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Proof step 9 from proof lastn-mklist (previous step)

mklist(a, n0 + 1) = a0 + y, m ≤ n0, m ≤ n0 + 1, ∀ m, a. m ≤ n0 → lastn(m, mklist(a, n0)) = mklist(a, m) ⊦ lastn(m, y) = mklist(a, m), mklist(a, n0 + 1) = []

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 10:
mklist(a, n0 + 1) = a0 ' + y, m ≤ n0 + 1, m ≤ n0, ∀ m, a. m ≤ n0 → lastn(m, mklist(a, n0)) = mklist(a, m) ⊦ lastn(m, y) = mklist(a, m)

Rule argument

Additional information

Used simplifier rules: ⊦ a ∈ b ' ↔ a = b; (s)% ⊦ a ∈ x + y ↔ a ∈ x ∨ a ∈ y; (s)%a: ⊦ (x + y) + z = x + y + z; from specification list%in-14: ⊦ a ' + x = y → a ∈ y; (forward) from specification list%c: ⊦ m + n = n + m; from specification nat-basic%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic% ⊦ m + 1 ≠ 0; (s)% ⊦ mklist(a, m) = [] ↔ m = 0; (s)% ⊦ a + x = a ' + x; (s)