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Proof step 138 from proof refine-rename-overwrite-keep-parent-different (previous step)

1 = fs0[ri0[inodekey(m3)]].nlink, fs0[ri0[dentrykey(m7, str0)]] = dentrynode(key0, m3), fs0[ri0[dentrykey(m7, str)]] = dentrynode(key2, m), fs0[ri0[inodekey(m7)]] = inodenode(key1, md2, true, m4, n0 + 1, m11 + 1), abs-children(m3, fs0, ri0) = ∅, dentrykeys(inodekey(m3), ri0) = ∅, dirs = abs-dirs(fs0, ri0)[m7, mkdir(m11, md2, m4, n0, (abs-children(m7, fs0, ri0) -- str)[str0, m])] [m3, (m3 = m7 ⊃ mkdir(m11, md2, m4, n0, (abs-children(m7, fs0, ri0) -- str)[str0, m]) ;mkdir(fs0[ri0[inodekey(m3)]].size, fs0[ri0[inodekey(m3)]].meta, 1, fs0[ri0[inodekey(m3)]].nsubdirs, ∅) ) .nlink:= ( (m3 = m7 ⊃ mkdir(m11, md2, m4, n0, (abs-children(m7, fs0, ri0) -- str)[str0, m]) ;mkdir(fs0[ri0[inodekey(m3)]].size, fs0[ri0[inodekey(m3)]].meta, 1, fs0[ri0[inodekey(m3)]].nsubdirs, ∅) ) .nlink - 1) ], files = abs-files(fs0, ri0), links(m3, fs0, ri0) = ∅ ++ dentrykey(m7, str0), (m3 = m7 ⊃ mkdir(m11, md2, m4, n0, (abs-children(m7, fs0, ri0) -- str)[str0, m]) ;mkdir(fs0[ri0[inodekey(m3)]].size, fs0[ri0[inodekey(m3)]].meta, 1, fs0[ri0[inodekey(m3)]].nsubdirs, ∅) ) .nlink ≠ 0, adr1 ≠ adr2, adr1 ≠ adr3, adr1 ≠ adr4, adr2 ≠ adr3, adr2 ≠ adr4, adr3 ≠ adr4, m3 ≠ ROOT_INO, m3 ≠ 0, m7 ≠ 0, mkdentry(str, m) ≠ mkdentry(str0, m3), fs0[ri0[inodekey(m3)]].directory, fs0[ri0[inodekey(m)]].directory, orphans(fs0, ri0).inodes?, fo.inodes?, afs-cons(abs-dirs(fs0, ri0), abs-files(fs0, ri0)), file-node-cons (fs0[adr1, dentrynode(dentrykey(m7, str), 0)][adr2, dentrynode(dentrykey(m7, str0), m)][adr3, inodenode(inodekey(m7), md1, true, m4, n0, m11)] [adr4, inodenode(inodekey(m3), md0, true, 0, fs0[ri0[inodekey(m3)]].nsubdirs, fs0[ri0[inodekey(m3)]].size) ], (ri0 -- dentrykey(m7, str))[dentrykey(m7, str0), adr2][inodekey(m7), adr3][inodekey(m3), adr4]), file-node-cons(fs0, ri0), log-cons (log0, fs0[adr1, dentrynode(dentrykey(m7, str), 0)][adr2, dentrynode(dentrykey(m7, str0), m)][adr3, inodenode(inodekey(m7), md1, true, m4, n0, m11)] [adr4, inodenode(inodekey(m3), md0, true, 0, fs0[ri0[inodekey(m3)]].nsubdirs, fs0[ri0[inodekey(m3)]].size) ]), log-cons(log0, fs0), orphans-cons (fs0[adr1, dentrynode(dentrykey(m7, str), 0)][adr2, dentrynode(dentrykey(m7, str0), m)][adr3, inodenode(inodekey(m7), md1, true, m4, n0, m11)] [adr4, inodenode(inodekey(m3), md0, true, 0, fs0[ri0[inodekey(m3)]].nsubdirs, fs0[ri0[inodekey(m3)]].size) ], (ri0 -- dentrykey(m7, str))[dentrykey(m7, str0), adr2][inodekey(m7), adr3][inodekey(m3), adr4], orphans(fs0, ri0) ++ inodekey(m3)), orphans-cons(fs0, ri0, orphans(fs0, ri0)), replay-cons-strong (fs0[adr1, dentrynode(dentrykey(m7, str), 0)][adr2, dentrynode(dentrykey(m7, str0), m)][adr3, inodenode(inodekey(m7), md1, true, m4, n0, m11)] [adr4, inodenode(inodekey(m3), md0, true, 0, fs0[ri0[inodekey(m3)]].nsubdirs, fs0[ri0[inodekey(m3)]].size) ], (ri0 -- dentrykey(m7, str))[dentrykey(m7, str0), adr2][inodekey(m7), adr3][inodekey(m3), adr4], orphans(fs0, ri0) ++ inodekey(m3), fi, fo, (((log0 + adr1 ') + adr2 ') + adr3 ') + adr4 '), replay-cons-strong(fs0, ri0, orphans(fs0, ri0), fi, fo, log0), ri-cons(ri0, fs0), ri-inj((ri0 -- dentrykey(m7, str))[dentrykey(m7, str0), adr2][inodekey(m7), adr3][inodekey(m3), adr4]), ri-inj(ri0), ri-inj(fi), ubifs-cons (fs0[adr1, dentrynode(dentrykey(m7, str), 0)][adr2, dentrynode(dentrykey(m7, str0), m)][adr3, inodenode(inodekey(m7), md1, true, m4, n0, m11)] [adr4, inodenode(inodekey(m3), md0, true, 0, fs0[ri0[inodekey(m3)]].nsubdirs, fs0[ri0[inodekey(m3)]].size) ], (ri0 -- dentrykey(m7, str))[dentrykey(m7, str0), adr2][inodekey(m7), adr3][inodekey(m3), adr4], orphans(fs0, ri0) ++ inodekey(m3), fi, fo, (((log0 + adr1 ') + adr2 ') + adr3 ') + adr4 '), ubifs-cons(fs0, ri0, orphans(fs0, ri0), fi, fo, log0), ri0[dentrykey(m7, str)] ∈ fs0, ri0[inodekey(m7)] ∈ fs0, ri0[dentrykey(m7, str0)] ∈ fs0, inodekey(m7) ∈ ri0, dentrykey(m7, str0) ∈ ri0, dentrykey(m7, str) ∈ ri0, inodekey(m3) ∈ ri0, inodekey(m) ∈ ri0, 1 ≤ (m3 = m7 ⊃ mkdir(m11, md2, m4, n0, (abs-children(m7, fs0, ri0) -- str)[str0, m]) ;mkdir(fs0[ri0[inodekey(m3)]].size, fs0[ri0[inodekey(m3)]].meta, 1, fs0[ri0[inodekey(m3)]].nsubdirs, ∅) ) .nlink, ¬ adr4 ∈ (ri0 -- dentrykey(m7, str))[dentrykey(m7, str0), adr2][inodekey(m7), adr3], ¬ adr2 ∈ ri0 -- dentrykey(m7, str), ¬ adr4 ∈ fs0, ¬ adr3 ∈ fs0, ¬ adr2 ∈ fs0, ¬ adr1 ∈ fs0, ¬ adr3 ∈ (ri0 -- dentrykey(m7, str))[dentrykey(m7, str0), adr2], boolvar3 → boolvar4, links(m7, abs-dirs(fs0, ri0)) ≠ ∅ ∨ m7 = ROOT_INO, m4 ≠ 0 ∨ m7 = ROOT_INO ⊦ ⟨afs_inode_sync#(mkinode(m7, md1, true, m4, n0 + 1, m11 + 1); dirs, files); afs_inode_sync#(mkinode(m7, md1, true, m4, n0 + 1, m11 + 1); dirs, files); new_child_inode := mkinode(m3, md0, true, 1, fs0[ri0[inodekey(m3)]].nsubdirs, fs0[ri0[inodekey(m3)]].size); if true then {afs_inode_sync#(new_child_inode; dirs, files); new_child_inode := (new_child_inode.ino ∈ dirs ⊃ mkinode (new_child_inode.ino, dirs[new_child_inode.ino].meta, true, dirs[new_child_inode.ino].nlink, dirs[new_child_inode.ino].nsubdirs, dirs[new_child_inode.ino].size) ;mkinode (new_child_inode.ino, files[new_child_inode.ino].meta, false, files[new_child_inode.ino].nlink, 0, files[new_child_inode.ino].size) )}; old_inode := (m7 ∈ dirs ⊃ mkinode(m7, dirs[m7].meta, true, dirs[m7].nlink, dirs[m7].nsubdirs, dirs[m7].size) ;mkinode(m7, files[m7].meta, false, files[m7].nlink, 0, files[m7].size) ); new_inode := (m7 ∈ dirs ⊃ mkinode(m7, dirs[m7].meta, true, dirs[m7].nlink, dirs[m7].nsubdirs, dirs[m7].size) ;mkinode(m7, files[m7].meta, false, files[m7].nlink, 0, files[m7].size) ); err := ESUCCESS; asynced := ?⟩ ( afs-cons(dirs, files) → dirs = abs-dirs (fs0[adr1, dentrynode(dentrykey(m7, str), 0)][adr2, dentrynode(dentrykey(m7, str0), m)] [adr3, inodenode(inodekey(m7), md1, true, m4, n0, m11) ] [adr4, inodenode(inodekey(m3), md0, true, 0, fs0[ri0[inodekey(m3)]].nsubdirs, fs0[ri0[inodekey(m3)]].size) ], (ri0 -- dentrykey(m7, str))[dentrykey(m7, str0), adr2][inodekey(m7), adr3][inodekey(m3), adr4]) ∧ files = abs-files (fs0[adr1, dentrynode(dentrykey(m7, str), 0)][adr2, dentrynode(dentrykey(m7, str0), m)] [adr3, inodenode(inodekey(m7), md1, true, m4, n0, m11) ] [adr4, inodenode(inodekey(m3), md0, true, 0, fs0[ri0[inodekey(m3)]].nsubdirs, fs0[ri0[inodekey(m3)]].size) ], (ri0 -- dentrykey(m7, str))[dentrykey(m7, str0), adr2][inodekey(m7), adr3][inodekey(m3), adr4]) ∧ orphans (fs0[adr1, dentrynode(dentrykey(m7, str), 0)][adr2, dentrynode(dentrykey(m7, str0), m)] [adr3, inodenode(inodekey(m7), md1, true, m4, n0, m11) ] [adr4, inodenode(inodekey(m3), md0, true, 0, fs0[ri0[inodekey(m3)]].nsubdirs, fs0[ri0[inodekey(m3)]].size) ], (ri0 -- dentrykey(m7, str))[dentrykey(m7, str0), adr2][inodekey(m7), adr3][inodekey(m3), adr4]) = orphans(fs0, ri0) ++ inodekey(m3) ∧ (asynced → boolvar5) ∧ mkinode(m7, md1, true, m4, n0, m11) = old_inode ∧ mkinode(m7, md1, true, m4, n0, m11) = new_inode ∧ mkinode(m3, md0, true, 0, fs0[ri0[inodekey(m3)]].nsubdirs, fs0[ri0[inodekey(m3)]].size) = new_child_inode ∧ ESUCCESS = err), m4 = 0 ∧ m7 ≠ ROOT_INO

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 139:
