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Proof step 8 from proof ri-cons-range-restrict-notin-gstore (previous step)

ri-cons(ri, nodes(gstore, ginval)), @(m, m0, m1) ∈ ri ⊦ #(range ri | m) = 0, range ri | m = ∅, m ∈ gstore

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 9:
⊦ adr ∈ ri ↔ (∃ key. key ∈ ri ∧ ri[key] = adr)
Proof step 10:
ri-cons(ri, nodes(gstore, ginval)), ∃ key. key ∈ ri ∧ ri[key] = @(m, m0, m1) ⊦ #(range ri | m) = 0, range ri | m = ∅, m ∈ gstore

Rule argument

spec: store+set, inst: node-index name: Data-in seq: ⊦ adr ∈ ri ↔ (∃ key. key ∈ ri ∧ ri[key] = adr) subst: [ri, adr] → [ri, @(m, m0, m1)] flags: <all paths>

Additional information

Used terms: ri, @(m, m0, m1)