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Proof step 4 from proof empty (previous step)

ins≤(a, a0 ' + x0) = [], ∀ a. ins≤(a, x0) ≠ [] ⊦

Heuristic cut applied rule cut formula

And closed the goal!

Rule argument

fma: a0 < a

Additional information

Used simplifier rules: ins-n: ⊦ b < a → ins≤(a, b ' + x) = b + ins≤(a, x);%ins-y: ⊦ ¬ b < a → ins≤(a, b ' + x) = a + b + x;%c: ⊦ a + x = a ' + x; from specification list%a: ⊦ (x + y) + z = x + y + z; from specification list%app-02-ant: ⊦ ¬ x + y ≠ [] ↔ x = [] ∧ y = []; from specification list%e: ⊦ a ' ≠ []; from specification list Used formulas: a0 < a