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Proof step 8 from proof adr-in-index-node-key (previous step)

# gndx1 = # lax1, ri[key] = @(n, n0, n1), 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 ∈ ri ⊦ nd.key ∈ ri ∧ ri[nd.key] = @(n, n0, n1)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 9:
⊦ ri-cons(ri, fs) ↔ (∀ key. key ∈ ri → ri[key] ∈ fs ∧ key-cons(key, fs[ri[key]]))
Proof step 10:
# gndx1 = # lax1, gstore[n] = groupblock(gndx0 + mkgnode(nd, m, boolvar, boolvar0) ' + gndx1, lax0 + @(n0, n1) ' + lax1, m0), ri[key] = @(n, n0, n1), inv(groupblock(gndx0 + mkgnode(nd, m, boolvar, boolvar0) ' + gndx1, lax0 + @(n0, n1) ' + lax1, m0)), key ∈ ri, ∀ key. key ∈ ri → ri[key] ∈ nodes(gstore ↓, ginval) ∧ key-cons(key, nodes(gstore ↓, ginval)[ri[key]]) ⊦ nd.key ∈ ri ∧ ri[nd.key] = @(n, n0, n1)

Rule argument

spec: aubifs-inv name: ri-cons seq: ⊦ ri-cons(ri, fs) ↔ (∀ key. key ∈ ri → ri[key] ∈ fs ∧ key-cons(key, fs[ri[key]])) subst: [fs, ri] → [nodes(gstore ↓, ginval), ri] flags: <all paths>

Additional information

Used terms: nodes(gstore ↓, ginval), ri