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refactor(library/logic/eq): use 'substvars' tactic

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Leonardo de Moura 2015-06-02 23:55:51 -07:00
parent a8c9121d2e
commit 16d03c17ee
1 changed files with 10 additions and 10 deletions
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20
library/logic/eq.lean
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@ -48,43 +48,43 @@ section
variables {a a' : A} {b b' : B} {c c' : C} {d d' : D} {e e' : E}
theorem congr_fun {B : A → Type} {f g : Π x, B x} (H : f = g) (a : A) : f a = g a :=
H ▸ rfl
by substvars
theorem congr_arg (f : A → B) (H : a = a') : f a = f a' :=
H ▸ rfl
by substvars
theorem congr_arg2 (f : A → B → C) (Ha : a = a') (Hb : b = b') : f a b = f a' b' :=
congr (congr_arg f Ha) Hb
by substvars
theorem congr_arg3 (f : A → B → C → D) (Ha : a = a') (Hb : b = b') (Hc : c = c')
: f a b c = f a' b' c' :=
congr (congr_arg2 f Ha Hb) Hc
by substvars
theorem congr_arg4 (f : A → B → C → D → E) (Ha : a = a') (Hb : b = b') (Hc : c = c') (Hd : d = d')
: f a b c d = f a' b' c' d' :=
congr (congr_arg3 f Ha Hb Hc) Hd
by substvars
theorem congr_arg5 (f : A → B → C → D → E → F)
(Ha : a = a') (Hb : b = b') (Hc : c = c') (Hd : d = d') (He : e = e')
: f a b c d e = f a' b' c' d' e' :=
congr (congr_arg4 f Ha Hb Hc Hd) He
by substvars
theorem congr2 (f f' : A → B → C) (Hf : f = f') (Ha : a = a') (Hb : b = b') : f a b = f' a' b' :=
Hf ▸ congr_arg2 f Ha Hb
by substvars
theorem congr3 (f f' : A → B → C → D) (Hf : f = f') (Ha : a = a') (Hb : b = b') (Hc : c = c')
: f a b c = f' a' b' c' :=
Hf ▸ congr_arg3 f Ha Hb Hc
by substvars
theorem congr4 (f f' : A → B → C → D → E)
(Hf : f = f') (Ha : a = a') (Hb : b = b') (Hc : c = c') (Hd : d = d')
: f a b c d = f' a' b' c' d' :=
Hf ▸ congr_arg4 f Ha Hb Hc Hd
by substvars
theorem congr5 (f f' : A → B → C → D → E → F)
(Hf : f = f') (Ha : a = a') (Hb : b = b') (Hc : c = c') (Hd : d = d') (He : e = e')
: f a b c d e = f' a' b' c' d' e' :=
Hf ▸ congr_arg5 f Ha Hb Hc Hd He
by substvars
end
theorem equal_f {A : Type} {B : A → Type} {f g : Π x, B x} (H : f = g) : ∀x, f x = g x :=