blob: e6a89d12937cf37ef65a600051af52b37c114b17 [file] [edit]
example (x : Nat) : x + 0 = x + 0 := by
generalize x + 0 = y
rfl
example (x : Nat) : x + 0 = x + 0 := by
generalize h : x + 0 = y
rfl
example (x y w : Nat) (h : y = w) : (x + x) + w = (x + x) + y := by
generalize h' : x + x = z
subst y
rfl
example (x y w : Nat) (h : x + x = y) : (x + x) + (x+x) = (x + x) + y := by
generalize h' : x + x = z
subst z
subst y
rfl
example (x y w : Nat) (h : y = w) : (x + x) + w = (x + x) + y := by
generalize h' : x + y = z -- just add equality
subst h
rfl
example (x y w : Nat) (h : y = w) (H : (x + x) + w = (x + x) + y) :
(x + x) + w = (x + x) + y := by
generalize h' : x + x = z at H
exact H