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Proof step 60 from proof refine-link (previous step)

fs0[ri[dentrykey(ino1, str)]].ino = fs0[ri[dentrykey(ino0, str)]].ino, fs0[ri[dentrykey(ino, str)]].ino = fs0[ri[dentrykey(ino0, str)]].ino, 0 = fs0[ri[inodekey(fs0[ri[dentrykey(ino0, str)]].ino)]].nsubdirs, adr4 = adr5, c_inode = mkinode(m3, md0, false, m4, 0, m6), dirs = abs-dirs(fs0, ri), err = ESUCCESS, files = abs-files(fs0, ri), fs = fs0[adr1, nd1][adr2, nd0][adr3, nd], log = ((log0 + adr1) + adr2) + adr3, m0 = fs0[ri[inodekey(m)]].nlink, m1 = fs0[ri[inodekey(m)]].nsubdirs, m2 = fs0[ri[inodekey(m)]].size, m3 = fs0[ri[dentrykey(ino0, str)]].ino, m4 = fs0[ri[inodekey(fs0[ri[dentrykey(ino0, str)]].ino)]].nlink, nd = inodenode(inodekey(m3), md0, false, m4 + 1, 0, m6), nd0 = dentrynode(dentrykey(m, str0), m3), nd1 = inodenode(inodekey(m), md, true, m0, m1, m2 + 1), new_dent = negdentry(str0), p_inode = mkinode(m, md, true, m0, m1, m2), ro = orphans(fs0, ri), fs0[ri[inodekey(ino0)]].directory, fs0[ri[inodekey(m)]].directory, fs0[ri[inodekey(ino1)]].directory, fs0[ri[inodekey(ino)]].directory, orphans(fs0, ri).inodes?, fo.inodes?, afs-cons(abs-dirs(fs0, ri), abs-files(fs0, ri)), file-node-cons(fs0, ri), log-cons(log0, fs0), new(adr1 ' + (adr2 ' + adr3), fs0), node-cons(nd1.key, nd1), node-cons(nd0.key, nd0), node-cons(nd.key, nd), orphans-cons(fs0, ri, orphans(fs0, ri)), replay-cons-strong(fs0, ri, orphans(fs0, ri), fi, fo, log0), ri-cons(ri, fs0), ri-inj(ri), ri-inj(fi), ubifs-cons(fs0, ri, orphans(fs0, ri), fi, fo, log0), dentrykey(ino0, str) ∈ ri, inodekey(ino0) ∈ ri, inodekey(m) ∈ ri, dentrykey(ino1, str) ∈ ri, inodekey(fs0[ri[dentrykey(ino0, str)]].ino) ∈ ri, inodekey(ino1) ∈ ri, inodekey(ino) ∈ ri, dentrykey(ino, str) ∈ ri, asynced → boolvar0, links(fs0[ri[dentrykey(ino0, str)]].ino, abs-dirs(fs0, ri)) ≠ ∅ ∨ fs0[ri[dentrykey(ino0, str)]].ino = ROOT_INO, links(m, abs-dirs(fs0, ri)) ≠ ∅ ∨ m = ROOT_INO, links(ino0, abs-dirs(fs0, ri)) ≠ ∅ ∨ ino0 = ROOT_INO, fs0[ri[inodekey(m)]].nlink ≠ 0 ∨ m = ROOT_INO, fs0[ri[inodekey(ino1)]].nlink ≠ 0 ∨ ino1 = ROOT_INO, fs0[ri[inodekey(ino)]].nlink ≠ 0 ∨ ino = ROOT_INO, fs0[ri[inodekey(fs0[ri[dentrykey(ino0, str)]].ino)]].nlink ≠ 0 ∨ fs0[ri[dentrykey(ino0, str)]].ino = ROOT_INO ⊦ [aubifs_core_index_store#(inodekey(p_inode.ino), adr1, fi, ro, fo, fs, log, boolvar; ri); aubifs_core_index_store#(dentrykey(m, str0), adr2, fi, ro, fo, fs, log, boolvar; ri); aubifs_core_index_store#(inodekey(m3), adr3, fi, ro, fo, fs, log, boolvar; ri); new_dent := mkdentry(new_dent.name, m3); p_inode := mkinode (p_inode.ino, inodenode(inodekey(m), md, true, m0, m1, m2 + 1).meta, inodenode(inodekey(m), md, true, m0, m1, m2 + 1).directory, inodenode(inodekey(m), md, true, m0, m1, m2 + 1).nlink, inodenode(inodekey(m), md, true, m0, m1, m2 + 1).nsubdirs, inodenode(inodekey(m), md, true, m0, m1, m2 + 1).size); c_inode := mkinode (m3, inodenode(inodekey(m3), md0, false, m4 + 1, 0, m6).meta, inodenode(inodekey(m3), md0, false, m4 + 1, 0, m6).directory, inodenode(inodekey(m3), md0, false, m4 + 1, 0, m6).nlink, inodenode(inodekey(m3), md0, false, m4 + 1, 0, m6).nsubdirs, inodenode(inodekey(m3), md0, false, m4 + 1, 0, m6).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) → ⟨old_dent0 := negdentry(str0); p_inode0 := mkinode(m, md, true, m0, m1, m2); p_inode1 := mkinode(m3, md0, false, m4, 0, m6); afs_link#(mkdentry(str, m3); p_inode0, p_inode1, old_dent0, 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 ∧ new_dent = old_dent0 ∧ err = err0)), fs0[ri[inodekey(fs0[ri[dentrykey(ino0, str)]].ino)]].directory, dups(adr1 ' + adr2 ' + adr3 '), dentrykey(m, str0) ∈ ri, fs0[ri[inodekey(ino1)]].nlink = 0 ∧ ino1 ≠ ROOT_INO, fs0[ri[inodekey(m)]].nlink = 0 ∧ m ≠ ROOT_INO, fs0[ri[inodekey(fs0[ri[dentrykey(ino0, str)]].ino)]].nlink = 0 ∧ fs0[ri[dentrykey(ino0, str)]].ino ≠ ROOT_INO

