[Imprint][Data Privacy Statement][E-Mail]



View long theorem info. View the proof. Back to main index. View the specification. View theorem base summary, View theorem base listing, the used properties by spec, the dependency list, the symbol table,

Proof step 36 from proof refine-rename-new-reparent (previous step)

m11 + 1 = fs[ri[inodekey(m3)]].size, dirs = abs-dirs(fs, ri), files = abs-files(fs, ri), m = fs[ri[dentrykey(m3, str)]].ino, m10 = fs[ri[inodekey(m7)]].size, m4 = fs[ri[inodekey(m3)]].nlink, m5 = fs[ri[inodekey(m3)]].nsubdirs, m8 = fs[ri[inodekey(m7)]].nlink, m9 = fs[ri[inodekey(m7)]].nsubdirs, old_dent = mkdentry(str, fs[ri[dentrykey(m3, str)]].ino), ro = orphans(fs, ri), m3 ≠ m7, fs[ri[inodekey(m3)]].directory, fs[ri[inodekey(m7)]].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(m3) ∈ ri, inodekey(fs[ri[dentrykey(m3, str)]].ino) ∈ ri, dentrykey(m3, str) ∈ ri, inodekey(m7) ∈ ri, (boolvar1 ⊃ 1;0) ≤ fs[ri[inodekey(m3)]].nsubdirs, ¬ dentrykey(m7, str0) ∈ ri, boolvar1 → 1 ≤ fs[ri[inodekey(m3)]].nsubdirs, boolvar3 → boolvar2, fs[ri[inodekey(m3)]].nlink ≠ 0 ∨ m3 = ROOT_INO, fs[ri[inodekey(m7)]].nlink ≠ 0 ∨ m7 = ROOT_INO, links(m3, abs-dirs(fs, ri)) ≠ ∅ ∨ m3 = ROOT_INO, links(m7, abs-dirs(fs, ri)) ≠ ∅ ∨ m7 = ROOT_INO, ¬ fs[ri[inodekey(fs[ri[dentrykey(m3, str)]].ino)]].directory ∧ ¬ boolvar1 ∧ m0 = fs[ri[inodekey(fs[ri[dentrykey(m3, str)]].ino)]].nlink ∧ m1 = fs[ri[inodekey(fs[ri[dentrykey(m3, str)]].ino)]].nsubdirs ∨ fs[ri[inodekey(fs[ri[dentrykey(m3, str)]].ino)]].directory ∧ boolvar1 ∧ m0 = fs[ri[inodekey(fs[ri[dentrykey(m3, str)]].ino)]].nlink ∧ m1 = fs[ri[inodekey(fs[ri[dentrykey(m3, str)]].ino)]].nsubdirs ∧ m2 = fs[ri[inodekey(fs[ri[dentrykey(m3, str)]].ino)]].size, fs[ri[inodekey(fs[ri[dentrykey(m3, str)]].ino)]].directory ∧ m0 = fs[ri[inodekey(fs[ri[dentrykey(m3, str)]].ino)]].nlink ∧ m2 = fs[ri[inodekey(fs[ri[dentrykey(m3, str)]].ino)]].size ∧ m1 = fs[ri[inodekey(fs[ri[dentrykey(m3, str)]].ino)]].nsubdirs ∧ boolvar1 ∨ ¬ fs[ri[inodekey(fs[ri[dentrykey(m3, str)]].ino)]].directory ∧ m0 = fs[ri[inodekey(fs[ri[dentrykey(m3, str)]].ino)]].nlink ∧ m1 = 0 ∧ ¬ boolvar1 ⊦ [aubifs_core_journal_add4# (dentrynode(dentrykey(m3, old_dent.name), 0), dentrynode(dentrykey(m7, str0), old_dent.ino), inodenode(inodekey(m3), md0, true, m4, m5 - (boolvar1 ⊃ 1;0), m11), inodenode(inodekey(m7), md1, true, m8, m9 + (boolvar1 ⊃ 1;0), m10 + 1), ri, fi, orphans(fs, ri), fo ; adr2, adr1, adr0, adr, fs, log ; boolvar2, err); nd0 := inodenode(inodekey(m3), md0, true, m4, m5 - (boolvar1 ⊃ 1;0), m11); nd := inodenode(inodekey(m7), md1, true, m8, m9 + (boolvar1 ⊃ 1;0), m10 + 1); new_dent := negdentry(str0); old_parent_inode := mkinode(m3, md0, true, m4, m5, m11 + 1); new_parent_inode := mkinode(m7, md1, true, m8, m9, m10); if err = ESUCCESS then {aubifs_core_index_remove#(dentrykey(m3, old_dent.name), fi, ro, fo, fs, log, boolvar2; ri); aubifs_core_index_store#(dentrykey(m7, new_dent.name), adr1, fi, ro, fo, fs, log, boolvar2; ri); aubifs_core_index_store#(inodekey(m3), adr0, fi, ro, fo, fs, log, boolvar2; ri); aubifs_core_index_store#(inodekey(m7), adr, fi, ro, fo, fs, log, boolvar2; ri); new_dent := mkdentry(new_dent.name, old_dent.ino); old_dent := negdentry(old_dent.name); old_parent_inode := mkinode(old_parent_inode.ino, nd0.meta, nd0.directory, nd0.nlink, nd0.nsubdirs, nd0.size); new_parent_inode := mkinode(new_parent_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) → ⟨old_dent_inode0 := mkinode(m, md, boolvar1, m0, m1, m2); new_dent_inode0 := new_dent_inode; old_dent0 := mkdentry(str, m); old_dent1 := negdentry(str0); old_dent_inode := mkinode(m, md, boolvar1, m0, m1, m2); old_inode := mkinode(m3, md0, true, m4, m5, m11 + 1); new_inode := mkinode(m7, md1, true, m8, m9, m10); afs_rename#(; old_inode, new_inode, old_dent_inode, new_dent_inode, old_dent0, old_dent1, err0, dirs, files; boolvar3)⟩ ( dirs = abs-dirs(fs, ri) ∧ files = abs-files(fs, ri) ∧ orphans(abs-dirs(fs, ri), abs-files(fs, ri)) = abs-keys(ro) ∧ (boolvar3 → boolvar2) ∧ old_parent_inode = old_inode ∧ new_parent_inode = new_inode ∧ old_dent_inode0 = old_dent_inode ∧ new_dent_inode0 = new_dent_inode ∧ old_dent = old_dent0 ∧ new_dent = old_dent1 ∧ err = err0)), fs[ri[inodekey(m7)]].nlink = 0 ∧ m7 ≠ ROOT_INO, fs[ri[inodekey(m3)]].nlink = 0 ∧ m3 ≠ ROOT_INO

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Rule argument

spec: nat name: elim-sub seq: n ≤ m ⊦ n0 = m - n ↔ m = n0 + n subst: [n, m, n0] → [(boolvar1 ⊃ 1;0), m5, n]

Additional information

Used simplifier rules: n ≤ m ⊦ n0 = m - n ↔ m = n0 + n; (elim) Used terms: (boolvar1 ⊃ 1;0), m5, n