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Proof step 19 from proof rmdup-del1-del (previous step)

∀ 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))

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 20:
∀ a. rmdup(x0) -1l a = rmdup(x0 -l a) ⊦ a = a0, a0 ' + (rmdup(x0) -1l a) = rmdup(a0 ' + (x0 -l a)), a0 ∈ x0

Rule argument

Additional information

Used simplifier rules: del1-n: ⊦ a ≠ b → (b ' + x) -1l a = b ' + (x -1l a);%a: ⊦ (x + y) + z = x + y + z; from specification list