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Proof step 11 from proof range-rem-in (previous step)

ri[key0] = ri[key], ri-cons(ri, nodes(gstore, ginval)), key ∈ ri, key0 ∈ ri ⊦ key0 = key

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[key0] = ri[key], key0 ∈ ri, key ∈ ri, ∀ key. key ∈ ri → ri[key] ∈ nodes(gstore, ginval) ∧ key-cons(key, nodes(gstore, ginval)[ri[key]]) ⊦ key0 = key

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