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Proof step 104 from proof rename-precond-abs (previous step)

fs[ri[dentrykey(ino, str1)]].ino = fs[ri[dentrykey(m3, str0)]].ino, fs[ri[inodekey(fs[ri[dentrykey(m3, str0)]].ino)]].nlink = 1, ¬ fs[ri[inodekey(fs[ri[dentrykey(m3, str0)]].ino)]].directory ↔ ¬ fs[ri[inodekey(fs[ri[dentrykey(m4, str)]].ino)]].directory, abs-dirs(fs, ri)[fs[ri[dentrykey(m3, str0)]].ino] = mkdir(m, md1, m0, m5, entries), fs[ri[inodekey(ino)]].directory, fs[ri[inodekey(ROOT_INO)]].directory, fs[ri[inodekey(m4)]].directory, fs[ri[inodekey(m3)]].directory, orphans(fs, ri).inodes?, file-node-cons(fs, ri), log-cons(log, fs), replay-cons-strong(fs, ri, orphans(fs, ri), fi, fo, log), ri-inj(fi), ri-inj(ri), ubifs-cons(fs, ri, orphans(fs, ri), fi, fo, log), dentrykey(ino, str1) ∈ ri, inodekey(ROOT_INO) ∈ ri, inodekey(fs[ri[dentrykey(m3, str0)]].ino) ∈ ri, inodekey(fs[ri[dentrykey(m4, str)]].ino) ∈ ri, dentrykey(m4, str) ∈ ri, inodekey(m3) ∈ ri, inodekey(m4) ∈ ri, dentrykey(m3, str0) ∈ ri, inodekey(ino) ∈ ri, fs[ri[inodekey(fs[ri[dentrykey(m3, str0)]].ino)]].directory → fs[ri[inodekey(fs[ri[dentrykey(m3, str0)]].ino)]].size = # abs-children(fs[ri[dentrykey(m3, str0)]].ino, fs, ri) ∧ fs[ri[inodekey(fs[ri[dentrykey(m3, str0)]].ino)]].nsubdirs = # subdirs(fs[ri[dentrykey(m3, str0)]].ino, abs-dirs(fs, ri)), fs[ri[inodekey(fs[ri[dentrykey(m3, str0)]].ino)]].directory → abs-children(fs[ri[dentrykey(m3, str0)]].ino, fs, ri) = ∅, m3 = m4 → md = md0, ∀ name. dentrykey(fs[ri[dentrykey(m3, str0)]].ino, name) ∈ ri → inodekey(entries[name]) ∈ ri ∧ fs[ri[inodekey(entries[name])]].directory ∨ inodekey(entries[name]) ∈ ri ∧ ¬ fs[ri[inodekey(entries[name])]].directory, ∀ alink. inodekey(alink.pino) ∈ ri ∧ dentrykey(alink.pino, alink.name) ∈ ri ∧ fs[ri[dentrykey(m3, str0)]].ino = fs[ri[dentrykey(alink.pino, alink.name)]].ino → alink = mklink(ino, str1), links(m4, abs-dirs(fs, ri)) ≠ ∅ ∨ m4 = ROOT_INO, links(m3, abs-dirs(fs, ri)) ≠ ∅ ∨ m3 = ROOT_INO, fs[ri[inodekey(fs[ri[dentrykey(m4, str)]].ino)]].directory ∧ m8 = fs[ri[inodekey(fs[ri[dentrykey(m4, str)]].ino)]].size ∧ m7 = fs[ri[inodekey(fs[ri[dentrykey(m4, str)]].ino)]].nsubdirs ∧ boolvar0 ∨ ¬ fs[ri[inodekey(fs[ri[dentrykey(m4, str)]].ino)]].directory ∧ m7 = 0 ∧ ¬ boolvar0, fs[ri[inodekey(fs[ri[dentrykey(m3, str0)]].ino)]].directory ∧ m2 = fs[ri[inodekey(fs[ri[dentrykey(m3, str0)]].ino)]].size ∧ m1 = fs[ri[inodekey(fs[ri[dentrykey(m3, str0)]].ino)]].nsubdirs ∧ boolvar ∨ ¬ fs[ri[inodekey(fs[ri[dentrykey(m4, str)]].ino)]].directory ∧ m1 = 0 ∧ ¬ boolvar ⊦ fs[ri[dentrykey(m3, str0)]].ino = ROOT_INO, dentrykey(ino, str1) = dentrykey(m3, str0)

User applied rule all left

And closed the goal!

Rule argument

pos: left 29 terms: mklink(m3, str0) abort: F discard: T computed: F

Additional information

Used simplifier rules: ⊦ mklink(m, str).pino = m; (s)% ⊦ mklink(m, str).name = str; (s)% ⊦ mklink(m, str) = mklink(m0, str0) ↔ m = m0 ∧ str = str0; (ws) Used terms: mklink(m3, str0)