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Proof step 4 from proof add-inter-rem (previous step)

a ∈ s1 ⊦ # s1 = 0, ((s0 ++ a) ∩ s1) -- a = (s0 ∩ s1) -- a, s1 = ∅, (s0 ++ a) ∩ s1 = s0 ∩ s1

Heuristic weak cut applied rule cut formula

And obtained the following new goals

Proof step 5:
a ∈ s1 ⊦ # s1 = 0, ((s0 ++ a) ∩ s1) -- a = (s0 ∩ s1) -- a, s1 = ∅, (s0 ++ a) ∩ s1 = s0 ∩ s1, a ∈ s0 ∩ s1

Rule argument

fma: a ∈ s0 ∩ s1

Additional information

Used simplifier rules: Intersect: ⊦ a ∈ s1 ∩ s2 ↔ a ∈ s1 ∧ a ∈ s2;%int-a: ⊦ (s ∩ s0) ∩ s1 = s ∩ s0 ∩ s1;%int-c: ⊦ s ∩ s0 = s0 ∩ s;% ⊦ a ∈ s → s ++ a = s; (s) Used formulas: a ∈ s0 ∩ s1