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Proof step 55 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)] ∧ key-cons(key, (∅)[adr1, inodenode(inodekey(ROOT_INO), md, true, 0, 0, 0)][(∅)[inodekey(ROOT_INO), adr1][key]])) ∧ 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], ∅)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 56:
⊦ 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], ∅)

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]);% ⊦ ROOT_INO ≠ 0; (s)% ⊦ inodekey(m) = inodekey(m0) ↔ m = m0; (s)% ⊦ inodenode(key, md, boolvar, m, m0, m1).key = key; (s)% ⊦ inodenode(key, md, boolvar, m, m0, m1).inode?; (s)%⊦ key-cons(inodekey(ino), nd) ↔ nd.inode? ∧ nd.key = inodekey(ino) ∧ ino ≠ 0; (s)% ⊦ adr ∈ fs[adr1, nd] ↔ adr = adr1 ∨ adr ∈ fs; (s)% ⊦ ¬ key ∈ ∅; (s)