15 lines
416 B
Text
15 lines
416 B
Text
variables a b c d : Nat
|
|
axiom H : a + (b + c) = a + (b + d)
|
|
|
|
set_option pp::implicit true
|
|
|
|
using Nat
|
|
check add_succr a
|
|
|
|
theorem mul_zerol2 (a : Nat) : 0 * a = 0
|
|
:= induction_on a
|
|
(have 0 * 0 = 0 : mul_zeror 0)
|
|
(λ (n : Nat) (iH : 0 * n = 0),
|
|
calc 0 * (n + 1) = (0 * n) + 0 : mul_succr 0 n
|
|
... = 0 + 0 : { iH }
|
|
... = 0 : add_zeror 0)
|