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Proof step 5 from proof mk-succ (previous step)

z1 = [], 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)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 6:
mklist(b, n + 1) = a0 ' + z0 ⊦ a0 ' + z0 = b ' + mklist(b, n), a0 = b

Rule argument

Additional information

Used simplifier rules: in-rec: ⊦ a ∈ b ' + x ↔ ¬ ¬(a = b ∨ a ∈ x); from specification list%in-14: ⊦ a ' + x = y → a ∈ y; (forward) from specification list%in-empty: ⊦ ¬ a ∈ []; from specification list%c-06: ⊦ a ' + x = b ' + y ↔ a = b ∧ x = y; from specification list%a: ⊦ (x + y) + z = x + y + z; from specification list%Nil: ⊦ [] + x = x; from specification list