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Proof step 1 from proof add-inter-rem (conclusion)

⊦ ((s0 ++ a) ∩ s1) -- a = (s0 ∩ s1) -- a

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 2:
⊦ ((s0 ++ a) ∩ s1) -- a = (s0 ∩ s1) -- a, (s0 ++ a) ∩ s1 = s0 ∩ s1

Rule argument

Additional information

Used simplifier rules: del-neq: ⊦ s -- a ≠ s0 -- a → s ≠ s0;