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Proof step 92 from proof refine-link (previous step)

fs0[ri0[dentrykey(ino, str)]].ino = fs0[ri0[dentrykey(ino2, str)]].ino, fs0[ri0[dentrykey(ino1, str)]].ino = fs0[ri0[dentrykey(ino2, str)]].ino, fs0[ri0[inodekey(fs0[ri0[dentrykey(ino2, str)]].ino)]] = inodenode(key1, md2, false, m3, 0, m5), fs0[ri0[dentrykey(ino0, str)]] = dentrynode(key, fs0[ri0[dentrykey(ino2, str)]].ino), fs0[ri0[inodekey(m)]] = inodenode(key0, md1, true, m0, m1, m2), dirs = abs-dirs(fs0, ri0), files = abs-files(fs0, ri0), old_dent0 = negdentry(str0), p_inode0 = mkinode(m, md, true, m0, m1, m2), p_inode1 = mkinode(fs0[ri0[dentrykey(ino2, str)]].ino, md0, false, m3, 0, m6), fs0[ri0[dentrykey(ino2, str)]].ino ≠ 0, adr1 ≠ adr3, adr1 ≠ adr2, adr2 ≠ adr3, m ≠ 0, fs0[ri0[inodekey(ino2)]].directory, fs0[ri0[inodekey(ino)]].directory, fs0[ri0[inodekey(ino1)]].directory, fs0[ri0[inodekey(ino0)]].directory, fo.inodes?, orphans(fs0, ri0).inodes?, afs-cons(abs-dirs(fs0, ri0), abs-files(fs0, ri0)), file-node-cons (fs0[adr1, inodenode(inodekey(m), md, true, m0, m1, m2 + 1)][adr2, dentrynode(dentrykey(m, str0), fs0[ri0[dentrykey(ino2, str)]].ino)] [adr3, inodenode(inodekey(fs0[ri0[dentrykey(ino2, str)]].ino), md0, false, m3 + 1, 0, m6) ], ri0[inodekey(m), adr1][dentrykey(m, str0), adr2][inodekey(fs0[ri0[dentrykey(ino2, str)]].ino), adr3]), file-node-cons(fs0, ri0), log-cons (log0, fs0[adr1, inodenode(inodekey(m), md, true, m0, m1, m2 + 1)][adr2, dentrynode(dentrykey(m, str0), fs0[ri0[dentrykey(ino2, str)]].ino)] [adr3, inodenode(inodekey(fs0[ri0[dentrykey(ino2, str)]].ino), md0, false, m3 + 1, 0, m6) ]), log-cons(log0, fs0), orphans-cons (fs0[adr1, inodenode(inodekey(m), md, true, m0, m1, m2 + 1)][adr2, dentrynode(dentrykey(m, str0), fs0[ri0[dentrykey(ino2, str)]].ino)] [adr3, inodenode(inodekey(fs0[ri0[dentrykey(ino2, str)]].ino), md0, false, m3 + 1, 0, m6) ], ri0[inodekey(m), adr1][dentrykey(m, str0), adr2][inodekey(fs0[ri0[dentrykey(ino2, str)]].ino), adr3], orphans(fs0, ri0)), orphans-cons(fs0, ri0, orphans(fs0, ri0)), replay-cons-strong (fs0[adr1, inodenode(inodekey(m), md, true, m0, m1, m2 + 1)][adr2, dentrynode(dentrykey(m, str0), fs0[ri0[dentrykey(ino2, str)]].ino)] [adr3, inodenode(inodekey(fs0[ri0[dentrykey(ino2, str)]].ino), md0, false, m3 + 1, 0, m6) ], ri0[inodekey(m), adr1][dentrykey(m, str0), adr2][inodekey(fs0[ri0[dentrykey(ino2, str)]].ino), adr3], orphans(fs0, ri0), fi, fo, ((log0 + adr1 ') + adr2 ') + adr3 '), replay-cons-strong(fs0, ri0, orphans(fs0, ri0), fi, fo, log0), ri-cons(ri0, fs0), ri-inj(ri0[inodekey(m), adr1][dentrykey(m, str0), adr2][inodekey(fs0[ri0[dentrykey(ino2, str)]].ino), adr3]), ri-inj(fi), ri-inj(ri0), ubifs-cons (fs0[adr1, inodenode(inodekey(m), md, true, m0, m1, m2 + 1)][adr2, dentrynode(dentrykey(m, str0), fs0[ri0[dentrykey(ino2, str)]].ino)] [adr3, inodenode(inodekey(fs0[ri0[dentrykey(ino2, str)]].ino), md0, false, m3 + 1, 0, m6) ], ri0[inodekey(m), adr1][dentrykey(m, str0), adr2][inodekey(fs0[ri0[dentrykey(ino2, str)]].ino), adr3], orphans(fs0, ri0), fi, fo, ((log0 + adr1 ') + adr2 ') + adr3 '), ubifs-cons(fs0, ri0, orphans(fs0, ri0), fi, fo, log0), dentrykey(ino2, str) ∈ ri0, inodekey(ino2) ∈ ri0, dentrykey(ino0, str) ∈ ri0, ri0[dentrykey(ino0, str)] ∈ fs0, inodekey(fs0[ri0[dentrykey(ino2, str)]].ino) ∈ ri0, ri0[inodekey(fs0[ri0[dentrykey(ino2, str)]].ino)] ∈ fs0, dentrykey(ino, str) ∈ ri0, dentrykey(ino1, str) ∈ ri0, inodekey(ino) ∈ ri0, inodekey(ino1) ∈ ri0, inodekey(ino0) ∈ ri0, ri0[inodekey(m)] ∈ fs0, inodekey(m) ∈ ri0, ¬ dentrykey(m, str0) ∈ ri0, ¬ adr1 ∈ fs0, ¬ adr2 ∈ fs0, ¬ adr3 ∈ fs0, asynced → boolvar0, links(ino2, abs-dirs(fs0, ri0)) ≠ ∅ ∨ ino2 = ROOT_INO, m3 ≠ 0 ∨ fs0[ri0[dentrykey(ino2, str)]].ino = ROOT_INO, fs0[ri0[inodekey(ino)]].nlink ≠ 0 ∨ ino = ROOT_INO, fs0[ri0[inodekey(ino1)]].nlink ≠ 0 ∨ ino1 = ROOT_INO, m0 ≠ 0 ∨ m = ROOT_INO, links(ino0, abs-dirs(fs0, ri0)) ≠ ∅ ∨ ino0 = ROOT_INO, links(m, abs-dirs(fs0, ri0)) ≠ ∅ ∨ m = ROOT_INO, links(fs0[ri0[dentrykey(ino2, str)]].ino, abs-dirs(fs0, ri0)) ≠ ∅ ∨ fs0[ri0[dentrykey(ino2, str)]].ino = ROOT_INO ⊦ ⟨afs_link#(mkdentry(str, fs0[ri0[dentrykey(ino, str)]].ino); p_inode0, p_inode1, old_dent0, err0, dirs, files; asynced)⟩ ( afs-cons(dirs, files) → dirs = abs-dirs (fs0[adr1, inodenode(inodekey(m), md, true, m0, m1, m2 + 1)][adr2, dentrynode(dentrykey(m, str0), fs0[ri0[dentrykey(ino, str)]].ino)] [adr3, inodenode(inodekey(fs0[ri0[dentrykey(ino, str)]].ino), md0, false, m3 + 1, 0, m6) ], ri0[inodekey(m), adr1][dentrykey(m, str0), adr2][inodekey(fs0[ri0[dentrykey(ino, str)]].ino), adr3]) ∧ files = abs-files (fs0[adr1, inodenode(inodekey(m), md, true, m0, m1, m2 + 1)][adr2, dentrynode(dentrykey(m, str0), fs0[ri0[dentrykey(ino, str)]].ino)] [adr3, inodenode(inodekey(fs0[ri0[dentrykey(ino, str)]].ino), md0, false, m3 + 1, 0, m6) ], ri0[inodekey(m), adr1][dentrykey(m, str0), adr2][inodekey(fs0[ri0[dentrykey(ino, str)]].ino), adr3]) ∧ orphans (fs0[adr1, inodenode(inodekey(m), md, true, m0, m1, m2 + 1)][adr2, dentrynode(dentrykey(m, str0), fs0[ri0[dentrykey(ino, str)]].ino)] [adr3, inodenode(inodekey(fs0[ri0[dentrykey(ino, str)]].ino), md0, false, m3 + 1, 0, m6) ], ri0[inodekey(m), adr1][dentrykey(m, str0), adr2][inodekey(fs0[ri0[dentrykey(ino, str)]].ino), adr3]) = orphans(fs0, ri0) ∧ (asynced → boolvar) ∧ mkinode(m, md, true, m0, m1, m2 + 1) = p_inode0 ∧ mkinode(fs0[ri0[dentrykey(ino, str)]].ino, md0, false, m3 + 1, 0, m6) = p_inode1 ∧ mkdentry(str0, fs0[ri0[dentrykey(ino, str)]].ino) = old_dent0 ∧ ESUCCESS = err0), m3 = 0 ∧ fs0[ri0[dentrykey(ino2, str)]].ino ≠ ROOT_INO, m0 = 0 ∧ m ≠ ROOT_INO, fs0[ri0[inodekey(ino1)]].nlink = 0 ∧ ino1 ≠ ROOT_INO

Heuristic unfold applied rule call right

And obtained the following new goals

Proof step 93:
fs0[ri0[dentrykey(ino1, str)]].ino = fs0[ri0[dentrykey(ino2, str)]].ino, fs0[ri0[dentrykey(ino, str)]].ino = fs0[ri0[dentrykey(ino2, str)]].ino, fs0[ri0[inodekey(m)]] = inodenode(key0, md1, true, m0, m1, m2), fs0[ri0[dentrykey(ino0, str)]] = dentrynode(key, fs0[ri0[dentrykey(ino2, str)]].ino), fs0[ri0[inodekey(fs0[ri0[dentrykey(ino2, str)]].ino)]] = inodenode(key1, md2, false, m3, 0, m5), c_inode = p_inode1, dirs = abs-dirs(fs0, ri0), err = err0, files = abs-files(fs0, ri0), new_dent = old_dent0, old_dent = mkdentry(str, fs0[ri0[dentrykey(ino, str)]].ino), old_dent0 = negdentry(str0), p_inode = p_inode0, p_inode0 = mkinode(m, md, true, m0, m1, m2), p_inode1 = mkinode(fs0[ri0[dentrykey(ino2, str)]].ino, md0, false, m3, 0, m6), fs0[ri0[dentrykey(ino, str)]].dentry?, fs0[ri0[inodekey(ino0)]].directory, fs0[ri0[inodekey(ino1)]].directory, fs0[ri0[inodekey(ino)]].directory, fs0[ri0[inodekey(ino2)]].directory, orphans(fs0, ri0).inodes?, fo.inodes?, afs-cons(abs-dirs(fs0, ri0), abs-files(fs0, ri0)), file-node-cons(fs0, ri0), file-node-cons (fs0[adr1, inodenode(inodekey(m), md, true, m0, m1, m2 + 1)][adr2, dentrynode(dentrykey(m, str0), fs0[ri0[dentrykey(ino2, str)]].ino)] [adr3, inodenode(inodekey(fs0[ri0[dentrykey(ino2, str)]].ino), md0, false, m3 + 1, 0, m6) ], ri0[inodekey(m), adr1][dentrykey(m, str0), adr2][inodekey(fs0[ri0[dentrykey(ino2, str)]].ino), adr3]), log-cons(log0, fs0), log-cons (log0, fs0[adr1, inodenode(inodekey(m), md, true, m0, m1, m2 + 1)][adr2, dentrynode(dentrykey(m, str0), fs0[ri0[dentrykey(ino2, str)]].ino)] [adr3, inodenode(inodekey(fs0[ri0[dentrykey(ino2, str)]].ino), md0, false, m3 + 1, 0, m6) ]), orphans-cons(fs0, ri0, orphans(fs0, ri0)), orphans-cons (fs0[adr1, inodenode(inodekey(m), md, true, m0, m1, m2 + 1)][adr2, dentrynode(dentrykey(m, str0), fs0[ri0[dentrykey(ino2, str)]].ino)] [adr3, inodenode(inodekey(fs0[ri0[dentrykey(ino2, str)]].ino), md0, false, m3 + 1, 