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Proof step 42 from proof inv-rename-overwrite-keep-parent (previous step)

m0 + 1 = fs[ri[inodekey(m)]].size, ¬ fs[ri[inodekey(fs[ri[dentrykey(m, str0)]].ino)]].directory ↔ ¬ fs[ri[inodekey(fs[ri[dentrykey(m, str)]].ino)]].directory, key = inodekey(fs[ri[dentrykey(m, str0)]].ino), m1 = fs[ri[inodekey(m)]].nlink, m2 = fs[ri[inodekey(m)]].nsubdirs, m4 = fs[ri[dentrykey(m, str0)]].ino, m5 = fs[ri[inodekey(fs[ri[dentrykey(m, str0)]].ino)]].nlink, m5 = m8 + 1, m7 = fs[ri[inodekey(fs[ri[dentrykey(m, str0)]].ino)]].nsubdirs, new_dent = mkdentry(str0, fs[ri[dentrykey(m, str0)]].ino), old_dent = mkdentry(str, fs[ri[dentrykey(m, str)]].ino), fs[ri[dentrykey(m, str)]].dentry?, fs[ri[inodekey(m)]].directory, fs[ri[inodekey(fs[ri[dentrykey(m, str)]].ino)]].inode?, ro.inodes?, fo.inodes?, file-node-cons(fs, ri), log-cons(log, fs), orphans-cons(fs, ri, ro), replay-cons-strong(fs, ri, ro, fi, fo, log), ri-inj(ri), ri-inj(fi), ubifs-cons(fs, ri, ro, fi, fo, log), ri[inodekey(fs[ri[dentrykey(m, str)]].ino)] ∈ fs, ri[dentrykey(m, str)] ∈ fs, inodekey(m) ∈ ri, inodekey(fs[ri[dentrykey(m, str0)]].ino) ∈ ri, dentrykey(m, str0) ∈ ri, inodekey(fs[ri[dentrykey(m, str)]].ino) ∈ ri, dentrykey(m, str) ∈ ri, 1 ≤ fs[ri[inodekey(fs[ri[dentrykey(m, str0)]].ino)]].nlink, (boolvar3 ⊃ 1;0) ≤ fs[ri[inodekey(m)]].nsubdirs, fs[ri[inodekey(fs[ri[dentrykey(m, str0)]].ino)]].directory → dentrykeys(inodekey(fs[ri[dentrykey(m, str0)]].ino), ri) = ∅, fs[ri[inodekey(fs[ri[dentrykey(m, str0)]].ino)]].nlink = 1 → links(fs[ri[dentrykey(m, str0)]].ino, fs, ri) = ∅ ++ dentrykey(m, str0), boolvar3 → 1 ≤ fs[ri[inodekey(m)]].nsubdirs, ¬ fs[ri[inodekey(fs[ri[dentrykey(m, str)]].ino)]].directory ∧ ¬ boolvar2 ∨ fs[ri[inodekey(fs[ri[dentrykey(m, str0)]].ino)]].directory ∧ boolvar2 ∧ m6 = fs[ri[inodekey(fs[ri[dentrykey(m, str0)]].ino)]].size, ¬ fs[ri[inodekey(fs[ri[dentrykey(m, str)]].ino)]].directory ∧ ¬ boolvar3 ∨ fs[ri[inodekey(fs[ri[dentrykey(m, str)]].ino)]].directory ∧ boolvar3 ∧ m3 = fs[ri[inodekey(fs[ri[dentrykey(m, str)]].ino)]].size, fs[ri[inodekey(m)]].nlink ≠ 0 ∨ m = ROOT_INO ⊦ ⟪aubifs_core_journal_add4# (dentrynode(dentrykey(m, old_dent.name), 0), dentrynode(dentrykey(m, new_dent.name), old_dent.ino), inodenode(inodekey(m), md, true, m1, m2 - (boolvar3 ⊃ 1;0), m0), inodenode(key, md1, boolvar2, m8, m7, m6), ri, fi, ro, fo ; adr2, adr1, adr0, adr, fs, log ; boolvar0, err); if err = ESUCCESS then {aubifs_core_index_remove#(dentrykey(m, old_dent.name), fi, ro, fo, fs, log, boolvar0; ri); aubifs_core_index_store#(dentrykey(m, new_dent.name), adr1, fi, ro, fo, fs, log, boolvar0; ri); aubifs_core_index_store#(inodekey(m), adr0, fi, ro, fo, fs, log, boolvar0; ri); aubifs_core_index_store#(key, adr, fi, ro, fo, fs, log, boolvar0; ri); nd := inodenode(key, md1, boolvar2, m8, m7, m6); if nd.nlink = 0 then aubifs_core_orphans_insert#(key, ri, fi, fo, fs, log, boolvar0; ro); new_dent := mkdentry(new_dent.name, old_dent.ino); old_dent := negdentry(old_dent.name); parent_inode0 := mkinode (m, inodenode(inodekey(m), md, true, m1, m2 - (boolvar3 ⊃ 1;0), m0).meta, inodenode(inodekey(m), md, true, m1, m2 - (boolvar3 ⊃ 1;0), m0).directory, inodenode(inodekey(m), md, true, m1, m2 - (boolvar3 ⊃ 1;0), m0).nlink, inodenode(inodekey(m), md, true, m1, m2 - (boolvar3 ⊃ 1;0), m0).nsubdirs, inodenode(inodekey(m), md, true, m1, m2 - (boolvar3 ⊃ 1;0), m0).size); new_child_inode := mkinode(m4, 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)), fs[ri[dentrykey(m, str0)]].ino = ROOT_INO, fs[ri[inodekey(fs[ri[dentrykey(m, str0)]].ino)]].nlink = 0, m5 = 0, mkdentry(str, fs[ri[dentrykey(m, str)]].ino) = mkdentry(str0, fs[ri[dentrykey(m, str0)]].ino), inodekey(m) ∈ ro

