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Proof step 18 from proof sw (previous step)

∀ a, b. ins≤(a, ins≤(b, x0)) = ins≤(b, ins≤(a, x0)) ⊦ b < a, ins≤(a, b ' + a0 ' + x0) = ins≤(b, ins≤(a, a0 ' + x0)), a0 < b

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 19:
∀ a, b. ins≤(a, ins≤(b, x0)) = ins≤(b, ins≤(a, x0)) ⊦ a ' + b ' + a0 ' + x0 = ins≤(b, a ' + a0 ' + x0), a0 < a, a0 < b, b < a

Rule argument

Additional information

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