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Proof step 4 from proof del1-empty (previous step)

(a0 ' + x0) -1l a = [], ∀ a. x0 -1l a = [] → x0 = [] ∨ x0 = a ' ⊦ a0 ' + x0 = a '

Heuristic weak cut applied rule cut formula

And closed the goal!

Rule argument

fma: a = a0

Additional information

Used simplifier rules: del1-y: ⊦ (a ' + x) -1l a = x;%del1-n: ⊦ a ≠ b → (b ' + x) -1l a = b ' + (x -1l a);%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%c-03: ⊦ a ' = b ' + x ↔ a = b ∧ x = []; from specification list Used formulas: a = a0