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

∀ a, y. # rmdup(x0 + a ' + y) = # rmdup(x0 + y) + 1 ∨ a ∈ y ∨ a ∈ x0 ⊦ a = a0, # (a0 ∈ x0 ∨ a0 ∈ y ⊃ rmdup(x0 + a ' + y);a0 ' + rmdup(x0 + a ' + y)) = # rmdup((a0 ' + x0) + y) + 1, a ∈ y, a ∈ x0

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 8:
⊦ rmdup(a ' + x) = (a ∈ x ⊃ rmdup(x);a ' + rmdup(x))
Proof step 9:
∀ a, y. # rmdup(x0 + a ' + y) = # rmdup(x0 + y) + 1 ∨ a ∈ y ∨ a ∈ x0 ⊦ a = a0, # (a0 ∈ x0 ∨ a0 ∈ y ⊃ rmdup(x0 + a ' + y);a0 ' + rmdup(x0 + a ' + y)) = # (a0 ∈ x0 + y ⊃ rmdup(x0 + y);a0 ' + rmdup(x0 + y)) + 1, a ∈ y, a ∈ x0

Rule argument

spec: inst: name: rm-ifrec seq: ⊦ rmdup(a ' + x) = (a ∈ x ⊃ rmdup(x);a ' + rmdup(x)) subst: [x, a] → [x0 + y, a0] flags: rewrite, current

Additional information

Used simplifier rules: a: ⊦ (x + y) + z = x + y + z; from specification list Used terms: x0 + y, a0