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Proof step 12 from proof first-mklist (previous step)

m = m0 + 1, m ≤ n0 + 1, ∀ m, a. m ≤ n0 → firstn(m, mklist(a, n0)) = mklist(a, m) ⊦ a ' + firstn(m0, mklist(a, n0)) = mklist(a, m), m = 0

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 13:
m0 ≤ n0, ∀ m, a. m ≤ n0 → firstn(m, mklist(a, n0)) = mklist(a, m) ⊦ a ' + firstn(m0, mklist(a, n0)) = mklist(a, m0 + 1)

Rule argument

Additional information

Used simplifier rules: ⊦ m + n ≤ m + n0 ↔ n ≤ n0; (s)%c: ⊦ m + n = n + m; from specification nat-basic%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic% ⊦ m + 1 ≠ 0; (s)