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 61:
fs0[ri[dentrykey(ino, str)]].ino = fs0[ri[dentrykey(ino0, str)]].ino, fs0[ri[dentrykey(ino1, str)]].ino = fs0[ri[dentrykey(ino0, str)]].ino, 0 = fs0[ri[inodekey(fs0[ri[dentrykey(ino0, str)]].ino)]].nsubdirs, dirs = abs-dirs(fs0, ri), files = abs-files(fs0, ri), fs = fs0[adr1, inodenode(inodekey(m), md, true, fs0[ri[inodekey(m)]].nlink, fs0[ri[inodekey(m)]].nsubdirs, fs0[ri[inodekey(m)]].size + 1)] [adr2, dentrynode(dentrykey(m, str0), fs0[ri[dentrykey(ino0, str)]].ino) ] [adr3, inodenode(inodekey(fs0[ri[dentrykey(ino0, str)]].ino), md0, false, fs0[ri[inodekey(fs0[ri[dentrykey(ino0, str)]].ino)]].nlink + 1, 0, m6) ], m0 = fs0[ri[inodekey(m)]].nlink, m1 = fs0[ri[inodekey(m)]].nsubdirs, m2 = fs0[ri[inodekey(m)]].size, m3 = fs0[ri[dentrykey(ino0, str)]].ino, m4 = fs0[ri[inodekey(fs0[ri[dentrykey(ino0, str)]].ino)]].nlink, ro = orphans(fs0, ri), fs0[ri[dentrykey(ino0, str)]].ino ≠ 0, adr1 ≠ adr2, adr1 ≠ adr3, adr2 ≠ adr3, m ≠ 0, fs0[ri[inodekey(ino)]].directory, fs0[ri[inodekey(ino1)]].directory, fs0[ri[inodekey(m)]].directory, fs0[ri[inodekey(ino0)]].directory, fo.inodes?, orphans(fs0, ri).inodes?, afs-cons(abs-dirs(fs0, ri), abs-files(fs0, ri)), file-node-cons(fs0, ri), log-cons(log0, fs0), orphans-cons(fs0, ri, orphans(fs0, ri)), replay-cons-strong(fs0, ri, orphans(fs0, ri), fi, fo, log0), ri-cons(ri, fs0), ri-inj(fi), ri-inj(ri), ubifs-cons(fs0, ri, orphans(fs0, ri), fi, fo, log0), dentrykey(ino, str) ∈ ri, inodekey(ino) ∈ ri, inodekey(ino1) ∈ ri, inodekey(fs0[ri[dentrykey(ino0, str)]].ino) ∈ ri, dentrykey(ino1, str) ∈ ri, inodekey(m) ∈ ri, inodekey(ino0) ∈ ri, dentrykey(ino0, str) ∈ ri, ¬ fs0[ri[inodekey(fs0[ri[dentrykey(ino0, str)]].ino)]].directory, ¬ adr3 ∈ fs0, ¬ adr2 ∈ fs0, ¬ adr1 ∈ fs0, ¬ dentrykey(m, str0) ∈ ri, asynced → boolvar0, fs0[ri[inodekey(fs0[ri[dentrykey(ino0, str)]].ino)]].nlink ≠ 0 ∨ fs0[ri[dentrykey(ino0, str)]].ino = ROOT_INO, fs0[ri[inodekey(ino)]].nlink ≠ 0 ∨ ino = ROOT_INO, fs0[ri[inodekey(ino1)]].nlink ≠ 0 ∨ ino1 = ROOT_INO, fs0[ri[inodekey(m)]].nlink ≠ 0 ∨ m = ROOT_INO, links(ino0, abs-dirs(fs0, ri)) ≠ ∅ ∨ ino0 = ROOT_INO, links(m, abs-dirs(fs0, ri)) ≠ ∅ ∨ m = ROOT_INO, links(fs0[ri[dentrykey(ino0, str)]].ino, abs-dirs(fs0, ri)) ≠ ∅ ∨ fs0[ri[dentrykey(ino0, str)]].ino = ROOT_INO ⊦ [aubifs_core_index_store#(inodekey(m), adr1, fi, orphans(fs0, ri), fo, fs, ((log0 + adr1 ') + adr2 ') + adr3 ', boolvar; ri); aubifs_core_index_store#(dentrykey(m, str0), adr2, fi, ro, fo, fs, ((log0 + adr1 ') + adr2 ') + adr3 ', boolvar; ri); aubifs_core_index_store#(inodekey(m3), adr3, fi, ro, fo, fs, ((log0 + adr1 ') + adr2 ') + adr3 ', boolvar; ri); new_dent := mkdentry(str0, m3); p_inode := mkinode (m, inodenode(inodekey(m), md, true, m0, m1, m2 + 1).meta, inodenode(inodekey(m), md, true, m0, m1, m2 + 1).directory, inodenode(inodekey(m), md, true, m0, m1, m2 + 1).nlink, inodenode(inodekey(m), md, true, m0, m1, m2 + 1).nsubdirs, inodenode(inodekey(m), md, true, m0, m1, m2 + 1).size); c_inode := mkinode (m3, inodenode(inodekey(m3), md0, false, m4 + 1, 0, m6).meta, inodenode(inodekey(m3), md0, false, m4 + 1, 0, m6).directory, inodenode(inodekey(m3), md0, false, m4 + 1, 0, m6).nlink, inodenode(inodekey(m3), md0, false, m4 + 1, 0, m6).nsubdirs, inodenode(inodekey(m3), md0, false, m4 + 1, 0, m6).size)] ( ubifs-cons(fs, ri, ro, fi, fo, ((log0 + adr1 ') + adr2 ') + adr3 ') ∧ replay-cons-strong(fs, ri, ro, fi, fo, ((log0 + adr1 ') + adr2 ') + adr3 ') ∧ file-node-cons(fs, ri) ∧ orphans-cons(fs, ri, ro) ∧ ri-inj(ri) ∧ log-cons(log0, fs) ∧ adr1 ∈ fs ∧ node-cons(fs[adr1].key, fs[adr1]) ∧ adr2 ∈ fs ∧ node-cons(fs[adr2].key, fs[adr2]) ∧ adr3 ∈ fs ∧ node-cons(fs[adr3].key, fs[adr3]) → ⟨old_dent0 := negdentry(str0); p_inode0 := mkinode(m, md, true, m0, m1, m2); p_inode1 := mkinode(m3, md0, false, m4, 0, m6); afs_link#(mkdentry(str, m3); p_inode0, p_inode1, old_dent0, 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 ∧ new_dent = old_dent0 ∧ ESUCCESS = err0)), fs0[ri[inodekey(fs0[ri[dentrykey(ino0, str)]].ino)]].nlink = 0 ∧ fs0[ri[dentrykey(ino0, str)]].ino ≠ ROOT_INO, fs0[ri[inodekey(m)]].nlink = 0 ∧ m ≠ ROOT_INO, fs0[ri[inodekey(ino1)]].nlink = 0 ∧ ino1 ≠ ROOT_INO