0, m6) ], ri0[inodekey(m), adr1][dentrykey(m, str0), adr2][inodekey(fs0[ri0[dentrykey(ino2, str)]].ino), adr3], orphans(fs0, ri0)), replay-cons-strong(fs0, ri0, orphans(fs0, ri0), fi, fo, log0), replay-cons-strong (fs0[adr1, inodenode(inodekey(m), md, true, m0, m1, m2 + 1)][adr2, dentrynode(dentrykey(m, str0), fs0[ri0[dentrykey(ino2, str)]].ino)] [adr3, inodenode(inodekey(fs0[ri0[dentrykey(ino2, str)]].ino), md0, false, m3 + 1, 0, m6) ], ri0[inodekey(m), adr1][dentrykey(m, str0), adr2][inodekey(fs0[ri0[dentrykey(ino2, str)]].ino), adr3], orphans(fs0, ri0), fi, fo, ((log0 + adr1 ') + adr2 ') + adr3 '), ri-cons(ri0, fs0), ri-inj(ri0), ri-inj(fi), ri-inj(ri0[inodekey(m), adr1][dentrykey(m, str0), adr2][inodekey(fs0[ri0[dentrykey(ino2, str)]].ino), adr3]), ubifs-cons(fs0, ri0, orphans(fs0, ri0), fi, fo, log0), ubifs-cons (fs0[adr1, inodenode(inodekey(m), md, true, m0, m1, m2 + 1)][adr2, dentrynode(dentrykey(m, str0), fs0[ri0[dentrykey(ino2, str)]].ino)] [adr3, inodenode(inodekey(fs0[ri0[dentrykey(ino2, str)]].ino), md0, false, m3 + 1, 0, m6) ], ri0[inodekey(m), adr1][dentrykey(m, str0), adr2][inodekey(fs0[ri0[dentrykey(ino2, str)]].ino), adr3], orphans(fs0, ri0), fi, fo, ((log0 + adr1 ') + adr2 ') + adr3 '), ri0[dentrykey(ino, str)] ∈ fs0, inodekey(m) ∈ ri0, ri0[inodekey(m)] ∈ fs0, inodekey(ino0) ∈ ri0, inodekey(ino1) ∈ ri0, inodekey(ino) ∈ ri0, dentrykey(ino1, str) ∈ ri0, dentrykey(ino, str) ∈ ri0, ri0[inodekey(fs0[ri0[dentrykey(ino2, str)]].ino)] ∈ fs0, inodekey(fs0[ri0[dentrykey(ino2, str)]].ino) ∈ ri0, ri0[dentrykey(ino0, str)] ∈ fs0, dentrykey(ino0, str) ∈ ri0, inodekey(ino2) ∈ ri0, dentrykey(ino2, str) ∈ ri0, asynced → boolvar0, links(fs0[ri0[dentrykey(ino2, str)]].ino, abs-dirs(fs0, ri0)) ≠ ∅ ∨ fs0[ri0[dentrykey(ino2, str)]].ino = ROOT_INO, links(m, abs-dirs(fs0, ri0)) ≠ ∅ ∨ m = ROOT_INO, links(ino0, abs-dirs(fs0, ri0)) ≠ ∅ ∨ ino0 = ROOT_INO, m0 ≠ 0 ∨ m = ROOT_INO, fs0[ri0[inodekey(ino1)]].nlink ≠ 0 ∨ ino1 = ROOT_INO, fs0[ri0[inodekey(ino)]].nlink ≠ 0 ∨ ino = ROOT_INO, m3 ≠ 0 ∨ fs0[ri0[dentrykey(ino2, str)]].ino = ROOT_INO, links(ino2, abs-dirs(fs0, ri0)) ≠ ∅ ∨ ino2 = ROOT_INO ⊦ ⟨if pre-link(p_inode, c_inode, old_dent, new_dent, dirs, files) then { let p_ino = p_inode.ino in {dirs[p_ino].entries[new_dent.name] := old_dent.ino; dirs[p_ino].size := dirs[p_ino].size + 1; let ino = old_dent.ino in afs_inc_nlink#(ino; dirs, files); new_dent := mkdentry(new_dent.name, old_dent.ino); afs_inode_sync#(p_inode; dirs, files); afs_inode_sync#(c_inode; dirs, files); p_inode := getinode(p_inode.ino, dirs, files); c_inode := getinode(old_dent.ino, dirs, files); err := ESUCCESS} or fail#(; ; err); asynced := ?