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Proof step 4 from proof size-rmdup-del (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 5:
∀ 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% ⊦ a ∈ b ' ↔ a = b; (s)% ⊦ a ∈ x + y ↔ a ∈ x ∨ a ∈ y; (s)% ⊦ a + x = a ' + x; (s)