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Proof step 9 from proof refsize-nonzero-notin-ginval (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 10:
⊦ ri-cons(ri, fs) ↔ (∀ key. key ∈ ri → ri[key] ∈ fs ∧ key-cons(key, fs[ri[key]]))
Proof step 11:
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 = ∅

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