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Proof step 303 from proof inv-rename-overwrite-keep-parent (previous step)

¬ boolvar1 ↔ ¬ boolvar0, fs0[ri0[inodekey(m1)]] = inodenode(key3, md3, boolvar1, m8 + 1, m11, m12), fs0[ri0[dentrykey(m, str0)]] = dentrynode(key4, m1), fs0[ri0[dentrykey(m, str)]] = dentrynode(key0, m2), fs0[ri0[inodekey(m2)]] = inodenode(key1, md0, boolvar0, m5, m9, m10), fs0[ri0[inodekey(m)]] = inodenode(key2, md2, true, m4, n0 + (boolvar3 ⊃ 1;0), m0 + 1), adr = adr4, fs = fs0[adr1, dentrynode(dentrykey(m, str), 0)][adr2, dentrynode(dentrykey(m, str0), m2)][adr3, inodenode(inodekey(m), md, true, m4, n0, m0)] [adr4, inodenode(inodekey(m1), md1, boolvar2, m8, m11, m6) ], fs1 = fs0[adr1, dentrynode(dentrykey(m, str), 0)][adr2, dentrynode(dentrykey(m, str0), m2)][adr3, inodenode(inodekey(m), md, true, m4, n0, m0)] [adr4, inodenode(inodekey(m1), md1, boolvar2, m8, m11, m6) ], key = inodekey(m1), log = (((log0 + adr1 ') + adr2 ') + adr3 ') + adr4 ', log1 = (((log0 + adr1 ') + adr2 ') + adr3 ') + adr4 ', nd = inodenode(inodekey(m1), md1, boolvar2, m8, m11, m6), ri = ri1[key, adr], ri1 = (ri0 -- dentrykey(m, str))[dentrykey(m, str0), adr2][inodekey(m), adr3], mkdentry(str, m2).dentry?, inodenode(inodekey(m), md, true, m4, n0, m0).inode?, nd.inode?, fo.inodes?, ro.inodes?, file-node-cons(fs0, ri0), key-cons(key, fs1[adr]), log-cons(log0, fs0), orphans-cons(fs0, ri0, ro), replay-cons-strong(fs0, ri0, ro, fi, fo, log0), ri-cons(ri0, fs0), ri-inj(fi), ri-inj(ri0), ubifs-cons(fs0, ri0, ro, fi, fo, log0), dentrykey(m, str) ∈ ri0, inodekey(m2) ∈ ri0, dentrykey(m, str0) ∈ ri0, inodekey(m1) ∈ ri0, ri0[dentrykey(m, str)] ∈ fs0, ri0[inodekey(m2)] ∈ fs0, inodekey(m) ∈ ri0, ri0[dentrykey(m, str0)] ∈ fs0, ri0[inodekey(m1)] ∈ fs0, ri0[inodekey(m)] ∈ fs0, adr ∈ fs1, m8 = 0 → links(m1, fs0, ri0) = ∅ ++ dentrykey(m, str0), boolvar1 → dentrykeys(inodekey(m1), ri0) = ∅, ¬ adr ∈ ri1 → adr ∈ fs1 → adr ∈ fs1, inodenode(inodekey(m), md, true, m4, n0, m0).trunc? ∨ inodenode(inodekey(m), md, true, m4, n0, m0).inode?, m4 ≠ 0 ∨ m = ROOT_INO, ¬ boolvar0 ∧ ¬ boolvar3 ∨ boolvar0 ∧ boolvar3 ∧ m3 = m10, ¬ boolvar0 ∧ ¬ boolvar2 ∨ boolvar1 ∧ boolvar2 ∧ m6 = m12 ⊦ ⟪new_child_inode := mkinode(m1, 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)), nd.nlink = 0, adr1 = adr2, adr1 = adr3, adr1 = adr4, adr2 = adr3, adr2 = adr4, adr3 = adr4, m = 0, m1 = ROOT_INO, m1 = 0, mkdentry(str, m2) = mkdentry(str0, m1), adr ∈ ri1, adr2 ∈ ri0 -- dentrykey(m, str), adr4 ∈ fs0, adr3 ∈ fs0, adr2 ∈ fs0, adr1 ∈ fs0, inodekey(m) ∈ ro, adr3 ∈ (ri0 -- dentrykey(m, str))[dentrykey(m, str0), adr2]

