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Proof step 11 from proof refsize-nonzero-notin-ginval (previous step)

gstore[m] = groupblock(gndx, lax, (range ri | m).size), inv(gstore \ ginval), m ∈ gstore, m ∈ ginval, @(m, m0, m1) ∈ ri, ∀ key. key ∈ ri → ri[key] ∈ nodes(gstore ↓, ginval) ∧ key-cons(key, nodes(gstore ↓, ginval)[ri[key]]) ⊦ # ginval = 0, ginval = ∅

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 12:
⊦ adr ∈ ri ↔ (∃ key. key ∈ ri ∧ ri[key] = adr)
Proof step 13:
gstore[m] = groupblock(gndx, lax, (range ri | m).size), inv(gstore \ ginval), m ∈ ginval, m ∈ gstore, ∀ key. key ∈ ri → ri[key] ∈ nodes(gstore ↓, ginval) ∧ key-cons(key, nodes(gstore ↓, ginval)[ri[key]]), ∃ key. key ∈ ri ∧ ri[key] = @(m, m0, m1) ⊦ # ginval = 0, ginval = ∅

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)