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Proof step 68 from proof initialization (previous step)

∅ = abs-files((∅)[adr1, inodenode(inodekey(ROOT_INO), md, true, 0, 0, 0)], (∅)[inodekey(ROOT_INO), adr1]) ⊦ ( inodekey(ino) ∈ (∅)[inodekey(ROOT_INO), adr1] ∧ (adr1 = (∅)[inodekey(ino)] ⊃ inodenode(inodekey(ROOT_INO), md, true, 0, 0, 0);(∅)[(∅)[inodekey(ino)]]).directory → ino = ROOT_INO) ∧ (ino = ROOT_INO → ∅ = abs-children(ROOT_INO, (∅)[adr1, inodenode(inodekey(ROOT_INO), md, true, 0, 0, 0)], (∅)[inodekey(ROOT_INO), adr1]))

User applied rule case distinction

And closed the goal!

Rule argument

pos: right 1

Additional information

Used simplifier rules: in-ri-dentry-inode: ⊦ dentrykey(ino, str) ∈ ri[inodekey(ino), adr] ↔ dentrykey(ino, str) ∈ ri;%⊦ entries = abs-children(ino, fs, ri) ↔ (∀ str. (str ∈ entries ↔ dentrykey(ino, str) ∈ ri) ∧ ( str ∈ entries → entries[str] = fs[ri[dentrykey(ino, str)]].ino)); (ss)% ⊦ ¬ str ∈ ∅; (s)% ⊦ ¬ key ∈ ∅; (s)% ⊦ key ∈ ri[key0, adr] ↔ key = key0 ∨ key ∈ ri; (las)% ⊦ inodekey(m) = inodekey(m0) ↔ m = m0; (s)