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Proof step 13 from proof mk-succ (previous step)

b ∈ mklist(a, n) → b = a, mklist(a, n + 1) = z1 + a0 ' + z0, a ' + mklist(a, n) = z1 + b ' + z, a ∈ z1 ⊦ mklist(a, n + 1) = a ' + mklist(a, n), a0 = b, z1 = []

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 14:
mklist(a, n + 1) = z1 + a0 ' + z0, a ' + mklist(a, n) = z1 + a ' + z, a ∈ z1 ⊦ mklist(a, n + 1) = a ' + mklist(a, n), a0 = a, z1 = []

Rule argument

Additional information

Used simplifier rules: in-11: ⊦ a ∈ x → a ∈ x + y; from specification list%in-14: ⊦ a ' + x = y → a ∈ y; (forward) from specification list%isin: ⊦ a ' + x = y + b ' + z ∧ y ≠ [] → b ∈ x; from specification list%a: ⊦ (x + y) + z = x + y + z; from specification list