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Proof step 15 from proof ole-01 (previous step)

ins≤(a, a2 ' + y0) = a1 ' + y, a0 < a, ∀ a3. ordered≤(ins≤(a3, a2 ' + y0)) ↔ ordered≤(a2 ' + y0) ⊦ ¬ a1 < a0 ∧ ordered≤(a1 ' + y) ↔ ¬ a2 < a0 ∧ ordered≤(a2 ' + y0)

Heuristic weak cut applied rule cut formula

And obtained the following new goals

Proof step 16:
ins≤(a, a2 ' + y0) = a1 ' + y, a0 < a, a2 < a, ∀ a3. ordered≤(ins≤(a3, a2 ' + y0)) ↔ ordered≤(a2 ' + y0) ⊦ ¬ a1 < a0 ∧ ordered≤(a1 ' + y) ↔ ¬ a2 < a0 ∧ ordered≤(a2 ' + y0)
Proof step 18:
ins≤(a, a2 ' + y0) = a1 ' + y, a0 < a, ∀ a3. ordered≤(ins≤(a3, a2 ' + y0)) ↔ ordered≤(a2 ' + y0) ⊦ ¬ a1 < a0 ∧ ordered≤(a1 ' + y) ↔ ¬ a2 < a0 ∧ ordered≤(a2 ' + y0), a2 < a

Rule argument

fma: a2 < a

Additional information

Used formulas: a2 < a