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Proof step 15 from proof abs-delorphans (previous step)

links(ino, dirs) = ∅, abs(tree, ROOT_INO)(dirs), ispath(p, ROOT_INO, ino, dirs, files), ino ∈ dirs, p ∈ tree, ∀ ino. ⌜ino⌝ ∈ tree.fids → ino ∈ files, ∀ ino. ¬ ino ∈ files ∨ ¬ ino ∈ dirs ⊦ # orphans(dirs, files) = 0, ino = ROOT_INO, orphans(dirs, files) = ∅

User applied rule cut formula

And obtained the following new goals

Proof step 16:
links(ino, dirs) = ∅, abs(tree, ROOT_INO)(dirs), ispath(p, ROOT_INO, ino, dirs, files), p ∈ tree, ino ∈ dirs, ∀ ino. ¬ ino ∈ files ∨ ¬ ino ∈ dirs, ∀ ino. ⌜ino⌝ ∈ tree.fids → ino ∈ files ⊦ # orphans(dirs, files) = 0, ino = ROOT_INO, orphans(dirs, files) = ∅, p = ε

Rule argument

fma: p = ε

Additional information

Used simplifier rules: ⊦ ε ∈ tree; (s)% ⊦ ispath(ε, n, m, dirs, files) ↔ valid-ino(n, dirs, files) ∧ m = n; (s)% ⊦ valid-ino(ino, dirs, files) ↔ ino ∈ dirs ∨ ino ∈ files; (s) Used formulas: p = ε