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Proof step 11 from proof mk-succ (previous step)

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 = []

User applied rule insert lemma

And obtained the following new goals

Proof step 12:
⊦ a ∈ mklist(b, n) → a = b
Proof step 13:
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 = []

Rule argument

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

Additional information

Used terms: b, a, n