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Proof step 5 from proof le-same (previous step)

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

User applied rule cut formula

And obtained the following new goals

Proof step 6:
m * n = m + m * n -1, m * n + n0 ≤ m ⊦ n = 0, n = 1 ∧ n0 = 0, m = 0 ∧ n0 = 0

Rule argument

fma: m * n = m + m * n -1

Additional information

Used simplifier rules: coef-17: ⊦ m * n + n = m1 * n ↔ m + 1 = m1 ∨ n = 0;%mult-a: ⊦ m0 * m * n = (m0 * m) * n;%mult-c: ⊦ m * n = n * m;% ⊦ n -1 = n - 1; (s)% ⊦ m ≤ n ↔ ¬ n < m; (ss)% ⊦ m < 1 ↔ m = 0; (s)%n ≤ m ⊦ (m - n) + n0 = n1 ↔ m + n0 = n + n1; (s)%c: ⊦ m + n = n + m; from specification nat-basic%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic Used formulas: m * n = m + m * n -1