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Proof step 5 from proof f-rm (previous step)

a ∈ y, ∀ y. filter(rmdup(x0), y) = rmdup(filter(x0, y)) ⊦ filter(rmdup(a ' + x0), y) = rmdup(a ' + filter(x0, y))

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 6:
⊦ a ∈ x → rmdup(a ' + x) = rmdup(x)
Proof step 7:
¬ a ∈ filter(x0, y), a ∈ y, ∀ y. filter(rmdup(x0), y) = rmdup(filter(x0, y)) ⊦ filter(rmdup(a ' + x0), y) = rmdup(a ' + filter(x0, y))
Proof step 12:
a ∈ filter(x0, y), a ∈ y, ∀ y. filter(rmdup(x0), y) = rmdup(filter(x0, y)) ⊦ filter(rmdup(a ' + x0), y) = rmdup(filter(x0, y))

Rule argument

spec: list-dup inst: name: rmdup-y seq: ⊦ a ∈ x → rmdup(a ' + x) = rmdup(x) subst: [x, a] → [filter(x0, y), a] flags: rewrite

Additional information

Used terms: filter(x0, y), a