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Proof step 4 from proof ocs-same-length-all (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 5:
∀ a. x0 = mklist(a, # x0) ↔ (∀ b. b ∈ x0 → b = a) ⊦ a0 ' + x0 = mklist(a, 1 + # x0) ↔ (∀ b. b = a0 ∨ b ∈ x0 → b = a)

Rule argument

Additional information

Used simplifier rules: ⊦ a ∈ b ' ↔ a = b; (s)% ⊦ a ∈ x + y ↔ a ∈ x ∨ a ∈ y; (s)%a: ⊦ (x + y) + z = x + y + z; from specification list% ⊦ # a ' = 0 +1; (s)% ⊦ #(x + y) = # x + # y; (s)% ⊦ a + x = a ' + x; (s)