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Proof step 31 from proof n2s-s2n-identity (previous step)

m0 = m + 1, m0 < 9, ∀ m1. m1 < m0 + 1 → true → s→n(n→s(m1)) = m1 ⊦ m0 = 0, pos (('2' ' + '3' ' + '4' ' + '5' ' + '6' ' + '7' ' + '8' ' + '9' ')[m], '0' ' + '1' ' + '2' ' + '3' ' + '4' ' + '5' ' + '6' ' + '7' ' + '8' ' + '9' ') = m0 + 1

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 32:
m < 8, ∀ m1. m1 < (m + 1) + 1 → true → s→n(n→s(m1)) = m1 ⊦ pos (('2' ' + '3' ' + '4' ' + '5' ' + '6' ' + '7' ' + '8' ' + '9' ')[m], '0' ' + '1' ' + '2' ' + '3' ' + '4' ' + '5' ' + '6' ' + '7' ' + '8' ' + '9' ') = 2 + m

Rule argument

Additional information

Used simplifier rules: l-num-05: n < n0 ⊦ m + (* n) < (* n0) ↔ m < n0 - n; from specification nat%c: ⊦ m + n = n + m; from specification nat-basic2%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic2%oz: ⊦ m + 1 ≠ 0; from specification nat-basic2