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Proof step 235 from proof refine-rename-new-keep-parent (previous step)

boolvar ↔ false, boolvar0 ↔ false, fs0[ri0[inodekey(m3)]] = inodenode(key0, md1, true, m4, m5, m6), fs0[ri0[dentrykey(m3, str)]] = dentrynode(key1, m), dirs = dirs0[old_ino, dirs0[old_ino].size:= (dirs0[old_ino].size - 1)], dirs0 = abs-dirs(fs0, ri0)[old_ino, abs-dirs(fs0, ri0)[old_ino].entries:= (abs-dirs(fs0, ri0)[old_ino].entries -- str)], new_ino = m3, old_dent = mkdentry(str, m), old_ino = m3, old_dent.dentry?, 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(m3, str), 0)][adr2, dentrynode(dentrykey(m3, str0), m)][adr3, inodenode(inodekey(m3), md0, true, m4, m5, m6)], (ri0 -- dentrykey(m3, str))[dentrykey(m3, str0), adr2][inodekey(m3), adr3]), log-cons(log0, fs0), log-cons (log0, fs0[adr1, dentrynode(dentrykey(m3, str), 0)][adr2, dentrynode(dentrykey(m3, str0), m)][adr3, inodenode(inodekey(m3), md0, true, m4, m5, m6)]), orphans-cons(fs0, ri0, orphans(fs0, ri0)), orphans-cons (fs0[adr1, dentrynode(dentrykey(m3, str), 0)][adr2, dentrynode(dentrykey(m3, str0), m)][adr3, inodenode(inodekey(m3), md0, true, m4, m5, m6)], (ri0 -- dentrykey(m3, str))[dentrykey(m3, str0), adr2][inodekey(m3), adr3], orphans(fs0, ri0)), replay-cons-strong(fs0, ri0, orphans(fs0, ri0), fi, fo, log0), replay-cons-strong (fs0[adr1, dentrynode(dentrykey(m3, str), 0)][adr2, dentrynode(dentrykey(m3, str0), m)][adr3, inodenode(inodekey(m3), md0, true, m4, m5, m6)], (ri0 -- dentrykey(m3, str))[dentrykey(m3, str0), adr2][inodekey(m3), adr3], orphans(fs0, ri0), fi, fo, ((log0 + adr1 ') + adr2 ') + adr3 '), ri-inj(fi), ri-inj(ri0), ri-inj((ri0 -- dentrykey(m3, str))[dentrykey(m3, str0), adr2][inodekey(m3), adr3]), ubifs-cons(fs0, ri0, orphans(fs0, ri0), fi, fo, log0), ubifs-cons (fs0[adr1, dentrynode(dentrykey(m3, str), 0)][adr2, dentrynode(dentrykey(m3, str0), m)][adr3, inodenode(inodekey(m3), md0, true, m4, m5, m6)], (ri0 -- dentrykey(m3, str))[dentrykey(m3, str0), adr2][inodekey(m3), adr3], orphans(fs0, ri0), fi, fo, ((log0 + adr1 ') + adr2 ') + adr3 '), ri0[dentrykey(m3, str)] ∈ fs0, ri0[inodekey(m3)] ∈ fs0, inodekey(m3) ∈ ri0, dentrykey(m3, str) ∈ ri0, inodekey(m) ∈ ri0, old_dent.ino ∈ dirs, 1 ≤ m6, dirs0[old_ino].size ≥ 1, boolvar3 → boolvar4, boolvar1 → 1 ≤ m5, fs0[ri0[inodekey(m)]].directory ∧ m0 = fs0[ri0[inodekey(m)]].nlink ∧ m2 = fs0[ri0[inodekey(m)]].size ∧ m1 = fs0[ri0[inodekey(m)]].nsubdirs ∧ boolvar1 ∨ ¬ fs0[ri0[inodekey(m)]].directory ∧ m0 = fs0[ri0[inodekey(m)]].nlink ∧ m1 = 0 ∧ ¬ boolvar1, ¬ fs0[ri0[inodekey(m)]].directory ∧ ¬ boolvar1 ∧ m0 = fs0[ri0[inodekey(m)]].nlink ∧ m1 = fs0[ri0[inodekey(m)]].nsubdirs ∨ fs0[ri0[inodekey(m)]].directory ∧ boolvar1 ∧ m0 = fs0[ri0[inodekey(m)]].nlink ∧ m1 = fs0[ri0[inodekey(m)]].nsubdirs ∧ m2 = fs0[ri0[inodekey(m)]].size, links(m3, abs-dirs(fs0, ri0)) ≠ ∅ ∨ m3 = ROOT_INO, m4 ≠ 0 ∨ m3 = ROOT_INO ⊦ adr1 = adr2, adr1 = adr3, adr2 = adr3, m3 = 0, m6 = 0, adr2 ∈ ri0 -- dentrykey(m3, str), adr3 ∈ fs0, adr2 ∈ fs0, adr1 ∈ fs0, dentrykey(m3, str0) ∈ ri0, adr3 ∈ (ri0 -- dentrykey(m3, str))[dentrykey(m3, str0), adr2], dirs[old_ino].nsubdirs ≥ 1, m4 = 0 ∧ m3 ≠ ROOT_INO

