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Proof step 25 from proof refine-link (previous step)

fs[ri[inodekey(fs[ri[dentrykey(ino, str)]].ino)]].nlink = 0, fs[ri[inodekey(m)]].directory, fs[ri[inodekey(ino)]].directory, fs[ri[inodekey(ROOT_INO)]].directory, orphans(fs, ri).inodes?, fo.inodes?, file-node-cons(fs, ri), log-cons(log, fs), orphans-cons(fs, ri, orphans(fs, ri)), replay-cons-strong(fs, ri, orphans(fs, ri), fi, fo, log), ri-inj(ri), ri-inj(fi), ubifs-cons(fs, ri, orphans(fs, ri), fi, fo, log), inodekey(ino) ∈ ri, inodekey(fs[ri[dentrykey(ino, str)]].ino) ∈ ri, inodekey(m) ∈ ri, dentrykey(ino, str) ∈ ri, inodekey(ROOT_INO) ∈ ri, asynced → boolvar, ∀ ino0. (inodekey(ino0) ∈ ri ∧ fs[ri[inodekey(ino0)]].directory ∧ ino0 ≠ ROOT_INO ∧ links(ino0, abs-dirs(fs, ri)) = ∅ → abs-children(ino0, fs, ri) = ∅) ∧ ( inodekey(ino0) ∈ ri ∧ fs[ri[inodekey(ino0)]].directory → fs[ri[inodekey(ino0)]].nlink = # links(ino0, abs-dirs(fs, ri)) ∧ fs[ri[inodekey(ino0)]].nlink ≤ 1 ∧ fs[ri[inodekey(ino0)]].size = # abs-children(ino0, fs, ri) ∧ fs[ri[inodekey(ino0)]].nsubdirs = # subdirs(ino0, abs-dirs(fs, ri))) ∧ (inodekey(ino0) ∈ ri ∧ ¬ fs[ri[inodekey(ino0)]].directory → fs[ri[inodekey(ino0)]].nlink = # links(ino0, abs-dirs(fs, ri))) ∧ (∀ name. inodekey(ino0) ∈ ri ∧ dentrykey(ino0, name) ∈ ri → inodekey(abs-dirs(fs, ri)[ino0].entries[name]) ∈ ri ∧ fs[ri[inodekey(abs-dirs(fs, ri)[ino0].entries[name])]].directory ∨ inodekey(abs-dirs(fs, ri)[ino0].entries[name]) ∈ ri ∧ ¬ fs[ri[inodekey(abs-dirs(fs, ri)[ino0].entries[name])]].directory), links(m, abs-dirs(fs, ri)) ≠ ∅ ∨ m = ROOT_INO, links(ino, abs-dirs(fs, ri)) ≠ ∅ ∨ ino = ROOT_INO ⊦ # links(fs[ri[dentrykey(ino, str)]].ino, abs-dirs(fs, ri)) = 0, fs[ri[dentrykey(ino, str)]].ino = ROOT_INO, links(fs[ri[dentrykey(ino, str)]].ino, abs-dirs(fs, ri)) = ∅, fs[ri[inodekey(fs[ri[dentrykey(ino, str)]].ino)]].directory, dentrykey(m, str0) ∈ ri

User applied rule all left

And closed the goal!

Rule argument

pos: left 20 terms: fs[ri[dentrykey(ino, str)]].ino abort: F discard: F computed: T

Additional information

Used simplifier rules: size-zero-02: ⊦ # ls = 0 → ls = ∅; (forward) from specification set-basic[alink-set] Used terms: fs[ri[dentrykey(ino, str)]].ino