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Proof step 7 from proof rm-rm-01 (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 8:
⊦ a ∈ x → rmdup(a ' + x) = rmdup(x)
Proof step 9:
¬ a ∈ rmdup(x0) + y, ∀ y. rmdup(rmdup(x0) + y) = rmdup(x0 + y) ⊦ rmdup((a ' + rmdup(x0)) + y) = rmdup((a ' + x0) + y), a ∈ x0
Proof step 14:
a ∈ rmdup(x0) + y, ∀ y. rmdup(rmdup(x0) + y) = rmdup(x0 + y) ⊦ rmdup(rmdup(x0) + y) = rmdup((a ' + x0) + y), a ∈ x0

Rule argument

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

Additional information

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