Heuristic symbolic execution applied rule assign right

And obtained the following new goals

Proof step 304:
¬ boolvar1 ↔ ¬ boolvar0, fs0[ri0[inodekey(m)]] = inodenode(key2, md2, true, m4, n0 + (boolvar3 ⊃ 1;0), m0 + 1), fs0[ri0[inodekey(m2)]] = inodenode(key1, md0, boolvar0, m5, m9, m10), fs0[ri0[dentrykey(m, str)]] = dentrynode(key0, m2), fs0[ri0[dentrykey(m, str0)]] = dentrynode(key4, m1), fs0[ri0[inodekey(m1)]] = inodenode(key3, md3, boolvar1, m8 + 1, m11, m12), adr = adr4, fs = fs0[adr1, dentrynode(dentrykey(m, str), 0)][adr2, dentrynode(dentrykey(m, str0), m2)][adr3, inodenode(inodekey(m), md, true, m4, n0, m0)] [adr4, inodenode(inodekey(m1), md1, boolvar2, m8, m11, m6) ], fs1 = fs0[adr1, dentrynode(dentrykey(m, str), 0)][adr2, dentrynode(dentrykey(m, str0), m2)][adr3, inodenode(inodekey(m), md, true, m4, n0, m0)] [adr4, inodenode(inodekey(m1), md1, boolvar2, m8, m11, m6) ], key = inodekey(m1), log = (((log0 + adr1 ') + adr2 ') + adr3 ') + adr4 ', log1 = (((log0 + adr1 ') + adr2 ') + adr3 ') + adr4 ', nd = inodenode(inodekey(m1), md1, boolvar2, m8, m11, m6), ri = ri1[key, adr], ri1 = (ri0 -- dentrykey(m, str))[dentrykey(m, str0), adr2][inodekey(m), adr3], mkdentry(str, m2).dentry?, nd.inode?, inodenode(inodekey(m), md, true, m4, n0, m0).inode?, ro.inodes?, fo.inodes?, file-node-cons(fs0, ri0), key-cons(key, fs1[adr]), log-cons(log0, fs0), orphans-cons(fs0, ri0, ro), replay-cons-strong(fs0, ri0, ro, fi, fo, log0), ri-cons(ri0, fs0), ri-inj(ri0), ri-inj(fi), ubifs-cons(fs0, ri0, ro, fi, fo, log0), adr ∈ fs1, ri0[inodekey(m)] ∈ fs0, ri0[inodekey(m1)] ∈ fs0, ri0[dentrykey(m, str0)] ∈ fs0, inodekey(m) ∈ ri0, ri0[inodekey(m2)] ∈ fs0, ri0[dentrykey(m, str)] ∈ fs0, inodekey(m1) ∈ ri0, dentrykey(m, str0) ∈ ri0, inodekey(m2) ∈ ri0, dentrykey(m, str) ∈ ri0, ¬ adr ∈ ri1 → adr ∈ fs1 → adr ∈ fs1, boolvar1 → dentrykeys(inodekey(m1), ri0) = ∅, m8 = 0 → links(m1, fs0, ri0) = ∅ ++ dentrykey(m, str0), nd.trunc? ∨ nd.inode?, ¬ boolvar0 ∧ ¬ boolvar2 ∨ boolvar1 ∧ boolvar2 ∧ m6 = m12, ¬ boolvar0 ∧ ¬ boolvar3 ∨ boolvar0 ∧ boolvar3 ∧ m3 = m10, m4 ≠ 0 ∨ m = ROOT_INO, inodenode(inodekey(m), md, true, m4, n0, m0).trunc? ∨ inodenode(inodekey(m), md, true, m4, n0, m0).inode? ⊦ nd.nlink = 0, adr1 = adr4, adr1 = adr3, adr1 = adr2, adr2 = adr4, adr2 = adr3, adr3 = adr4, m = 0, m1 = 0, m1 = ROOT_INO, mkdentry(str, m2) = mkdentry(str0, m1), adr3 ∈ (ri0 -- dentrykey(m, str))[dentrykey(m, str0), adr2], inodekey(m) ∈ ro, adr1 ∈ fs0, adr2 ∈ fs0, adr3 ∈ fs0, adr4 ∈ fs0, adr2 ∈ ri0 -- dentrykey(m, str), adr ∈ ri1, 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)

Rule argument

Additional information

Used simplifier rules: at-fs: ⊦ fs[adr0, nd][adr1] = (adr0 = adr1 ⊃ nd;fs[adr1]);% ⊦ inodenode(key, md, boolvar, m, m0, m1).nlink = m; (s)% ⊦ adr ∈ fs[adr1, nd] ↔ adr = adr1 ∨ adr ∈ fs; (s)%⊦ key-cons(inodekey(ino), nd) ↔ nd.inode? ∧ nd.key = inodekey(ino) ∧ ino ≠ 0; (s)% ⊦ inodenode(key, md, boolvar, m, m0, m1).inode?; (s)% ⊦ inodenode(key, md, boolvar, m, m0, m1).key = key; (s)% ⊦ inodekey(m) = inodekey(m0) ↔ m = m0; (s)% ⊦ mkdentry(str, m).dentry?; (s)% ⊦ ¬ inodenode(key, md, boolvar, m, m0, m1).trunc?; (s)