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Proof step 43 from proof refine-rename-overwrite-reparent-file (previous step)

m14 + 1 = fs[ri[inodekey(m9)]].size, 0 = fs[ri[inodekey(fs[ri[dentrykey(m9, str)]].ino)]].nsubdirs, 0 = fs[ri[inodekey(fs[ri[dentrykey(m4, str0)]].ino)]].nsubdirs, dirs = abs-dirs(fs, ri), files = abs-files(fs, ri), m = fs[ri[dentrykey(m9, str)]].ino, m0 = fs[ri[inodekey(fs[ri[dentrykey(m9, str)]].ino)]].nlink, m1 = fs[ri[dentrykey(m4, str0)]].ino, m10 = fs[ri[inodekey(m9)]].nlink, m11 = fs[ri[inodekey(m9)]].nsubdirs, m3 = fs[ri[inodekey(fs[ri[dentrykey(m4, str0)]].ino)]].nlink, m3 = m12 + 1, m6 = fs[ri[inodekey(m4)]].nlink, m7 = fs[ri[inodekey(m4)]].nsubdirs, m8 = fs[ri[inodekey(m4)]].size, new_dent = mkdentry(str0, fs[ri[dentrykey(m4, str0)]].ino), old_dent = mkdentry(str, fs[ri[dentrykey(m9, str)]].ino), ro = orphans(fs, ri), fs[ri[inodekey(m4)]].directory, fs[ri[inodekey(m9)]].directory, orphans(fs, ri).inodes?, fo.inodes?, afs-cons(abs-dirs(fs, ri), abs-files(fs, ri)), file-node-cons(fs, ri), log-cons(log, fs), orphans-cons(fs, ri, orphans(fs, ri)), replay-cons-strong(fs, ri, orphans(fs, ri), fi, fo, log), ri-inj(ri), ri-inj(fi), ubifs-cons(fs, ri, orphans(fs, ri), fi, fo, log), inodekey(m9) ∈ ri, inodekey(m4) ∈ ri, dentrykey(m4, str0) ∈ ri, inodekey(fs[ri[dentrykey(m4, str0)]].ino) ∈ ri, dentrykey(m9, str) ∈ ri, inodekey(fs[ri[dentrykey(m9, str)]].ino) ∈ ri, 1 ≤ fs[ri[inodekey(fs[ri[dentrykey(m4, str0)]].ino)]].nlink, fs[ri[inodekey(fs[ri[dentrykey(m4, str0)]].ino)]].nlink = 1 → links(fs[ri[dentrykey(m4, str0)]].ino, fs, ri) = ∅ ++ dentrykey(m4, str0), boolvar2 → boolvar1, fs[ri[inodekey(m4)]].nlink ≠ 0 ∨ m4 = ROOT_INO, fs[ri[inodekey(m9)]].nlink ≠ 0 ∨ m9 = ROOT_INO, links(m4, abs-dirs(fs, ri)) ≠ ∅ ∨ m4 = ROOT_INO, links(m9, abs-dirs(fs, ri)) ≠ ∅ ∨ m9 = ROOT_INO ⊦ [aubifs_core_journal_add5# (dentrynode(dentrykey(m9, old_dent.name), 0), dentrynode(dentrykey(m4, new_dent.name), old_dent.ino), inodenode(inodekey(m9), md2, true, m10, m11 - 0, m14), inodenode(inodekey(m4), md1, true, m6, m7, m8), inodenode(inodekey(new_dent.ino), md0, false, m12, 0, m5), ri, fi, orphans(fs, ri), fo ; adr3, adr2, adr1, adr0, adr, fs, log ; boolvar1, err); nd1 := inodenode(inodekey(m9), md2, true, m10, m11 - 0, m14); m13 := m4; old_parent_inode := mkinode(m9, md2, true, m10, m11, m14 + 1); new_child_inode := mkinode(m1, md0, false, m3, 0, m5); if err = ESUCCESS then {aubifs_core_index_remove#(dentrykey(m9, old_dent.name), fi, ro, fo, fs, log, boolvar1; ri); aubifs_core_index_store#(dentrykey(m13, new_dent.name), adr2, fi, ro, fo, fs, log, boolvar1; ri); aubifs_core_index_store#(inodekey(m9), adr1, fi, ro, fo, fs, log, boolvar1; ri); aubifs_core_index_store#(inodekey(m13), adr0, fi, ro, fo, fs, log, boolvar1; ri); aubifs_core_index_store#(inodekey(new_dent.ino), adr, fi, ro, fo, fs, log, boolvar1; ri); nd := inodenode(inodekey(new_dent.ino), md0, false, m12, 0, m5); if nd.nlink = 0 then aubifs_core_orphans_insert#(inodekey(new_dent.ino), ri, fi, fo, fs, log, boolvar1; ro); new_dent := mkdentry(new_dent.name, old_dent.ino); old_dent := negdentry(old_dent.name); old_parent_inode := mkinode(old_parent_inode.ino, nd1.meta, nd1.directory, nd1.nlink, nd1.nsubdirs, nd1.size); new_child_inode := mkinode(new_child_inode.ino, 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) ∧ ri-inj(ri) ∧ log-cons(log, fs) ∧ ro.inodes? → ⟨old_dent_inode0 := mkinode(m, md, false, m0, 0, m2); old_dent0 := mkdentry(str, m); old_dent1 := mkdentry(str0, m1); old_dent_inode := mkinode(m, md, false, m0, 0, m2); new_dent_inode := mkinode(m1, md0, false, m3, 0, m5); new_inode := mkinode(m4, md1, true, m6, m7, m8); old_inode := mkinode(m9, md2, true, m10, m11, m14 + 1); afs_rename#(; old_inode, new_inode, old_dent_inode, new_dent_inode, old_dent0, old_dent1, err0, dirs, files; boolvar2)⟩ ( dirs = abs-dirs(fs, ri) ∧ files = abs-files(fs, ri) ∧ orphans(abs-dirs(fs, ri), abs-files(fs, ri)) = abs-keys(ro) ∧ (boolvar2 → boolvar1) ∧ old_parent_inode = old_inode ∧ mkinode(m13, md1, true, m6, m7, m8) = new_inode ∧ old_dent_inode0 = old_dent_inode ∧ new_child_inode = new_dent_inode ∧ old_dent = old_dent0 ∧ new_dent = old_dent1 ∧ err = err0)), fs[ri[dentrykey(m4, str0)]].ino = ROOT_INO, fs[ri[inodekey(fs[ri[dentrykey(m4, str0)]].ino)]].nlink = 0, m3 = 0, m9 = m4, fs[ri[inodekey(fs[ri[dentrykey(m4, str0)]].ino)]].directory, fs[ri[inodekey(fs[ri[dentrykey(m9, str)]].ino)]].directory, fs[ri[inodekey(m9)]].nlink = 0 ∧ m9 ≠ ROOT_INO, fs[ri[inodekey(m4)]].nlink = 0 ∧ m4 ≠ ROOT_INO

Heuristic simplifier applied rule simplifier

And obtained the following new goals

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)