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

a + mklist(a, n0 + 1 - 1) = a0 ' + y, m ≤ n0, m ≤ n0 + 1, ∀ m, a. m ≤ n0 → lastn(m, mklist(a, n0)) = mklist(a, m) ⊦ n0 + 1 = 0, lastn(m, y) = mklist(a, m)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 13:
m ≤ n0, m ≤ n0 + 1, ∀ m, a. m ≤ n0 → lastn(m, mklist(a, n0)) = mklist(a, m) ⊦ lastn(m, mklist(a0, n0)) = mklist(a0, m)

Rule argument

Additional information

Used simplifier rules: ⊦ m + 1 ≠ 0; (s)%a: ⊦ (x + y) + z = x + y + z; from specification list% ⊦ a ' + x = b ' + y ↔ a = b ∧ x = y; (ws)% ⊦ a + x = a ' + x; (s)%c: ⊦ m + n = n + m; from specification nat-basic%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic% ⊦ n + 0 = n; (s)% ⊦ n ≤ m → m + n0 - n = (m - n) + n0; (s)