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Proof step 3 from proof size-rmdup-del (previous step)

∀ a. a ∈ x0 → # rmdup(x0 -l a) = # rmdup(x0) - 1 ⊦ a ∈ a0 + x0 → # rmdup((a0 + x0) -l a) = # rmdup(a0 + x0) - 1

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 4:
∀ a. a ∈ x0 → # rmdup(x0 -l a) = # rmdup(x0) - 1, a = a0 ∨ a ∈ x0 ⊦ # rmdup((a0 ' + x0) -l a) = # rmdup(a0 ' + x0) - 1

Rule argument

Additional information

Used simplifier rules: a: ⊦ (x + y) + z = x + y + z; from specification list%in-17: ⊦ a ∈ b ' ↔ a = b; from specification list%in-append: ⊦ a ∈ x + y ↔ ¬ ¬(a ∈ x ∨ a ∈ y); from specification list%c: ⊦ a + x = a ' + x; from specification list