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Proof step 91 from proof refine-rmdir (previous step)

1 = fs[ri[inodekey(fs[ri[dentrykey(m, str)]].ino)]].nlink, abs-children(fs[ri[dentrykey(m, str)]].ino, fs, ri) = ∅, c_inode = mkinode (fs[ri[dentrykey(m, str)]].ino, md0, true, 1, fs[ri[inodekey(fs[ri[dentrykey(m, str)]].ino)]].nsubdirs, fs[ri[inodekey(fs[ri[dentrykey(m, str)]].ino)]].size), dent = mkdentry(str, fs[ri[dentrykey(m, str)]].ino), dentrykeys(inodekey(fs[ri[dentrykey(m, str)]].ino), ri) = ∅, dirs = abs-dirs(fs, ri), files = abs-files(fs, ri), links(fs[ri[dentrykey(m, str)]].ino, 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, m5 = fs[ri[inodekey(fs[ri[dentrykey(m, str)]].ino)]].nsubdirs, m6 = fs[ri[inodekey(fs[ri[dentrykey(m, str)]].ino)]].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), fs[ri[dentrykey(m, str)]].ino ≠ ROOT_INO, fs[ri[inodekey(m)]].nsubdirs ≠ 0, fs[ri[inodekey(m)]].size ≠ 0, fs[ri[inodekey(fs[ri[dentrykey(m, str)]].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(fs[ri[dentrykey(m, str)]].ino) ∈ ri, dentrykey(m, str) ∈ ri, 1 ≤ fs[ri[inodekey(m)]].nsubdirs, 1 ≤ fs[ri[inodekey(m)]].size, asynced → boolvar, links(m, abs-dirs(fs, ri)) ≠ ∅ ∨ m = ROOT_INO, fs[ri[inodekey(m)]].nlink ≠ 0 ∨ m = ROOT_INO ⊦ [aubifs_core_journal_add3# (inodenode(inodekey(p_inode.ino), p_inode.meta, p_inode.directory, p_inode.nlink, p_inode.nsubdirs - 1, p_inode.size - 1), dentrynode(dentrykey(p_inode.ino, dent.name), 0), inodenode(inodekey(c_inode.ino), c_inode.meta, c_inode.directory, c_inode.nlink - 1, c_inode.nsubdirs, c_inode.size), ri, fi, orphans(fs, ri), fo ; adr1, adr0, adr, fs, log ; boolvar, err); nd1 := inodenode(inodekey(p_inode.ino), p_inode.meta, p_inode.directory, p_inode.nlink, p_inode.nsubdirs - 1, p_inode.size - 1); nd := inodenode(inodekey(c_inode.ino), c_inode.meta, c_inode.directory, c_inode.nlink - 1, c_inode.nsubdirs, c_inode.size); ino := c_inode.ino; if err = ESUCCESS then {aubifs_core_index_store#(inodekey(p_inode.ino), adr1, fi, ro, fo, fs, log, boolvar; ri); aubifs_core_index_remove#(dentrykey(p_inode.ino, dent.name), fi, ro, fo, fs, log, boolvar; ri); aubifs_core_index_store#(inodekey(c_inode.ino), adr, fi, ro, fo, fs, log, boolvar; ri); aubifs_core_orphans_insert#(inodekey(c_inode.ino), ri, fi, fo, fs, log, boolvar; ro); dent := negdentry(dent.name); p_inode := mkinode(p_inode.ino, nd1.meta, nd1.directory, nd1.nlink, nd1.nsubdirs, nd1.size); c_inode := mkinode(ino, nd.meta, nd.directory, nd.nlink, nd.nsubdirs, nd.size)}] ( 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); p_inode1 := mkinode(m3, md0, true, 1, m5, m6); 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 92:
1 = fs[ri[inodekey(fs[ri[dentrykey(m, str)]].ino)]].nlink, abs-children(fs[ri[dentrykey(m, str)]].ino, fs, ri) = ∅, c_inode = mkinode (fs[ri[dentrykey(m, str)]].ino, md0, true, 1, fs[ri[inodekey(fs[ri[dentrykey(m, str)]].ino)]].nsubdirs, fs[ri[inodekey(fs[ri[dentrykey(m, str)]].ino)]].size), dent = mkdentry(str, fs[ri[dentrykey(m, str)]].ino), dentrykeys(inodekey(fs[ri[dentrykey(m, str)]].ino), ri) = ∅, dirs = abs-dirs(fs, ri), files = abs-files(fs, ri), links(fs[ri[dentrykey(m, str)]].ino, 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, m5 = fs[ri[inodekey(fs[ri[dentrykey(m, str)]].ino)]].nsubdirs, m6 = fs[ri[inodekey(fs[ri[dentrykey(m, str)]].ino)]].size, p_inode = mkinode(m, md, true, fs[ri[inodekey(m)]].nlink, fs[ri[inodekey(m)]].nsubdirs, fs[ri[inodekey(m)]].size), p_inode = mkinode(m4, md1, boolvar0, m7, m8, m9), ro = orphans(fs, ri), fs[ri[inodekey(m)]].directory, fs[ri[inodekey(fs[ri[dentrykey(m, str)]].ino)]].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(fs[ri[dentrykey(m, str)]].ino) ∈ ri, inodekey(m) ∈ ri, 1 ≤ fs[ri[inodekey(m)]].size, 1 ≤ fs[ri[inodekey(m)]].nsubdirs, asynced → boolvar, fs[ri[inodekey(m)]].nlink ≠ 0 ∨ m = ROOT_INO, links(m, abs-dirs(fs, ri)) ≠ ∅ ∨ m = ROOT_INO ⊦ [aubifs_core_journal_add3# (inodenode(inodekey(m4), md1, boolvar0, m7, m8 - 1, m9 - 1), dentrynode(dentrykey(m4, dent.name), 0), inodenode(inodekey(c_inode.ino), c_inode.meta, c_inode.directory, c_inode.nlink - 1, c_inode.nsubdirs, c_inode.size), ri, fi, orphans(fs, ri), fo ; adr1, adr0, adr, fs, log ; boolvar, err); nd1 := inodenode(inodekey(m4), md1, boolvar0, m7, m8 - 1, m9 - 1); nd := inodenode(inodekey(c_inode.ino), c_inode.meta, c_inode.directory, c_inode.nlink - 1, c_inode.nsubdirs, c_inode.size); ino := c_inode.ino; if err = ESUCCESS then {aubifs_core_index_store#(inodekey(m4), adr1, fi, ro, fo, fs, log, boolvar; ri); aubifs_core_index_remove#(dentrykey(m4, dent.name), fi, ro, fo, fs, log, boolvar; ri); aubifs_core_index_store#(inodekey(c_inode.ino), adr, fi, ro, fo, fs, log, boolvar; ri); aubifs_core_orphans_insert#(inodekey(c_inode.ino), ri, fi, fo, fs, log, boolvar; ro); dent := negdentry(dent.name); p_inode := mkinode(p_inode.ino, nd1.meta, nd1.directory, nd1.nlink, nd1.nsubdirs, nd1.size); c_inode := mkinode(ino, nd.meta, nd.directory, nd.nlink, nd.nsubdirs, nd.size)}] ( 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); p_inode1 := mkinode(m3, md0, true, 1, m5, m6); 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[dentrykey(m, str)]].ino = ROOT_INO, fs[ri[inodekey(m)]].nsubdirs = 0, fs[ri[inodekey(m)]].size = 0, 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_inode, m4, md1, boolvar, m7, m8, m9]

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_inode, m4, md1, boolvar, m7, m8, m9