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Proof step 20 from proof rmdup-last (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 21:
⊦ rmdup(a ' + x) = (a ∈ x ⊃ rmdup(x);a ' + rmdup(x))
Proof step 22:
∀ a. rmdup(x0 + a ') = rmdup(x0 -l a) + a ' ⊦ a = a0, a0 ' + rmdup(x0 + a ') = (a0 ∈ x0 -l a ⊃ rmdup(x0 -l a);a0 ' + rmdup(x0 -l a)) + a ', a0 ∈ x0

Rule argument

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

Additional information

Used terms: x0 -l a, a0