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Proof step 10 from proof size-0 (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 11:
⊦ ri-cons(ri, fs) ↔ (∀ key. key ∈ ri → ri[key] ∈ fs ∧ key-cons(key, fs[ri[key]]))
Proof step 12:
(range ri | m).size = 0, ri[key] = @(m, m0, m1), inv(gstore \ ginval), key ∈ ri, ∀ key. key ∈ ri → ri[key] ∈ nodes(gstore ↓, ginval) ∧ key-cons(key, nodes(gstore ↓, ginval)[ri[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