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Proof step 17 from proof intersection-size (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 18:
# s0 + # s1 < #(s0 ∩ s1), a ∈ s1, a0 ∈ s1, ∀ s0. ¬ # s0 + # s1 < #(s0 ∩ s1) ⊦

Rule argument

Additional information

Used simplifier rules: ⊦ ¬ a ∈ ∅; (s)% ⊦ s1 = s2 ↔ (∀ a. a ∈ s1 ↔ a ∈ s2); (s)% ⊦ m < n → n ≠ 0; (s)%ne-01: ⊦ a ∈ s → s ≠ ∅; (forward) from specification set-basic%f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic