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Proof step 3 from proof del1-02 (previous step)

∀ a. ins≤(a, x0) -1l a = x0 ⊦ ins≤(a, a0 ' + x0) -1l a = a0 ' + x0

Heuristic weak cut applied rule cut formula

And obtained the following new goals

Proof step 4:
a0 < a, ∀ a. ins≤(a, x0) -1l a = x0 ⊦ ins≤(a, a0 ' + x0) -1l a = a0 ' + x0

Rule argument

fma: a0 < a

Additional information

Used simplifier rules: ins-y: ⊦ ¬ b < a → ins≤(a, b ' + x) = a + b + x;% ⊦ a + x = a ' + x; (s)%a: ⊦ (x + y) + z = x + y + z; from specification list% ⊦ (a ' + x) -1l a = x; (s)% ⊦ x + y = x + z ↔ y = z; (s) Used formulas: a0 < a