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Proof step 13 from proof restrict-union-inter-empty-left (previous step)

⊦ m = n ∧ @(n, m0, m1) ∈ as0 ∧ (@(n, m0, m1) ∈ as1 \ (as1 | n) ∨ @(n, m0, m1) ∈ as2) ↔ @(m, m0, m1) ∈ (as0 | n) ∩ as2

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: set-union, inst: address-store name: Difference seq: ⊦ adr ∈ as \ as0 ↔ adr ∈ as ∧ ¬ adr ∈ as0 subst: [as0, as, adr] → [as1 | n, as1, @(n, m0, m1)] flags: <all paths>

Additional information

Used simplifier rules: restrict-in: ⊦ @(m, m0, m1) ∈ as | m ↔ @(m, m0, m1) ∈ as;%restrict-leb: ⊦ adr ∈ as | n ↔ adr.lnum = n ∧ adr ∈ as;% ⊦ adr ∈ as ∩ as0 ↔ adr ∈ as ∧ adr ∈ as0; (ws)%int-a: ⊦ (as ∩ as0) ∩ as1 = as ∩ as0 ∩ as1; from specification set-union[address-store]%int-c: ⊦ as ∩ as0 = as0 ∩ as; from specification set-union[address-store]% ⊦ @(m, m0, m1).lnum = m; (s) Used terms: as1 | n, as1, @(n, m0, m1)