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Proof step 7 from proof intersection-size (previous step)

# s0 + #(s1 ++ a) < #(s0 ∩ (s1 ++ a)), ∀ s0. ¬ # s0 + # s1 < #(s0 ∩ s1) ⊦ a ∈ s1

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 8:
# s0 + # s1 + 1 < #(s0 ∩ (s1 ++ a)), ∀ s0. ¬ # s0 + # s1 < #(s0 ∩ s1) ⊦ a ∈ s1

Rule argument

Additional information

Used simplifier rules: ⊦ ¬ a ∈ s → #(s ++ a) = # s + 1; (s)