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 236:
abs-dirs(fs0, ri0)[m3].nsubdirs = 0, fs0[ri0[inodekey(m3)]] = inodenode(key0, md1, true, m4, m5, m6), fs0[ri0[dentrykey(m3, str)]] = dentrynode(key1, m), fs0[ri0[inodekey(m)]].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(m3, str), 0)][adr2, dentrynode(dentrykey(m3, str0), m)][adr3, inodenode(inodekey(m3), md0, true, m4, m5, m6)], (ri0 -- dentrykey(m3, str))[dentrykey(m3, str0), adr2][inodekey(m3), adr3]), log-cons(log0, fs0), log-cons (log0, fs0[adr1, dentrynode(dentrykey(m3, str), 0)][adr2, dentrynode(dentrykey(m3, str0), m)][adr3, inodenode(inodekey(m3), md0, true, m4, m5, m6)]), orphans-cons(fs0, ri0, orphans(fs0, ri0)), orphans-cons (fs0[adr1, dentrynode(dentrykey(m3, str), 0)][adr2, dentrynode(dentrykey(m3, str0), m)][adr3, inodenode(inodekey(m3), md0, true, m4, m5, m6)], (ri0 -- dentrykey(m3, str))[dentrykey(m3, str0), adr2][inodekey(m3), adr3], orphans(fs0, ri0)), replay-cons-strong(fs0, ri0, orphans(fs0, ri0), fi, fo, log0), replay-cons-strong (fs0[adr1, dentrynode(dentrykey(m3, str), 0)][adr2, dentrynode(dentrykey(m3, str0), m)][adr3, inodenode(inodekey(m3), md0, true, m4, m5, m6)], (ri0 -- dentrykey(m3, str))[dentrykey(m3, str0), adr2][inodekey(m3), adr3], orphans(fs0, ri0), fi, fo, ((log0 + adr1 ') + adr2 ') + adr3 '), ri-inj(fi), ri-inj(ri0), ri-inj((ri0 -- dentrykey(m3, str))[dentrykey(m3, str0), adr2][inodekey(m3), adr3]), ubifs-cons(fs0, ri0, orphans(fs0, ri0), fi, fo, log0), ubifs-cons (fs0[adr1, dentrynode(dentrykey(m3, str), 0)][adr2, dentrynode(dentrykey(m3, str0), m)][adr3, inodenode(inodekey(m3), md0, true, m4, m5, m6)], (ri0 -- dentrykey(m3, str))[dentrykey(m3, str0), adr2][inodekey(m3), adr3], orphans(fs0, ri0), fi, fo, ((log0 + adr1 ') + adr2 ') + adr3 '), ri0[dentrykey(m3, str)] ∈ fs0, ri0[inodekey(m3)] ∈ fs0, inodekey(m3) ∈ ri0, dentrykey(m3, str) ∈ ri0, inodekey(m) ∈ ri0, 1 ≤ m5, 1 ≤ m6, boolvar3 → boolvar4, links(m3, abs-dirs(fs0, ri0)) ≠ ∅ ∨ m3 = ROOT_INO, m4 ≠ 0 ∨ m3 = ROOT_INO ⊦ adr1 = adr2, adr1 = adr3, adr2 = adr3, m3 = 0, m5 = 0, m6 = 0, adr2 ∈ ri0 -- dentrykey(m3, str), adr3 ∈ fs0, adr2 ∈ fs0, adr1 ∈ fs0, dentrykey(m3, str0) ∈ ri0, adr3 ∈ (ri0 -- dentrykey(m3, str))[dentrykey(m3, str0), adr2], m4 = 0 ∧ m3 ≠ ROOT_INO