} else abort⟩ ( afs-cons(dirs, files) → dirs = abs-dirs (fs0[adr1, inodenode(inodekey(m), md, true, m0, m1, m2 + 1)][adr2, dentrynode(dentrykey(m, str0), fs0[ri0[dentrykey(ino, str)]].ino)] [adr3, inodenode(inodekey(fs0[ri0[dentrykey(ino, str)]].ino), md0, false, m3 + 1, 0, m6) ], ri0[inodekey(m), adr1][dentrykey(m, str0), adr2][inodekey(fs0[ri0[dentrykey(ino, str)]].ino), adr3]) ∧ files = abs-files (fs0[adr1, inodenode(inodekey(m), md, true, m0, m1, m2 + 1)][adr2, dentrynode(dentrykey(m, str0), fs0[ri0[dentrykey(ino, str)]].ino)] [adr3, inodenode(inodekey(fs0[ri0[dentrykey(ino, str)]].ino), md0, false, m3 + 1, 0, m6) ], ri0[inodekey(m), adr1][dentrykey(m, str0), adr2][inodekey(fs0[ri0[dentrykey(ino, str)]].ino), adr3]) ∧ orphans (fs0[adr1, inodenode(inodekey(m), md, true, m0, m1, m2 + 1)][adr2, dentrynode(dentrykey(m, str0), fs0[ri0[dentrykey(ino, str)]].ino)] [adr3, inodenode(inodekey(fs0[ri0[dentrykey(ino, str)]].ino), md0, false, m3 + 1, 0, m6) ], ri0[inodekey(m), adr1][dentrykey(m, str0), adr2][inodekey(fs0[ri0[dentrykey(ino, str)]].ino), adr3]) = orphans(fs0, ri0) ∧ (asynced → boolvar) ∧ mkinode(m, md, true, m0, m1, m2 + 1) = p_inode ∧ mkinode(fs0[ri0[dentrykey(ino, str)]].ino, md0, false, m3 + 1, 0, m6) = c_inode ∧ mkdentry(str0, fs0[ri0[dentrykey(ino, str)]].ino) = new_dent ∧ ESUCCESS = err), fs0[ri0[dentrykey(ino2, str)]].ino = 0, adr1 = adr3, adr1 = adr2, adr2 = adr3, m = 0, dentrykey(m, str0) ∈ ri0, adr1 ∈ fs0, adr2 ∈ fs0, adr3 ∈ fs0, fs0[ri0[inodekey(ino1)]].nlink = 0 ∧ ino1 ≠ ROOT_INO, m0 = 0 ∧ m ≠ ROOT_INO, m3 = 0 ∧ fs0[ri0[dentrykey(ino2, str)]].ino ≠ ROOT_INO

Rule argument

pos: right 1

Additional information

Used simplifier rules: afs_link# (OLD_DENT; P_INODE, C_INODE, NEW_DENT, ERR, DIRS, FILES; ASYNCED) {if pre-link(P_INODE, C_INODE, OLD_DENT, NEW_DENT, DIRS, FILES) then { let P_INO = P_INODE.ino in {DIRS[P_INO].entries[NEW_DENT.name] := OLD_DENT.ino; DIRS[P_INO].size := DIRS[P_INO].size + 1; let INO = OLD_DENT.ino in afs_inc_nlink#(INO; DIRS, FILES); NEW_DENT := mkdentry(NEW_DENT.name, OLD_DENT.ino); afs_inode_sync#(P_INODE; DIRS, FILES); afs_inode_sync#(C_INODE; DIRS, FILES); P_INODE := getinode(P_INODE.ino, DIRS, FILES); C_INODE := getinode(OLD_DENT.ino, DIRS, FILES); ERR := ESUCCESS} or fail#(; ; ERR); ASYNCED := ?} else abort };%⊦ dentrykey(ino, str) ∈ ri ∧ ri[dentrykey(ino, str)] ∈ fs ∧ ubifs-cons(fs, ri, ro, fi, fo, log) → fs[ri[dentrykey(ino, str)]].dentry?; (ss)% ⊦ key ∈ ri ∧ ri-cons(ri, fs) → ri[key] ∈ fs; (ss)