(m3 = m7 ⊃ mkdir(m11, md2, m4, n0, (abs-children(m7, fs0, ri0) -- str)[str0, m]) ;mkdir(fs0[ri0[inodekey(m3)]].size, fs0[ri0[inodekey(m3)]].meta, 1, fs0[ri0[inodekey(m3)]].nsubdirs, ∅) ) .nlink = m0 + 1, 1 = fs0[ri0[inodekey(m3)]].nlink, fs0[ri0[inodekey(m7)]] = inodenode(key1, md2, true, m4, n0 + 1, m11 + 1), fs0[ri0[dentrykey(m7, str)]] = dentrynode(key2, m), fs0[ri0[dentrykey(m7, str0)]] = dentrynode(key0, m3), abs-children(m3, fs0, ri0) = ∅, dentrykeys(inodekey(m3), ri0) = ∅, dirs = abs-dirs(fs0, ri0)[m7, mkdir(m11, md2, m4, n0, (abs-children(m7, fs0, ri0) -- str)[str0, m])] [m3, (m3 = m7 ⊃ mkdir(m11, md2, m4, n0, (abs-children(m7, fs0, ri0) -- str)[str0, m]) ;mkdir(fs0[ri0[inodekey(m3)]].size, fs0[ri0[inodekey(m3)]].meta, 1, fs0[ri0[inodekey(m3)]].nsubdirs, ∅) ) .nlink:= m0 ], files = abs-files(fs0, ri0), links(m3, fs0, ri0) = ∅ ++ dentrykey(m7, str0), fs0[ri0[inodekey(m)]].directory, fs0[ri0[inodekey(m3)]].directory, fo.inodes?, orphans(fs0, ri0).inodes?, afs-cons(abs-dirs(fs0, ri0), abs-files(fs0, ri0)), file-node-cons(fs0, ri0), file-node-cons (fs0[adr1, dentrynode(dentrykey(m7, str), 0)][adr2, dentrynode(dentrykey(m7, str0), m)][adr3, inodenode(inodekey(m7), md1, true, m4, n0, m11)] [adr4, inodenode(inodekey(m3), md0, true, 0, fs0[ri0[inodekey(m3)]].nsubdirs, fs0[ri0[inodekey(m3)]].size) ], (ri0 -- dentrykey(m7, str))[dentrykey(m7, str0), adr2][inodekey(m7), adr3][inodekey(m3), adr4]), log-cons(log0, fs0), log-cons (log0, fs0[adr1, dentrynode(dentrykey(m7, str), 0)][adr2, dentrynode(dentrykey(m7, str0), m)][adr3, inodenode(inodekey(m7), md1, true, m4, n0, m11)] [adr4, inodenode(inodekey(m3), md0, true, 0, fs0[ri0[inodekey(m3)]].nsubdirs, fs0[ri0[inodekey(m3)]].size) ]), orphans-cons(fs0, ri0, orphans(fs0, ri0)), orphans-cons (fs0[adr1, dentrynode(dentrykey(m7, str), 0)][adr2, dentrynode(dentrykey(m7, str0), m)][adr3, inodenode(inodekey(m7), md1, true, m4, n0, m11)] [adr4, inodenode(inodekey(m3), md0, true, 0, fs0[ri0[inodekey(m3)]].nsubdirs, fs0[ri0[inodekey(m3)]].size) ], (ri0 -- dentrykey(m7, str))[dentrykey(m7, str0), adr2][inodekey(m7), adr3][inodekey(m3), adr4], orphans(fs0, ri0) ++ inodekey(m3)), replay-cons-strong(fs0, ri0, orphans(fs0, ri0), fi, fo, log0), replay-cons-strong (fs0[adr1, dentrynode(dentrykey(m7, str), 0)][adr2, dentrynode(dentrykey(m7, str0), m)][adr3, inodenode(inodekey(m7), md1, true, m4, n0, m11)] [adr4, inodenode(inodekey(m3), md0, true, 0, fs0[ri0[inodekey(m3)]].nsubdirs, fs0[ri0[inodekey(m3)]].size) ], (ri0 -- dentrykey(m7, str))[dentrykey(m7, str0), adr2][inodekey(m7), adr3][inodekey(m3), adr4], orphans(fs0, ri0) ++ inodekey(m3), fi, fo, (((log0 + adr1 ') + adr2 ') + adr3 ') + adr4 '), ri-cons(ri0, fs0), ri-inj(fi), ri-inj(ri0), ri-inj((ri0 -- dentrykey(m7, str))[dentrykey(m7, str0), adr2][inodekey(m7), adr3][inodekey(m3), adr4]), ubifs-cons(fs0, ri0, orphans(fs0, ri0), fi, fo, log0), ubifs-cons (fs0[adr1, dentrynode(dentrykey(m7, str), 0)][adr2, dentrynode(dentrykey(m7, str0), m)][adr3, inodenode(inodekey(m7), md1, true, m4, n0, m11)] [adr4, inodenode(inodekey(m3), md0, true, 0, fs0[ri0[inodekey(m3)]].nsubdirs, fs0[ri0[inodekey(m3)]].size) ], (ri0 -- dentrykey(m7, str))[dentrykey(m7, str0), adr2][inodekey(m7), adr3][inodekey(m3), adr4], orphans(fs0, ri0) ++ inodekey(m3), fi, fo, (((log0 + adr1 ') + adr2 ') + adr3 ') + adr4 '), inodekey(m) ∈ ri0, inodekey(m3) ∈ ri0, dentrykey(m7, str) ∈ ri0, dentrykey(m7, str0) ∈ ri0, inodekey(m7) ∈ ri0, ri0[dentrykey(m7, str0)] ∈ fs0, ri0[inodekey(m7)] ∈ fs0, ri0[dentrykey(m7, str)] ∈ fs0, 1 ≤ (m3 = m7 ⊃ mkdir(m11, md2, m4, n0, (abs-children(m7, fs0, ri0) -- str)[str0, m]) ;mkdir(fs0[ri0[inodekey(m3)]].size, fs0[ri0[inodekey(m3)]].meta, 1, fs0[ri0[inodekey(m3)]].nsubdirs, ∅) ) .nlink, boolvar3 → boolvar4, m4 ≠ 0 ∨ m7 = ROOT_INO, links(m7, abs-dirs(fs0, ri0)) ≠ ∅ ∨ m7 = ROOT_INO ⊦ ⟨afs_inode_sync#(mkinode(m7, md1, true, m4, n0 + 1, m11 + 1); dirs, files); afs_inode_sync#(mkinode(m7, md1, true, m4, n0 + 1, m11 + 1); dirs, files); new_child_inode := mkinode(m3, md0, true, 1, fs0[ri0[inodekey(m3)]].nsubdirs, fs0[ri0[inodekey(m3)]].size); if true then {afs_inode_sync#(new_child_inode; dirs, files); new_child_inode := (new_child_inode.ino ∈ dirs ⊃ mkinode (new_child_inode.ino, dirs[new_child_inode.ino].meta, true, dirs[new_child_inode.ino].nlink, dirs[new_child_inode.ino].nsubdirs, dirs[new_child_inode.ino].size) ;mkinode (new_child_inode.ino, files[new_child_inode.ino].meta, false, files[new_child_inode.ino].nlink, 0, files[new_child_inode.ino].size) )}; old_inode := (m7 ∈ dirs ⊃ mkinode(m7, dirs[m7].meta, true, dirs[m7].nlink, dirs[m7].nsubdirs, dirs[m7].size) ;mkinode(m7, files[m7].meta, false, files[m7].nlink, 0, files[m7].size) ); new_inode := (m7 ∈ dirs ⊃ mkinode(m7, dirs[m7].meta, true, dirs[m7].nlink, dirs[m7].nsubdirs, dirs[m7].size) ;mkinode(m7, files[m7].meta, false, files[m7].nlink, 0, files[m7].size) ); err := ESUCCESS; asynced := ?