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Proof step 6 from proof mk-inj-01 (previous step)

m0 + 1 ≠ 0, a + mklist(a, m0 + 1 - 1) = mklist(a, n), ∀ a, n. mklist(a, m0) = mklist(a, n) → m0 = n ⊦ m0 + 1 = n

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Rule argument

Additional information

Used simplifier rules: mk-in: ⊦ a ∈ mklist(a, m) ↔ m ≠ 0;%a: ⊦ (x + y) + z = x + y + z; from specification list%in-14: ⊦ a ' + x = y → a ∈ y; (forward) from specification list%oz: ⊦ m + 1 ≠ 0; from specification nat-basic2%c: ⊦ a + x = a ' + x; from specification list%c: ⊦ m + n = n + m; from specification nat-basic2%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic2%add-base: ⊦ n + 0 = n; from specification nat-basic2%add-01: ⊦ n ≤ m → m + n0 - n = (m - n) + n0; from specification nat