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Proof step 5 from proof rmdup-last (previous step)

∀ a. rmdup(x0 + a ') = rmdup(x0 -l a) + a ' ⊦ rmdup((a0 ' + x0) + a0 ') = rmdup(x0 -l a0) + a0 '

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 6:
⊦ rmdup(a ' + x) = (a ∈ x ⊃ rmdup(x);a ' + rmdup(x))
Proof step 7:
∀ a. rmdup(x0 + a ') = rmdup(x0 -l a) + a ' ⊦ (a0 ∈ x0 + a0 ' ⊃ rmdup(x0 + a0 ');a0 ' + rmdup(x0 + a0 ')) = rmdup(x0 -l a0) + a0 '

Rule argument

spec: list-dup inst: name: rm-ifrec seq: ⊦ rmdup(a ' + x) = (a ∈ x ⊃ rmdup(x);a ' + rmdup(x)) subst: [x, a] → [x0 + a0 ', a0] flags: rewrite

Additional information

Used simplifier rules: a: ⊦ (x + y) + z = x + y + z; from specification list Used terms: x0 + a0 ', a0