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Proof step 124 from proof rename-precond-abs (previous step)

fs[ri[inodekey(m4)]].nsubdirs = 0, fs[ri[inodekey(fs[ri[dentrykey(m4, str)]].ino)]].directory, fs[ri[inodekey(m3)]].directory, fs[ri[inodekey(m4)]].directory, orphans(fs, ri).inodes?, afs-cons(abs-dirs(fs, ri), abs-files(fs, ri)), file-node-cons(fs, ri), log-cons(log, fs), 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(m4) ∈ ri, inodekey(m3) ∈ ri, dentrykey(m4, str) ∈ ri, inodekey(fs[ri[dentrykey(m4, str)]].ino) ∈ ri, m3 = m4 → md = md0, (links(m3, abs-dirs(fs, ri)) ≠ ∅ ∨ m3 = ROOT_INO) ∧ ¬ dentrykey(m3, new_dent.name) ∈ ri ∧ new_dent.negdentry? ∨ (links(m3, abs-dirs(fs, ri)) ≠ ∅ ∨ m3 = ROOT_INO) ∧ inodekey(new_dent.ino) ∈ ri ∧ fs[ri[inodekey(new_dent.ino)]].directory ∧ dentrykey(m3, new_dent.name) ∈ ri ∧ new_dent.ino = fs[ri[dentrykey(m3, new_dent.name)]].ino ∧ new_dent.dentry? ∧ m0 = fs[ri[inodekey(new_dent.ino)]].nlink ∧ m2 = fs[ri[inodekey(new_dent.ino)]].size ∧ m1 = fs[ri[inodekey(new_dent.ino)]].nsubdirs ∧ boolvar ∧ m = new_dent.ino ∧ new_dent.ino ≠ ROOT_INO ∧ abs-children(new_dent.ino, fs, ri) = ∅, links(m4, abs-dirs(fs, ri)) ≠ ∅ ∨ m4 = ROOT_INO ⊦

User applied rule apply lemma

And obtained the following new goals

Proof step 125:
⊦ afs-cons(abs-dirs(fs, ri), abs-files(fs, ri)) ∧ ino ∈ abs-dirs(fs, ri) ∧ subdirs(ino, abs-dirs(fs, ri)) ≠ ∅ → fs[ri[inodekey(ino)]].nsubdirs ≥ 1
Proof step 126:
fs[ri[inodekey(m4)]].nsubdirs = 0, fs[ri[inodekey(m4)]].directory, fs[ri[inodekey(m3)]].directory, fs[ri[inodekey(fs[ri[dentrykey(m4, str)]].ino)]].directory, orphans(fs, ri).inodes?, afs-cons(abs-dirs(fs, ri), abs-files(fs, ri)), 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), inodekey(fs[ri[dentrykey(m4, str)]].ino) ∈ ri, dentrykey(m4, str) ∈ ri, inodekey(m3) ∈ ri, inodekey(m4) ∈ ri, m3 = m4 → md = md0, afs-cons(abs-dirs(fs, ri), abs-files(fs, ri)) ∧ m4 ∈ abs-dirs(fs, ri) ∧ subdirs(m4, abs-dirs(fs, ri)) ≠ ∅ → fs[ri[inodekey(m4)]].nsubdirs ≥ 1, links(m4, abs-dirs(fs, ri)) ≠ ∅ ∨ m4 = ROOT_INO, (links(m3, abs-dirs(fs, ri)) ≠ ∅ ∨ m3 = ROOT_INO) ∧ ¬ dentrykey(m3, new_dent.name) ∈ ri ∧ new_dent.negdentry? ∨ (links(m3, abs-dirs(fs, ri)) ≠ ∅ ∨ m3 = ROOT_INO) ∧ inodekey(new_dent.ino) ∈ ri ∧ fs[ri[inodekey(new_dent.ino)]].directory ∧ dentrykey(m3, new_dent.name) ∈ ri ∧ new_dent.ino = fs[ri[dentrykey(m3, new_dent.name)]].ino ∧ new_dent.dentry? ∧ m0 = fs[ri[inodekey(new_dent.ino)]].nlink ∧ m2 = fs[ri[inodekey(new_dent.ino)]].size ∧ m1 = fs[ri[inodekey(new_dent.ino)]].nsubdirs ∧ boolvar ∧ m = new_dent.ino ∧ new_dent.ino ≠ ROOT_INO ∧ abs-children(new_dent.ino, fs, ri) = ∅ ⊦

Rule argument

spec: <toplevel> name: afs-cons-abs-dir-subdirs seq: ⊦ afs-cons(abs-dirs(fs, ri), abs-files(fs, ri)) ∧ ino ∈ abs-dirs(fs, ri) ∧ subdirs(ino, abs-dirs(fs, ri)) ≠ ∅ → fs[ri[inodekey(ino)]].nsubdirs ≥ 1 subst: [fs, ri, ino] → [fs, ri, m4]

Additional information

Used terms: fs, ri, m4