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Proof step 56 from proof inv-format (previous step)

⊦ ri-closed((∅)[inodekey(ROOT_INO), adr1], (∅)[adr1, inodenode(inodekey(ROOT_INO), md, true, 0, 0, 0)], ∅) ∧ replay-cons-strong((∅)[adr1, inodenode(inodekey(ROOT_INO), md, true, 0, 0, 0)], (∅)[inodekey(ROOT_INO), adr1], ∅, ∅, ∅, adr1 ') ∧ file-node-cons((∅)[adr1, inodenode(inodekey(ROOT_INO), md, true, 0, 0, 0)], (∅)[inodekey(ROOT_INO), adr1]) ∧ orphans-cons((∅)[adr1, inodenode(inodekey(ROOT_INO), md, true, 0, 0, 0)], (∅)[inodekey(ROOT_INO), adr1], ∅)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 57:
⊦ ri-closed(ri, fs, ro) ↔ (∀ key. key ∈ ri → ri[key] ∈ fs ∧ node-closed(fs[ri[key]], ri, fs, ro))
Proof step 58:
⊦ (∀ key. key ∈ (∅)[inodekey(ROOT_INO), adr1] → (∅)[inodekey(ROOT_INO), adr1][key] ∈ (∅)[adr1, inodenode(inodekey(ROOT_INO), md, true, 0, 0, 0)] ∧ node-closed ((∅)[adr1, inodenode(inodekey(ROOT_INO), md, true, 0, 0, 0)][(∅)[inodekey(ROOT_INO), adr1][key]], (∅)[inodekey(ROOT_INO), adr1], (∅)[adr1, inodenode(inodekey(ROOT_INO), md, true, 0, 0, 0)], ∅)) ∧ replay-cons-strong((∅)[adr1, inodenode(inodekey(ROOT_INO), md, true, 0, 0, 0)], (∅)[inodekey(ROOT_INO), adr1], ∅, ∅, ∅, adr1 ') ∧ file-node-cons((∅)[adr1, inodenode(inodekey(ROOT_INO), md, true, 0, 0, 0)], (∅)[inodekey(ROOT_INO), adr1]) ∧ orphans-cons((∅)[adr1, inodenode(inodekey(ROOT_INO), md, true, 0, 0, 0)], (∅)[inodekey(ROOT_INO), adr1], ∅)

Rule argument

spec: aubifs-inv name: ri-closed seq: ⊦ ri-closed(ri, fs, ro) ↔ (∀ key. key ∈ ri → ri[key] ∈ fs ∧ node-closed(fs[ri[key]], ri, fs, ro)) subst: [ro, fs, ri] → [∅, (∅)[adr1, inodenode(inodekey(ROOT_INO), md, true, 0, 0, 0)], (∅)[inodekey(ROOT_INO), adr1]] flags: <all paths>

Additional information

Used terms: ∅, (∅)[adr1, inodenode(inodekey(ROOT_INO), md, true, 0, 0, 0)], (∅)[inodekey(ROOT_INO), adr1]