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Proof step 64 from proof initialization (previous step)

∅ = abs-files((∅)[adr1, inodenode(inodekey(ROOT_INO), md, true, 0, 0, 0)], (∅)[inodekey(ROOT_INO), adr1]) ⊦ # orphans(abs-dirs((∅)[adr1, inodenode(inodekey(ROOT_INO), md, true, 0, 0, 0)], (∅)[inodekey(ROOT_INO), adr1]), ∅) = 0, ∀ ino. ino ∈ orphans(abs-dirs((∅)[adr1, inodenode(inodekey(ROOT_INO), md, true, 0, 0, 0)], (∅)[inodekey(ROOT_INO), adr1]), ∅) ↔ ino ∈ ∅

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 65:
∅ = abs-files((∅)[adr1, inodenode(inodekey(ROOT_INO), md, true, 0, 0, 0)], (∅)[inodekey(ROOT_INO), adr1]), ino ∈ orphans(abs-dirs((∅)[adr1, inodenode(inodekey(ROOT_INO), md, true, 0, 0, 0)], (∅)[inodekey(ROOT_INO), adr1]), ∅) ⊦ # orphans(abs-dirs((∅)[adr1, inodenode(inodekey(ROOT_INO), md, true, 0, 0, 0)], (∅)[inodekey(ROOT_INO), adr1]), ∅) = 0

Rule argument

Additional information

Used simplifier rules: ⊦ ¬ ino ∈ ∅; (s)