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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

Rule argument

fma: a2 < a

Additional information

Used simplifier rules: ins-y: ⊦ ¬ b < a → ins≤(a, b ' + x) = a + b + x;%le-r: ⊦ ordered≤(a ' + b ' + x) ↔ ¬ b < a ∧ ordered≤(b + x);%cons-02: ⊦ ordered≤(a ' + x) → ordered≤(x);%app-01: ⊦ ordered≤(x + y) → ordered≤(y);%c: ⊦ a + x = a ' + x; from specification list%a: ⊦ (x + y) + z = x + y + z; from specification list%c-06: ⊦ a ' + x = b ' + y ↔ a = b ∧ x = y; from specification list%in-14: ⊦ a ' + x = y → a ∈ y; (forward) from specification list%nen: ⊦ ¬ b < a ∧ a = c → ¬ b < c; (forward) from specification oelem%in-rec: ⊦ a ∈ b ' + x ↔ ¬ ¬(a = b ∨ a ∈ x); from specification list%transitivity: ⊦ a < b ∧ b < c → a < c; (forward) from specification oelem%irreflexivity: ⊦ ¬ a < a; from specification oelem%nll: ⊦ ¬ b < a ∧ b < c → a < c; (forward) from specification oelem Used formulas: a2 < a