| 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 |