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Proof step 13 from proof rmdup-last (previous step)

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

Heuristic cut applied rule cut formula

And obtained the following new goals

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

Rule argument

fma: a0 ∈ x0

Additional information

Used formulas: a0 ∈ x0