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Proof step 5 from proof rmdup-del1-del (previous step)

∀ a. rmdup(x0) -1l a = rmdup(x0 -l a) ⊦ rmdup(a0 ' + x0) -1l a0 = rmdup(x0 -l 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) -1l a = rmdup(x0 -l a) ⊦ (a0 ∈ x0 ⊃ rmdup(x0);a0 ' + rmdup(x0)) -1l a0 = rmdup(x0 -l 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] flags: rewrite

Additional information

Used terms: x0, a0