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Proof step 14 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 ⊦ a = a0, # rmdup(a0 ' + (x0 -l a)) = m, x0 = []

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 15:
⊦ a ∈ x → rmdup(a ' + x) = rmdup(x)
Proof step 16:
¬ a0 ∈ x0 -l a, # rmdup(x0) = m0 + 1, # rmdup(a0 ' + x0) = m + 1, a ∈ x0, ∀ a. a ∈ x0 → # rmdup(x0 -l a) = m0 ⊦ a = a0, # rmdup(a0 ' + (x0 -l a)) = m, x0 = []
Proof step 21:
a0 ∈ x0 -l a, # rmdup(x0) = m0 + 1, # rmdup(a0 ' + x0) = m + 1, a ∈ x0, ∀ a. a ∈ x0 → # rmdup(x0 -l a) = m0 ⊦ a = a0, # rmdup(x0 -l a) = m, x0 = []

Rule argument

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

Additional information

Used terms: x0 -l a, a0