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Proof step 19 from proof sw (previous step)

∀ 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

Heuristic weak cut applied rule cut formula

And closed the goal!

Rule argument

fma: a < b

Additional information

Used simplifier rules: ins-n: ⊦ b < a → ins≤(a, b ' + x) = b + ins≤(a, x);%ins-y: ⊦ ¬ b < a → ins≤(a, b ' + x) = a + b + x;%ins-y: ⊦ ¬ b < a → ins≤(a, b ' + x) = a + b + x;% ⊦ a + x = a ' + x; (s)%a: ⊦ (x + y) + z = x + y + z; from specification list% ⊦ x + y = z + y ↔ x = z; (s)% ⊦ ¬ b < a → (a < b ↔ a ≠ b); (ss)% ⊦ x + y = x + z ↔ y = z; (s) Used formulas: a < b