?L_isIn_b_false; auto.
++ simpl.
destruct (isIn_b a (FSetC_to_FSet x0)), (isIn_b b (FSetC_to_FSet x0))
destruct (a ∈_d (FSetC_to_FSet x0)), (b ∈_d (FSetC_to_FSet x0))
; reflexivity.
++ intro p. contradiction (Hab p^).
Defined.