Rule argument

Additional information

Used simplifier rules: ⊦ mkdir(m, md, m0, m1, entries).size = m; (s)% ⊦ inodenode(key, md, boolvar, m, m0, m1).nsubdirs = m0; (s)% ⊦ inodenode(key, md, boolvar, m, m0, m1).nlink = m; (s)% ⊦ inodenode(key, md, boolvar, m, m0, m1).meta = md; (s)% ⊦ inodenode(key, md, boolvar, m, m0, m1).size = m1; (s)% ⊦ inodenode(key, md, boolvar, m, m0, m1).directory ↔ boolvar; (s)%not-zero: 0 < n ⊦ (* n) ≤ m → m ≠ 0; (forward) from specification nat% ⊦ m < 1 ↔ m = 0; (s)% ⊦ m ≤ n ↔ ¬ n < m; (ss)% ⊦ (ad.entries:= entries).nsubdirs = ad.nsubdirs; (s)% ⊦ (ad.size:= m).nsubdirs = ad.nsubdirs; (s)% ⊦ (ad.entries:= entries).size = ad.size; (s)%⊦ dentrykey(ino, str) ∈ ri ∧ ubifs-cons(fs, ri, ro, fi, fo, log) → fs[ri[inodekey(ino)]].directory; (ss)% ⊦ mkdentry(str, m).dentry?; (s)% ⊦ ino ∈ dirs[ino0, ad] ↔ ino ∈ dirs; (s)% ⊦ dirs[ino, ad][ino, ad0] = dirs[ino, ad0]; (s)% ⊦ mkdentry(str, m).ino = m; (s)% ⊦ n ≥ m ↔ m ≤ n; (s)%⊦ mkdir(m, md, m0, m1, entries).entries:= entries0 = mkdir(m, md, m0, m1, entries0); (s)% ⊦ mkdir(m, md, m0, m1, entries).entries = entries; (s)%⊦ abs-dir(ino, fs, ri) = mkdir (fs[ri[inodekey(ino)]].size, fs[ri[inodekey(ino)]].meta, fs[ri[inodekey(ino)]].nlink, fs[ri[inodekey(ino)]].nsubdirs, abs-children(ino, fs, ri)); (s)%⊦ inodekey(ino) ∈ ri ∧ fs[ri[inodekey(ino)]].directory → abs-dirs(fs, ri)[ino] = abs-dir(ino, fs, ri); (s)%⊦ ino ∈ abs-dirs(fs, ri) ↔ inodekey(ino) ∈ ri ∧ fs[ri[inodekey(ino)]].directory; (s)% ⊦ dirs[ino, ad][ino0] = (ino0 = ino ∧ ino ∈ dirs ⊃ ad;dirs[ino0]); (s)