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Proof step 78 from proof refine-rmdir (previous step)

p_inode1.ino = fs[ri[dentrykey(m, str)]].ino, p_inode1.nlink = 1, p_inode1.nsubdirs = fs[ri[inodekey(p_inode1.ino)]].nsubdirs, p_inode1.size = fs[ri[inodekey(p_inode1.ino)]].size, 1 = fs[ri[inodekey(p_inode1.ino)]].nlink, abs-children(p_inode1.ino, fs, ri) = ∅, boolvar0, c_inode = p_inode1, dent = mkdentry(str, p_inode1.ino), dentrykeys(inodekey(p_inode1.ino), ri) = ∅, dirs = abs-dirs(fs, ri), err = err0, files = abs-files(fs, ri), links(p_inode1.ino, fs, ri) = ∅ ++ dentrykey(m, str), m0 = fs[ri[inodekey(m)]].nlink, m1 = fs[ri[inodekey(m)]].nsubdirs, m2 = fs[ri[inodekey(m)]].size, p_inode = p_inode0, p_inode0 = mkinode(m, md, boolvar0, m0, m1, m2), ro = orphans(fs, ri), p_inode1.directory, fs[ri[inodekey(p_inode1.ino)]].directory, 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-inj(ri), ri-inj(fi), ubifs-cons(fs, ri, orphans(fs, ri), fi, fo, log), inodekey(m) ∈ ri, inodekey(p_inode1.ino) ∈ ri, dentrykey(m, str) ∈ ri, 1 ≤ m2, 1 ≤ m1, asynced → boolvar, links(m, abs-dirs(fs, ri)) ≠ ∅ ∨ m = ROOT_INO, m0 ≠ 0 ∨ m = ROOT_INO ⊦ [aubifs_rmdir#(fi, fo; p_inode, c_inode, dent, err, ri, ro, fs, log, boolvar)] ( ubifs-cons(fs, ri, ro, fi, fo, log) ∧ replay-cons-strong(fs, ri, ro, fi, fo, log) ∧ file-node-cons(fs, ri) ∧ orphans-cons(fs, ri, ro) ∧ ri-inj(ri) ∧ log-cons(log, fs) ∧ ro.inodes? → ⟨old_dent := mkdentry(str, p_inode1.ino); afs_rmdir#(; p_inode0, p_inode1, old_dent, err0, dirs, files; asynced)⟩ ( dirs = abs-dirs(fs, ri) ∧ files = abs-files(fs, ri) ∧ orphans(abs-dirs(fs, ri), abs-files(fs, ri)) = abs-keys(ro) ∧ (asynced → boolvar) ∧ p_inode = p_inode0 ∧ c_inode = p_inode1 ∧ dent = old_dent ∧ err = err0)), p_inode1.ino = ROOT_INO, m1 = 0, m2 = 0, m0 = 0 ∧ m ≠ ROOT_INO

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 79:
p_inode1.ino = fs[ri[dentrykey(m, str)]].ino, p_inode1.nlink = 1, p_inode1.nsubdirs = fs[ri[inodekey(p_inode1.ino)]].nsubdirs, p_inode1.size = fs[ri[inodekey(p_inode1.ino)]].size, 1 = fs[ri[inodekey(p_inode1.ino)]].nlink, abs-children(p_inode1.ino, fs, ri) = ∅, c_inode = p_inode1, dent = mkdentry(str, p_inode1.ino), dentrykeys(inodekey(p_inode1.ino), ri) = ∅, dirs = abs-dirs(fs, ri), err = err0, files = abs-files(fs, ri), links(p_inode1.ino, fs, ri) = ∅ ++ dentrykey(m, str), m0 = fs[ri[inodekey(m)]].nlink, m1 = fs[ri[inodekey(m)]].nsubdirs, m2 = fs[ri[inodekey(m)]].size, p_inode = mkinode(m, md, true, fs[ri[inodekey(m)]].nlink, fs[ri[inodekey(m)]].nsubdirs, fs[ri[inodekey(m)]].size), ro = orphans(fs, ri), p_inode1.ino ≠ ROOT_INO, fs[ri[inodekey(m)]].nsubdirs ≠ 0, fs[ri[inodekey(m)]].size ≠ 0, fs[ri[inodekey(m)]].directory, fs[ri[inodekey(p_inode1.ino)]].directory, p_inode1.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-inj(fi), ri-inj(ri), ubifs-cons(fs, ri, orphans(fs, ri), fi, fo, log), dentrykey(m, str) ∈ ri, inodekey(p_inode1.ino) ∈ ri, inodekey(m) ∈ ri, 1 ≤ fs[ri[inodekey(m)]].nsubdirs, 1 ≤ fs[ri[inodekey(m)]].size, asynced → boolvar, fs[ri[inodekey(m)]].nlink ≠ 0 ∨ m = ROOT_INO, links(m, abs-dirs(fs, ri)) ≠ ∅ ∨ m = ROOT_INO ⊦ [aubifs_rmdir#(fi, fo; p_inode, c_inode, dent, err, ri, ro, fs, log, boolvar)] ( ubifs-cons(fs, ri, ro, fi, fo, log) ∧ replay-cons-strong(fs, ri, ro, fi, fo, log) ∧ file-node-cons(fs, ri) ∧ orphans-cons(fs, ri, ro) ∧ ri-inj(ri) ∧ log-cons(log, fs) ∧ ro.inodes? → ⟨old_dent := mkdentry(str, p_inode1.ino); p_inode0 := mkinode(m, md, true, m0, m1, m2); afs_rmdir#(; p_inode0, p_inode1, old_dent, err0, dirs, files; asynced)⟩ ( dirs = abs-dirs(fs, ri) ∧ files = abs-files(fs, ri) ∧ orphans(abs-dirs(fs, ri), abs-files(fs, ri)) = abs-keys(ro) ∧ (asynced → boolvar) ∧ p_inode = p_inode0 ∧ c_inode = p_inode1 ∧ dent = old_dent ∧ err = err0)), fs[ri[inodekey(m)]].nlink = 0 ∧ m ≠ ROOT_INO

Rule argument

Additional information

Used simplifier rules: not-zero: 0 < n ⊦ (* n) ≤ m → m ≠ 0; (forward) from specification nat%ubifs-parent-in: ⊦ dentrykey(ino, str) ∈ ri ∧ ubifs-cons(fs, ri, ro, fi, fo, log) → inodekey(ino) ∈ ri; (forward) from specification aubifs-inv