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Proof step 3 from proof ole-01 (previous step)

∀ a. ordered≤(ins≤(a, x0)) ↔ ordered≤(x0) ⊦ ordered≤(ins≤(a, a0 ' + x0)) ↔ ordered≤(a0 ' + x0)

Heuristic weak cut applied rule cut formula

And obtained the following new goals

Proof step 4:
a0 < a, ∀ a. ordered≤(ins≤(a, x0)) ↔ ordered≤(x0) ⊦ ordered≤(ins≤(a, a0 ' + x0)) ↔ ordered≤(a0 ' + x0)

Rule argument

fma: a0 < a

Additional information

Used simplifier rules: ins-y: ⊦ ¬ b < a → ins≤(a, b ' + x) = a + b + x;%app-01: ⊦ ordered≤(x + y) → ordered≤(y);%le-r: ⊦ ordered≤(a ' + b ' + x) ↔ ¬ b < a ∧ ordered≤(b + x);%c: ⊦ a + x = a ' + x; from specification list%a: ⊦ (x + y) + z = x + y + z; from specification list Used formulas: a0 < a