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Proof step 58 from proof inv-format (previous step)

⊦ (∀ 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], ∅)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 59:
⊦ 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

Additional information

Used simplifier rules: in-ri: ⊦ key0 ∈ ri[key1, adr] ↔ key0 = key1 ∨ key0 ∈ ri;%at-ri: ⊦ ri[key0, adr][key1] = (key0 = key1 ⊃ adr;ri[key1]);%at-fs: ⊦ fs[adr0, nd][adr1] = (adr0 = adr1 ⊃ nd;fs[adr1]);% ⊦ node-closed(inodenode(key, md, boolvar, n, n0, m), ri, fs, ro); (s)% ⊦ adr ∈ fs[adr1, nd] ↔ adr = adr1 ∨ adr ∈ fs; (s)% ⊦ ¬ key ∈ ∅; (s)