⟩ ( afs-cons(dirs, files) → dirs = abs-dirs (fs0[adr1, dentrynode(dentrykey(m7, str), 0)][adr2, dentrynode(dentrykey(m7, str0), m)] [adr3, inodenode(inodekey(m7), md1, true, m4, n0, m11) ] [adr4, inodenode(inodekey(m3), md0, true, 0, fs0[ri0[inodekey(m3)]].nsubdirs, fs0[ri0[inodekey(m3)]].size) ], (ri0 -- dentrykey(m7, str))[dentrykey(m7, str0), adr2][inodekey(m7), adr3][inodekey(m3), adr4]) ∧ files = abs-files (fs0[adr1, dentrynode(dentrykey(m7, str), 0)][adr2, dentrynode(dentrykey(m7, str0), m)] [adr3, inodenode(inodekey(m7), md1, true, m4, n0, m11) ] [adr4, inodenode(inodekey(m3), md0, true, 0, fs0[ri0[inodekey(m3)]].nsubdirs, fs0[ri0[inodekey(m3)]].size) ], (ri0 -- dentrykey(m7, str))[dentrykey(m7, str0), adr2][inodekey(m7), adr3][inodekey(m3), adr4]) ∧ orphans (fs0[adr1, dentrynode(dentrykey(m7, str), 0)][adr2, dentrynode(dentrykey(m7, str0), m)] [adr3, inodenode(inodekey(m7), md1, true, m4, n0, m11) ] [adr4, inodenode(inodekey(m3), md0, true, 0, fs0[ri0[inodekey(m3)]].nsubdirs, fs0[ri0[inodekey(m3)]].size) ], (ri0 -- dentrykey(m7, str))[dentrykey(m7, str0), adr2][inodekey(m7), adr3][inodekey(m3), adr4]) = orphans(fs0, ri0) ++ inodekey(m3) ∧ (asynced → boolvar5) ∧ mkinode(m7, md1, true, m4, n0, m11) = old_inode ∧ mkinode(m7, md1, true, m4, n0, m11) = new_inode ∧ mkinode(m3, md0, true, 0, fs0[ri0[inodekey(m3)]].nsubdirs, fs0[ri0[inodekey(m3)]].size) = new_child_inode ∧ ESUCCESS = err), (m3 = m7 ⊃ mkdir(m11, md2, m4, n0, (abs-children(m7, fs0, ri0) -- str)[str0, m]) ;mkdir(fs0[ri0[inodekey(m3)]].size, fs0[ri0[inodekey(m3)]].meta, 1, fs0[ri0[inodekey(m3)]].nsubdirs, ∅) ) .nlink = 0, adr1 = adr2, adr1 = adr3, adr1 = adr4, adr2 = adr3, adr2 = adr4, adr3 = adr4, m3 = ROOT_INO, m3 = 0, m7 = 0, mkdentry(str, m) = mkdentry(str0, m3), adr4 ∈ (ri0 -- dentrykey(m7, str))[dentrykey(m7, str0), adr2][inodekey(m7), adr3], adr2 ∈ ri0 -- dentrykey(m7, str), adr4 ∈ fs0, adr3 ∈ fs0, adr2 ∈ fs0, adr1 ∈ fs0, adr3 ∈ (ri0 -- dentrykey(m7, str))[dentrykey(m7, str0), adr2], m4 = 0 ∧ m7 ≠ ROOT_INO

Rule argument

spec: nat name: elim-pred-c seq: n ≠ 0 ⊦ m = n - 1 ↔ n = m + 1 subst: [n, m] → [(m3 = m7 ⊃ mkdir (m11, md2, m4, n0, (abs-children(m7, fs0, ri0) -- str)[str0, m]) ;mkdir (fs0[ri0[inodekey(m3)]].size, fs0[ri0[inodekey(m3)]].meta, 1, fs0[ri0[inodekey(m3)]].nsubdirs, ∅) ) .nlink, m0]

Additional information

Used simplifier rules: n ≠ 0 ⊦ m = n - 1 ↔ n = m + 1; (elim) Used terms: (m3 = m7 ⊃ mkdir (m11, md2, m4, n0, (abs-children(m7, fs0, ri0) -- str)[str0, m]) ;mkdir (fs0[ri0[inodekey(m3)]].size, fs0[ri0[inodekey(m3)]].meta, 1, fs0[ri0[inodekey(m3)]].nsubdirs, ∅) ) .nlink, m0