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Proof step 16 from proof ole-01 (previous step)

a2 < a, ins≤(a, a2 ' + y0) = a1 ' + y, a0 < a, ∀ a3. ordered≤(ins≤(a3, a2 ' + y0)) ↔ ordered≤(a2 ' + y0) ⊦ ¬ a1 < a0 ∧ ordered≤(a1 ' + y) ↔ ¬ a2 < a0 ∧ ordered≤(a2 ' + y0)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Rule argument

Additional information

Used simplifier rules: ins-n: ⊦ b < a → ins≤(a, b ' + x) = b + ins≤(a, x);%nll: ⊦ ¬ b < a ∧ b < c → a < c; (forward) from specification oelem%lel: ⊦ a < b ∧ a = c → c < b; (forward) from specification oelem%c-06: ⊦ a ' + x = b ' + y ↔ a = b ∧ x = y; from specification list%a: ⊦ (x + y) + z = x + y + z; from specification list%c: ⊦ a + x = a ' + x; from specification list