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Proof step 426 from proof refine-rmdir (previous step)

1 = fs[ri[inodekey(m)]].nlink, fs[ri[inodekey(m2)]] = inodenode(key0, md1, true, m3, m1 + 1, m0 + 1), fs[ri[dentrykey(m2, str)]] = dentrynode(key, m), abs-children(m, fs, ri) = ∅, dentrykeys(inodekey(m), ri) = ∅, dirs = abs-dirs(fs, ri)[m2, mkdir(m0, md1, m3, m1, abs-children(m2, fs, ri) -- str)], files = abs-files(fs, ri), ino = mkdentry(str, m).ino, links(m, fs, ri) = ∅ ++ dentrykey(m2, str), mkdentry(str, m).dentry?, fs[ri[inodekey(m)]].directory, fo.inodes?, orphans(fs, ri).inodes?, afs-cons(abs-dirs(fs, ri), abs-files(fs, ri)), 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-cons(ri, fs), ri-inj(fi), ri-inj(ri), ubifs-cons(fs, ri, orphans(fs, ri), fi, fo, log), inodekey(m2) ∈ ri, dentrykey(m2, str) ∈ ri, ri[dentrykey(m2, str)] ∈ fs, inodekey(m) ∈ ri, ri[inodekey(m2)] ∈ fs, asynced → boolvar0, ∀ adr, adr0, adr1. adr ∈ fs ∨ adr0 ∈ fs ∨ adr1 ∈ fs ∨ adr = adr0 ∨ adr = adr1 ∨ adr0 = adr1, m3 ≠ 0 ∨ m2 = ROOT_INO, links(m2, abs-dirs(fs, ri)) ≠ ∅ ∨ m2 = ROOT_INO ⊦ ⟨fail#(; ; err); asynced := ?⟩ ((asynced → boolvar) ∧ ENOSPC = err), m = 0, m = ROOT_INO, m2 = 0, dirs[ino].nlink ≥ 1, m3 = 0 ∧ m2 ≠ ROOT_INO

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 427:
(m = m2 ⊃ mkdir(m0, md1, m3, m1, abs-children(m2, fs, ri) -- str) ;mkdir(fs[ri[inodekey(m)]].size, fs[ri[inodekey(m)]].meta, 1, fs[ri[inodekey(m)]].nsubdirs, ∅) ) .nlink = 0, 1 = fs[ri[inodekey(m)]].nlink, fs[ri[dentrykey(m2, str)]] = dentrynode(key, m), fs[ri[inodekey(m2)]] = inodenode(key0, md1, true, m3, m1 + 1, m0 + 1), abs-children(m, fs, ri) = ∅, dentrykeys(inodekey(m), ri) = ∅, links(m, fs, ri) = ∅ ++ dentrykey(m2, str), # links(m2, abs-dirs(fs, ri)) ≠ 0, links(m2, abs-dirs(fs, ri)) ≠ ∅, m ≠ ROOT_INO, m ≠ 0, m2 ≠ ROOT_INO, m2 ≠ 0, m3 ≠ 0, fs[ri[inodekey(m)]].directory, orphans(fs, ri).inodes?, fo.inodes?, afs-cons(abs-dirs(fs, ri), abs-files(fs, ri)), 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-cons(ri, fs), ri-inj(ri), ri-inj(fi), ubifs-cons(fs, ri, orphans(fs, ri), fi, fo, log), ri[inodekey(m2)] ∈ fs, inodekey(m) ∈ ri, ri[dentrykey(m2, str)] ∈ fs, dentrykey(m2, str) ∈ ri, inodekey(m2) ∈ ri, asynced → boolvar0, ∀ adr, adr0, adr1. adr ∈ fs ∨ adr0 ∈ fs ∨ adr1 ∈ fs ∨ adr = adr0 ∨ adr = adr1 ∨ adr0 = adr1 ⊦ ⟨fail#(; ; err); asynced := ?⟩ ((asynced → boolvar) ∧ ENOSPC = err)

Rule argument

Additional information

Used simplifier rules: size-zero: ⊦ # ls ≠ 0 → ls ≠ ∅; (forward) from specification set-basic[alink-set]%size-zero-01: ⊦ ls ≠ ∅ → # ls ≠ 0; (forward) from specification set-basic[alink-set]% ⊦ mkdir(m, md, m0, m1, entries).nlink = m0; (s)% ⊦ m < 1 ↔ m = 0; (s)% ⊦ m ≤ n ↔ ¬ n < m; (ss)% ⊦ n ≥ m ↔ m ≤ n; (s)%⊦ abs-dir(ino, fs, ri) = mkdir (fs[ri[inodekey(ino)]].size, fs[ri[inodekey(ino)]].meta, fs[ri[inodekey(ino)]].nlink, fs[ri[inodekey(ino)]].nsubdirs, abs-children(ino, fs, ri)); (s)%⊦ inodekey(ino) ∈ ri ∧ fs[ri[inodekey(ino)]].directory → abs-dirs(fs, ri)[ino] = abs-dir(ino, fs, ri); (s)%⊦ dentrykey(ino, str) ∈ ri ∧ ubifs-cons(fs, ri, ro, fi, fo, log) → fs[ri[inodekey(ino)]].directory; (ss)%⊦ ino ∈ abs-dirs(fs, ri) ↔ inodekey(ino) ∈ ri ∧ fs[ri[inodekey(ino)]].directory; (s)% ⊦ dirs[ino, ad][ino0] = (ino0 = ino ∧ ino ∈ dirs ⊃ ad;dirs[ino0]); (s)% ⊦ mkdentry(str, m).ino = m; (s)% ⊦ mkdentry(str, m).dentry?; (s)