Rule argument

Additional information

Used simplifier rules: ⊦ inodenode(key, md, boolvar, m, m0, m1).inode?; (s)% ⊦ log-cons(adr ', fs) ↔ adr ∈ fs ∧ node-cons(fs[adr].key, fs[adr]); (s)% ⊦ log-cons(log0 + log1, fs) ↔ log-cons(log0, fs) ∧ log-cons(log1, fs); (s)% ⊦ negdentry(str).name = str; (s)% ⊦ mkinode(m, md, boolvar, m0, m1, m2).ino = m; (s)% ⊦ adr ∈ adr0 ' ↔ adr = adr0; (s)% ⊦ adr ∈ adr0 ' + ax ↔ adr = adr0 ∨ adr ∈ ax; (s)% ⊦ dups(adr ' + adr0 ') ↔ adr = adr0; (s)% ⊦ dups(adr ' + ax) ↔ dups(ax) ∨ adr ∈ ax; (ws)% ⊦ new(adr ', fs) ↔ ¬ adr ∈ fs; (s)% ⊦ new(adr ' + log, fs) ↔ ¬ adr ∈ fs ∧ new(log, fs); (s)%a: ⊦ (ax + ax0) + ax1 = ax + ax0 + ax1; from specification list[address-list-set]% ⊦ ax + adr = ax + adr '; (s)% ⊦ dentrykey(m, str).dentry?; (s)% ⊦ node-cons(key0, dentrynode(key1, ino)) ↔ key0.dentry?; (s)% ⊦ dentrynode(key, m).key = key; (s)% ⊦ inodekey(m).ino = m; (s)% ⊦ inodekey(m).inode?; (s)%⊦ node-cons(key0, inodenode(key1, md, boolvar, n, n0, m)) ↔ key0.inode? ∧ key0.ino ≠ 0; (s)% ⊦ inodenode(key, md, boolvar, m, m0, m1).key = key; (s)