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Proof step 14 from proof mk-succ (previous step)

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 = []

User applied rule insert lemma

And obtained the following new goals

Proof step 15:
⊦ a ∈ mklist(b, n) → a = b

Rule argument

spec: list-last inst: name: mk-elem seq: ⊦ a ∈ mklist(b, n) → a = b subst: [a, b, n] → [a0, a, n + 1] flags: current, []

Additional information

Used simplifier rules: a: ⊦ (x + y) + z = x + y + z; from specification list%in-13: ⊦ x = y + a ' + z → a ∈ x; from specification list Used terms: a0, a, n + 1