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Proof step 3 from proof adr-in-ri-leb-notin-ginval (previous step)

ri[key] = @(m0, m1, m2), ri-cons(ri, nodes(gstore ↓, ginval)), m0 ∈ ginval, key ∈ ri ⊦ # ginval = 0, ginval = ∅

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 4:
⊦ ri-cons(ri, fs) ↔ (∀ key. key ∈ ri → ri[key] ∈ fs ∧ key-cons(key, fs[ri[key]]))
Proof step 5:
ri[key] = @(m0, m1, m2), key ∈ ri, m0 ∈ ginval, ∀ 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