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Proof step 3 from proof mk-succ (previous step)

∃ z, a0, b, z0, z1. a0 ≠ b ∧ mklist(a, n + 1) = z + a0 ' + z0 ∧ a ' + mklist(a, n) = z + b ' + z1 ⊦ mklist(a, n + 1) = a ' + mklist(a, n)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 4:
a ' + mklist(a, n) = z1 + b ' + z, mklist(a, n + 1) = z1 + a0 ' + z0, a ∈ z1 ∨ a = b ∨ a ∈ z ⊦ a0 = b, mklist(a, n + 1) = a ' + mklist(a, n)

Rule argument

Additional information

Used simplifier rules: in-rec: ⊦ a ∈ b ' + x ↔ ¬ ¬(a = b ∨ a ∈ x); from specification list%in-append: ⊦ a ∈ x + y ↔ ¬ ¬(a ∈ x ∨ a ∈ y); from specification list%a: ⊦ (x + y) + z = x + y + z; from specification list%in-14: ⊦ a ' + x = y → a ∈ y; (forward) from specification list