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Proof step 11 from proof sw (previous step)

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

Heuristic weak cut applied rule cut formula

And obtained the following new goals

Proof step 12:
a0 < b, a0 < a, ∀ a, b. ins≤(a, ins≤(b, x0)) = ins≤(b, ins≤(a, x0)) ⊦ ins≤(a, a0 ' + ins≤(b, x0)) = ins≤(b, ins≤(a, a0 ' + x0))

Rule argument

fma: a0 < a

Additional information

Used simplifier rules: ins-y: ⊦ ¬ b < a → ins≤(a, b ' + x) = a + b + x;%ins-n: ⊦ b < a → ins≤(a, b ' + x) = b + ins≤(a, x);% ⊦ a + x = a ' + x; (s)%a: ⊦ (x + y) + z = x + y + z; from specification list%nll: ⊦ ¬ b < a ∧ b < c → a < c; (forward) from specification oelem% ⊦ x + y = x + z ↔ y = z; (s) Used formulas: a0 < a