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Proof step 13 from proof lebs-write-subseteq0 (previous step)

@(m0, m3, m4) ∈ ri[key, @(m, m1, m2)], m ∈ gstore ⊦ m0 ∈ gstore, ri[key, @(m, m1, m2)].lebs ⊆ ri.lebs, ∃ adr. adr.lnum = m0 ∧ adr ∈ ri

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 14:
⊦ adr ≠ adr0 ∧ ¬ adr ∈ ri → ¬ adr ∈ ri[key, adr0]
Proof step 15:
m ∈ gstore, @(m0, m3, m4) ∈ ri[key, @(m, m1, m2)] ⊦ m0 ∈ gstore, ri[key, @(m, m1, m2)].lebs ⊆ ri.lebs, ∃ adr. adr.lnum = m0 ∧ adr ∈ ri, @(m0, m3, m4) ≠ @(m, m1, m2) ∧ ¬ @(m0, m3, m4) ∈ ri

Rule argument

spec: store+set, inst: node-index name: Data-notin-other seq: ⊦ adr ≠ adr0 ∧ ¬ adr ∈ ri → ¬ adr ∈ ri[key, adr0] subst: [adr0, key, ri, adr] → [@(m, m1, m2), key, ri, @(m0, m3, m4)] flags: <all paths>

Additional information

Used terms: @(m, m1, m2), key, ri, @(m0, m3, m4)