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Proof step 17 from proof size-rmdup-del (previous step)

# rmdup(x0) = m0 + 1, # rmdup(a0 ' + x0) = m + 1, a ∈ x0, ∀ a. a ∈ x0 → # rmdup(x0 -l a) = m0 ⊦ x0 = [], a = a0, 1 + # rmdup(x0 -l a) = m, a0 ∈ x0 -l a

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 18:
⊦ a ∈ x → rmdup(a ' + x) = rmdup(x)
Proof step 19:
¬ a0 ∈ x0, # rmdup(x0) = m0 + 1, # rmdup(a0 ' + x0) = m + 1, a ∈ x0, ∀ a. a ∈ x0 → # rmdup(x0 -l a) = m0 ⊦ x0 = [], a = a0, 1 + # rmdup(x0 -l a) = m, a0 ∈ x0 -l a

Rule argument

spec: list-dup inst: name: rmdup-y seq: ⊦ a ∈ x → rmdup(a ' + x) = rmdup(x) subst: [x, a] → [x0, a0] flags: rewrite

Additional information

Used simplifier rules: in: ⊦ a ∈ x ∧ a ≠ b → a ∈ x -l b; Used terms: x0, a0