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Proof step 17 from proof nodes-referenced-adrs-leb (previous step)

ri[key] = @(n, m1, m2), gstore[n] = groupblock(gndx, lax, m), ri-cons(ri, nodes(gstore ↓, ginval)), key ∈ ri, n ∈ gstore ⊦ @(m1, m2) ∈ lax, n ∈ ginval

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 18:
⊦ ri-cons(ri, fs) ↔ (∀ key. key ∈ ri → ri[key] ∈ fs ∧ key-cons(key, fs[ri[key]]))
Proof step 19:
gstore[n] = groupblock(gndx, lax, m), ri[key] = @(n, m1, m2), n ∈ gstore, key ∈ ri, ∀ key. key ∈ ri → ri[key] ∈ nodes(gstore ↓, ginval) ∧ key-cons(key, nodes(gstore ↓, ginval)[ri[key]]) ⊦ n ∈ ginval, @(m1, m2) ∈ lax

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