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Proof step 4 from proof del-del1-nodups (previous step)

∀ a1. x0 -l a1 = x0 -1l a1 ⊦ (a0 ' + x0) -l a = (a0 ' + x0) -1l a, a0 ∈ x0, dups(x0)

Heuristic cut applied rule cut formula

And obtained the following new goals

Proof step 5:
∀ a1. x0 -l a1 = x0 -1l a1 ⊦ a = a0, (a0 ' + x0) -l a = (a0 ' + x0) -1l a, a0 ∈ x0, dups(x0)

Rule argument

fma: a = a0

Additional information

Used simplifier rules: del-y: ⊦ (a ' + x) -l a = x -l a;%in-03: ⊦ ¬ a ∈ x → x -l a = x;%del1-y: ⊦ (a ' + x) -1l a = x;%a: ⊦ (x + y) + z = x + y + z; from specification list Used formulas: a = a0