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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, # x0 + 1) ↔ (∀ b. b = a0 ∨ b ∈ x0 → b = a)

Rule argument

Additional information

Used simplifier rules: in-rec: ⊦ a ∈ b ' + x ↔ ¬ ¬(a = b ∨ a ∈ x); from specification list%a: ⊦ (x + y) + z = x + y + z; from specification list%succ: ⊦ m +1 = m + 1; from specification nat-basic2%len-05: ⊦ #(a ' + x) = (# x)+1; from specification list%c: ⊦ a + x = a ' + x; from specification list