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 43:
m0 + 1 = fs[ri[inodekey(m)]].size, m8 + 1 = fs[ri[inodekey(fs[ri[dentrykey(m, str0)]].ino)]].nlink, ¬ fs[ri[inodekey(fs[ri[dentrykey(m, str0)]].ino)]].directory ↔ ¬ fs[ri[inodekey(fs[ri[dentrykey(m, str)]].ino)]].directory, key = inodekey(fs[ri[dentrykey(m, str0)]].ino), m1 = fs[ri[inodekey(m)]].nlink, m2 = fs[ri[inodekey(m)]].nsubdirs, m4 = fs[ri[dentrykey(m, str0)]].ino, m7 = fs[ri[inodekey(fs[ri[dentrykey(m, str0)]].ino)]].nsubdirs, new_dent = mkdentry(str0, fs[ri[dentrykey(m, str0)]].ino), old_dent = mkdentry(str, fs[ri[dentrykey(m, str)]].ino), fs[ri[dentrykey(m, str0)]].ino ≠ ROOT_INO, mkdentry(str, fs[ri[dentrykey(m, str)]].ino) ≠ mkdentry(str0, fs[ri[dentrykey(m, str0)]].ino), fs[ri[dentrykey(m, str)]].dentry?, fs[ri[inodekey(m)]].directory, fs[ri[inodekey(fs[ri[dentrykey(m, str)]].ino)]].inode?, ro.inodes?, fo.inodes?, file-node-cons(fs, ri), log-cons(log, fs), orphans-cons(fs, ri, ro), replay-cons-strong(fs, ri, ro, fi, fo, log), ri-inj(ri), ri-inj(fi), ubifs-cons(fs, ri, ro, fi, fo, log), ri[inodekey(fs[ri[dentrykey(m, str)]].ino)] ∈ fs, ri[dentrykey(m, str)] ∈ fs, inodekey(m) ∈ ri, inodekey(fs[ri[dentrykey(m, str0)]].ino) ∈ ri, dentrykey(m, str0) ∈ ri, inodekey(fs[ri[dentrykey(m, str)]].ino) ∈ ri, dentrykey(m, str) ∈ ri, (boolvar3 ⊃ 1;0) ≤ fs[ri[inodekey(m)]].nsubdirs, ¬ inodekey(m) ∈ ro, fs[ri[inodekey(fs[ri[dentrykey(m, str0)]].ino)]].directory → dentrykeys(inodekey(fs[ri[dentrykey(m, str0)]].ino), ri) = ∅, boolvar3 → 1 ≤ fs[ri[inodekey(m)]].nsubdirs, m8 = 0 → links(fs[ri[dentrykey(m, str0)]].ino, fs, ri) = ∅ ++ dentrykey(m, str0), ¬ fs[ri[inodekey(fs[ri[dentrykey(m, str)]].ino)]].directory ∧ ¬ boolvar2 ∨ fs[ri[inodekey(fs[ri[dentrykey(m, str0)]].ino)]].directory ∧ boolvar2 ∧ m6 = fs[ri[inodekey(fs[ri[dentrykey(m, str0)]].ino)]].size, ¬ fs[ri[inodekey(fs[ri[dentrykey(m, str)]].ino)]].directory ∧ ¬ boolvar3 ∨ fs[ri[inodekey(fs[ri[dentrykey(m, str)]].ino)]].directory ∧ boolvar3 ∧ m3 = fs[ri[inodekey(fs[ri[dentrykey(m, str)]].ino)]].size, fs[ri[inodekey(m)]].nlink ≠ 0 ∨ m = ROOT_INO ⊦ ⟪aubifs_core_journal_add4# (dentrynode(dentrykey(m, old_dent.name), 0), dentrynode(dentrykey(m, new_dent.name), old_dent.ino), inodenode(inodekey(m), md, true, m1, m2 - (boolvar3 ⊃ 1;0), m0), inodenode(key, md1, boolvar2, m8, m7, m6), ri, fi, ro, fo ; adr2, adr1, adr0, adr, fs, log ; boolvar0, err); if err = ESUCCESS then {aubifs_core_index_remove#(dentrykey(m, old_dent.name), fi, ro, fo, fs, log, boolvar0; ri); aubifs_core_index_store#(dentrykey(m, new_dent.name), adr1, fi, ro, fo, fs, log, boolvar0; ri); aubifs_core_index_store#(inodekey(m), adr0, fi, ro, fo, fs, log, boolvar0; ri); aubifs_core_index_store#(key, adr, fi, ro, fo, fs, log, boolvar0; ri); nd := inodenode(key, md1, boolvar2, m8, m7, m6); if nd.nlink = 0 then aubifs_core_orphans_insert#(key, ri, fi, fo, fs, log, boolvar0; ro); new_dent := mkdentry(new_dent.name, old_dent.ino); old_dent := negdentry(old_dent.name); parent_inode0 := mkinode (m, inodenode(inodekey(m), md, true, m1, m2 - (boolvar3 ⊃ 1;0), m0).meta, inodenode(inodekey(m), md, true, m1, m2 - (boolvar3 ⊃ 1;0), m0).directory, inodenode(inodekey(m), md, true, m1, m2 - (boolvar3 ⊃ 1;0), m0).nlink, inodenode(inodekey(m), md, true, m1, m2 - (boolvar3 ⊃ 1;0), m0).nsubdirs, inodenode(inodekey(m), md, true, m1, m2 - (boolvar3 ⊃ 1;0), m0).size); new_child_inode := mkinode(m4, 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))

Rule argument

Additional information

Used simplifier rules: ⊦ 1 = m + 1 ↔ m = 0; (s)% ⊦ m ≤ m + n; (s)%not-zero: 0 < n ⊦ (* n) ≤ m → m ≠ 0; (forward) from specification nat%c: ⊦ m + n = n + m; from specification nat-basic%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic% ⊦ m + 1 ≠ 0; (s)