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Proof step 10 from proof max-ins-max (previous step)

∀ a. max(ins≤(a, x0)) = a ∨ a < max(x0) ⊦ max(ins≤(a, a0 ' + x0)) = a, a < max(a0 ' + x0), ¬ a0 < a ∧ ordered≤(a0 ' + x0)

Heuristic cut applied rule cut formula

And obtained the following new goals

Proof step 11:
a0 < a, ∀ a. max(ins≤(a, x0)) = a ∨ a < max(x0) ⊦ max(ins≤(a, a0 ' + x0)) = a, a < max(a0 ' + x0), ¬ a0 < a ∧ ordered≤(a0 ' + x0)
Proof step 31:
∀ a. max(ins≤(a, x0)) = a ∨ a < max(x0) ⊦ a0 < a, max(ins≤(a, a0 ' + x0)) = a, a < max(a0 ' + x0), ¬ a0 < a ∧ ordered≤(a0 ' + x0)

Rule argument

fma: a0 < a

Additional information

Used formulas: a0 < a