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refactor(library/data/fin): simplify 'fin' module using new inversion tactic

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Leonardo de Moura 2014-11-28 22:46:06 -08:00
parent ad0dfb4c64
commit 011e955fed
1 changed files with 6 additions and 20 deletions
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library/data/fin.lean
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@ -8,32 +8,18 @@ fs : Π {n}, fin n → fin (succ n)
namespace fin namespace fin
definition z_cases_on (C : fin zero → Type) (p : fin zero) : C p := definition z_cases_on (C : fin zero → Type) (p : fin zero) : C p :=
have aux : Π (C : Type) (n : nat) (p : fin n), n = zero → C, from by cases p
λ C n p, fin.rec_on p
(λ n h, nat.no_confusion h)
(λ n f ih h, nat.no_confusion h),
aux (C p) zero p rfl
definition nz_cases_on {C : Π n, fin (succ n) → Type} definition nz_cases_on {C : Π n, fin (succ n) → Type}
(H₁ : Π n, C n (fz n)) (H₁ : Π n, C n (fz n))
(H₂ : Π n (f : fin n), C n (fs f)) (H₂ : Π n (f : fin n), C n (fs f))
{n : nat} {n : nat}
(f : fin (succ n)) : C n f := (f : fin (succ n)) : C n f :=
have aux : Π (n₁ : nat) (f₁ : fin n₁) (heq₁ : n₁ = succ n) (f : fin (succ n)) (heq₂ : f₁ == f), C n f, from begin
λ n₁ f₁, fin.rec_on f₁ cases f with (n', n', f'),
(λ (n₁ : nat) (heq₁ : succ n₁ = succ n), apply (H₁ n'),
have heq₁' : n₁ = n, from nat.no_confusion heq₁ (λ e, e), apply (H₂ n' f')
eq.rec_on heq₁' (λ (f : fin (succ n₁)) (heq₂ : fz n₁ == f), end
have heq₂' : fz n₁ = f, from heq.to_eq heq₂,
have Cfz : C n₁ (fz n₁), from H₁ n₁,
eq.rec_on heq₂' Cfz))
(λ (n₁ : nat) (f₁ : fin n₁) (ih : _) (heq₁ : succ n₁ = succ n),
have heq₁' : n₁ = n, from nat.no_confusion heq₁ (λ e, e),
eq.rec_on heq₁' (λ (f : fin (succ n₁)) (heq₂ : @fs n₁ f₁ == f),
have heq₂' : @fs n₁ f₁ = f, from heq.to_eq heq₂,
have Cfs : C n₁ (@fs n₁ f₁), from H₂ n₁ f₁,
eq.rec_on heq₂' Cfs)),
aux (succ n) f rfl f !heq.refl
definition to_nat {n : nat} (f : fin n) : nat := definition to_nat {n : nat} (f : fin n) : nat :=
fin.rec_on f fin.rec_on f