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Proof step 5 from proof rm-in-01 (previous step)

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

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 ∈ (a0 ∈ x0 ⊃ rmdup(x0);a0 ' + rmdup(x0)), ∀ a. a ∈ rmdup(x0) → a ∈ x0 ⊦ a = a0, a ∈ x0

Rule argument

spec: <toplevel> name: rm-ifrec seq: ⊦ rmdup(a ' + x) = (a ∈ x ⊃ rmdup(x);a ' + rmdup(x)) subst: [x, a] → [x0, a0] flags: <all paths>

Additional information

Used terms: x0, a0