| theorem ex1 (x : Nat) : 0 + x = x := by | |
| cases x with | |
| | zero => skip -- Error: unsolved goals | |
| | succ y => skip -- Error: unsolved goals | |
| theorem ex2 (x : Nat) : 0 + x = x := by | |
| induction x with | |
| | zero => skip -- Error: unsolved goals | |
| | succ y ih => skip -- Error: unsolved goals | |
| theorem ex3 (x : Nat) : 0 + x = x := by | |
| cases x with | |
| | zero => rfl | |
| | succ y => skip -- Error: unsolved goals | |
| theorem ex4 (x : Nat) {y : Nat} (h : y > 0) : x % y < y := by | |
| induction x, y using Nat.mod.inductionOn with | |
| | ind x y h₁ ih => skip -- Error: unsolved goals | |
| | base x y h₁ => skip -- Error: unsolved goals | |
| theorem ex5 (x : Nat) {y : Nat} (h : y > 0) : x % y < y := by | |
| cases x, y using Nat.mod.inductionOn with | |
| | ind x y h₁ ih => skip -- Error: unsolved goals | |
| | base x y h₁ => skip -- Error: unsolved goals |