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Proof step 5 from proof adr-in-index-node-key (previous step)

# gndx1 = # lax1, gstore[n] = groupblock(gndx0 + mkgnode(nd, m, boolvar, boolvar0) ' + gndx1, lax0 + @(n0, n1) ' + lax1, m0), inv(groupblock(gndx0 + mkgnode(nd, m, boolvar, boolvar0) ' + gndx1, lax0 + @(n0, n1) ' + lax1, m0)), ri-cons(ri, nodes(gstore ↓, ginval)), @(n, n0, n1) ∈ ri ⊦ nd.key ∈ ri ∧ ri[nd.key] = @(n, n0, n1)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 6:
⊦ adr ∈ ri ↔ (∃ key. key ∈ ri ∧ ri[key] = adr)
Proof step 7:
# gndx1 = # lax1, gstore[n] = groupblock(gndx0 + mkgnode(nd, m, boolvar, boolvar0) ' + gndx1, lax0 + @(n0, n1) ' + lax1, m0), inv(groupblock(gndx0 + mkgnode(nd, m, boolvar, boolvar0) ' + gndx1, lax0 + @(n0, n1) ' + lax1, m0)), ri-cons(ri, nodes(gstore ↓, ginval)), ∃ key. key ∈ ri ∧ ri[key] = @(n, n0, n1) ⊦ nd.key ∈ ri ∧ ri[nd.key] = @(n, n0, n1)

Rule argument

spec: store+set, inst: node-index name: Data-in seq: ⊦ adr ∈ ri ↔ (∃ key. key ∈ ri ∧ ri[key] = adr) subst: [ri, adr] → [ri, @(n, n0, n1)] flags: <all paths>

Additional information

Used terms: ri, @(n, n0, n1)