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Proof step 9 from proof sw (previous step)

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

Heuristic weak cut applied rule cut formula

And obtained the following new goals

Proof step 10:
a0 < b, ∀ a, b. ins≤(a, ins≤(b, x0)) = ins≤(b, ins≤(a, x0)) ⊦ ins≤(a, ins≤(b, a0 ' + x0)) = ins≤(b, ins≤(a, a0 ' + x0))
Proof step 14:
∀ a, b. ins≤(a, ins≤(b, x0)) = ins≤(b, ins≤(a, x0)) ⊦ a0 < b, ins≤(a, ins≤(b, a0 ' + x0)) = ins≤(b, ins≤(a, a0 ' + x0))

Rule argument

fma: a0 < b

Additional information

Used formulas: a0 < b