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Proof step 79 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) = ∅, 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

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 80:
1 = fs[ri[inodekey(m3)]].nlink, abs-children(m3, fs, ri) = ∅, boolvar0, c_inode = p_inode1, dent = mkdentry(str, m3), dentrykeys(inodekey(m3), ri) = ∅, dirs = abs-dirs(fs, ri), err = err0, files = abs-files(fs, ri), links(m3, fs, ri) = ∅ ++ dentrykey(m, str), m0 = fs[ri[inodekey(m)]].nlink, m1 = fs[ri[inodekey(m)]].nsubdirs, m2 = fs[ri[inodekey(m)]].size, m3 = fs[ri[dentrykey(m, str)]].ino, m4 = 1, m5 = fs[ri[inodekey(m3)]].nsubdirs, m6 = fs[ri[inodekey(m3)]].size, p_inode = mkinode(m, md, true, fs[ri[inodekey(m)]].nlink, fs[ri[inodekey(m)]].nsubdirs, fs[ri[inodekey(m)]].size), p_inode1 = mkinode(m3, md0, boolvar0, m4, m5, m6), ro = orphans(fs, ri), fs[ri[inodekey(m3)]].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(m3) ∈ ri, dentrykey(m, str) ∈ ri, 1 ≤ fs[ri[inodekey(m)]].size, 1 ≤ fs[ri[inodekey(m)]].nsubdirs, asynced → boolvar, links(m, abs-dirs(fs, ri)) ≠ ∅ ∨ m = ROOT_INO, fs[ri[inodekey(m)]].nlink ≠ 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, m3); 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)]].nsubdirs = 0, fs[ri[inodekey(m)]].size = 0, m3 = ROOT_INO, fs[ri[inodekey(m)]].nlink = 0 ∧ m ≠ ROOT_INO

Rule argument

spec: inode name: elim seq: ⊦ ( ( ( (m = inode.ino ∧ md = inode.meta) ∧ (boolvar ↔ inode.directory)) ∧ m0 = inode.nlink) ∧ m1 = inode.nsubdirs) ∧ m2 = inode.size ↔ inode = mkinode(m, md, boolvar, m0, m1, m2) subst: [inode, m, md, boolvar, m0, m1, m2] → [p_inode1, m3, md0, boolvar0, m4, m5, m6]

Additional information

Used simplifier rules: ⊦ ( ( ( (m = inode.ino ∧ md = inode.meta) ∧ (boolvar ↔ inode.directory)) ∧ m0 = inode.nlink) ∧ m1 = inode.nsubdirs) ∧ m2 = inode.size ↔ inode = mkinode(m, md, boolvar, m0, m1, m2); (elim) Used terms: p_inode1, m3, md0, boolvar0, m4, m5, m6