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Proof step 10 from proof le-same (previous step)

m * n = m + m * n -1, m * n + n0 ≤ m, n0 ≤ m ⊦ n0 = 0, n = 0, n = 1 ∧ n0 = 0

User applied rule insert equation

And closed the goal!

Rule argument

pos: left 1 flags: discard

Additional information

Used simplifier rules: pred-03: ⊦ n -1 = n - 1; from specification nat%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic2%le-add: ⊦ m + m0 ≤ m ↔ m0 = 0; from specification nat%z-01: ⊦ m + n = 0 ↔ m = 0 ∧ n = 0; from specification nat-basic2%c: ⊦ m + n = n + m; from specification nat-basic2