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Proof step 7 from proof rmdup-del1-del (previous step)

∀ a. rmdup(x0) -1l a = rmdup(x0 -l a) ⊦ (a0 ∈ x0 ⊃ rmdup(x0);a0 ' + rmdup(x0)) -1l a0 = rmdup(x0 -l a0)

Heuristic cut applied rule cut formula

And obtained the following new goals

Proof step 8:
a0 ∈ x0, ∀ a. rmdup(x0) -1l a = rmdup(x0 -l a) ⊦ (a0 ∈ x0 ⊃ rmdup(x0);a0 ' + rmdup(x0)) -1l a0 = rmdup(x0 -l a0)

Rule argument

fma: a0 ∈ x0

Additional information

Used simplifier rules: del1-y: ⊦ (a ' + x) -1l a = x;%in-03: ⊦ ¬ a ∈ x → x -l a = x;%a: ⊦ (x + y) + z = x + y + z; from specification list Used formulas: a0 ∈ x0