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Proof step 13 from proof rmdup-del1-del (previous step)

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

Heuristic cut applied rule cut formula

And obtained the following new goals

Proof step 14:
a0 ∈ x0, ∀ a. rmdup(x0) -1l a = rmdup(x0 -l a) ⊦ a = a0, (a0 ∈ x0 ⊃ rmdup(x0);a0 ' + rmdup(x0)) -1l a = rmdup(a0 ' + (x0 -l a))
Proof step 19:
∀ a. rmdup(x0) -1l a = rmdup(x0 -l a) ⊦ a0 ∈ x0, a = a0, (a0 ∈ x0 ⊃ rmdup(x0);a0 ' + rmdup(x0)) -1l a = rmdup(a0 ' + (x0 -l a))

Rule argument

fma: a0 ∈ x0

Additional information

Used formulas: a0 ∈ x0