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Proof step 11 from proof size-rmdup-del (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 12:
# rmdup(a0 ' + x0) = m + 1, a ∈ x0, ∀ a. a ∈ x0 → # rmdup(x0 -l a) = # rmdup(x0) - 1 ⊦ a = a0, # rmdup(a0 ' + (x0 -l a)) = m

Rule argument

Additional information

Used simplifier rules: del-n: ⊦ a ≠ b → (b ' + x) -l a = b ' + (x -l a);%a: ⊦ (x + y) + z = x + y + z; from specification list