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Proof step 9 from proof two-ppred (previous step)

m0 * 2 + n0 - 2 = m1 * 2 + n1, n1 < 2, n0 < 2 ⊦ m0 * 2 + n0 = 0, m0 = m1 + 1, m0 = 0 ∧ n0 = 1

User applied rule constructor cut

And closed the goal!

Rule argument

var: m0

Additional information

Used simplifier rules: nat freely generated by 0, +1;;% ⊦ m +1 = m + 1; (s)% ⊦ m * (n + 1) = m * n + m; (s)%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic%c: ⊦ m + n = n + m; from specification nat-basic%mult-a: ⊦ m0 * m * n = (m0 * m) * n; from specification nat-mult%mult-c: ⊦ m * n = n * m; from specification nat-mult% ⊦ n ≤ m → m + n0 - n = (m - n) + n0; (s)% ⊦ n + 0 = n; (s)% ⊦ n0 < n ∧ n1 < n → (m * n + n0 = m0 * n + n1 ↔ m = m0 ∧ n0 = n1); (ws)% ⊦ m + n = m + n0 ↔ n = n0; (s)% ⊦ m + 1 ≠ 0; (s)% ⊦ m ≠ 0 → (m < 2 ↔ m = 1); (s)