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Proof step 11 from proof ri-cons-range-restrict-notin-gstore (previous step)

ri[key] = @(m, m0, m1), ri-cons(ri, nodes(gstore, ginval)), key ∈ ri ⊦ #(range ri | m) = 0, range ri | m = ∅, m ∈ gstore

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 12:
⊦ ri-cons(ri, fs) ↔ (∀ key. key ∈ ri → ri[key] ∈ fs ∧ key-cons(key, fs[ri[key]]))
Proof step 13:
ri[key] = @(m, m0, m1), key ∈ ri, ∀ key. key ∈ ri → ri[key] ∈ nodes(gstore, ginval) ∧ key-cons(key, nodes(gstore, ginval)[ri[key]]) ⊦ #(range ri | m) = 0, range ri | m = ∅, m ∈ gstore

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