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Proof step 10 from proof rm-rm-01 (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 11:
⊦ ¬ a ∈ x → rmdup(a ' + x) = a + rmdup(x)
Proof step 12:
∀ y. rmdup(rmdup(x0) + y) = rmdup(x0 + y) ⊦ a ' + rmdup(rmdup(x0) + y) = a + rmdup(x0 + y), a ∈ x0, a ∈ y, a ∈ rmdup(x0), a ∈ x0 + y

Rule argument

spec: <toplevel> name: rmdup-n seq: ⊦ ¬ a ∈ x → rmdup(a ' + x) = a + rmdup(x) subst: [x, a] → [x0 + y, a] flags: <all paths>

Additional information

Used simplifier rules: rmdup-y: ⊦ a ∈ x → rmdup(a ' + x) = rmdup(x);% ⊦ a ∈ x + y ↔ a ∈ x ∨ a ∈ y; (s)%a: ⊦ (x + y) + z = x + y + z; from specification list Used terms: x0 + y, a