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Proof step 3 from proof ocs-same-length-all (previous step)

⊦ x = mklist(a, # x) ↔ (∀ b. b ∈ x → b = a)

User applied rule structural induction

And obtained the following new goals

Proof step 4:
∀ a. x0 = mklist(a, # x0) ↔ (∀ b. b ∈ x0 → b = a) ⊦ a0 + x0 = mklist(a, #(a0 + x0)) ↔ (∀ b. b ∈ a0 + x0 → b = a)

Rule argument

indvar: x

Additional information

Used simplifier rules: list freely generated by [], +;;%size-01: ⊦ # [] = 0; from specification list-data%mk-zero: ⊦ mklist(a, 0) = []; from specification list-last%in-empty: ⊦ ¬ a ∈ []; from specification list