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Proof step 8 from proof mk-succ (previous step)

mklist(b, n + 1) = a0 ' + z0 ⊦ a0 ' + z0 = b ' + mklist(b, n), a0 = b

User applied rule insert lemma

And obtained the following new goals

Proof step 9:
⊦ 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, b, n + 1] flags: current, []

Additional information

Used simplifier rules: in-06: ⊦ ¬ a ∈ b ' + x ↔ a ≠ b ∧ ¬ a ∈ x; from specification list%a: ⊦ (x + y) + z = x + y + z; from specification list Used terms: a0, b, n + 1