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Proof step 73 from proof refine-rename-overwrite-reparent-dir (previous step)

m16 + 1 = fs0[ri0[inodekey(m11)]].nsubdirs, m13 + 1 = fs0[ri0[inodekey(m11)]].size, m14 + 1 = fs0[ri0[inodekey(m0)]].nlink, fs0[ri0[dentrykey(m7, str0)]] = dentrynode(key0, m0), fs0[ri0[dentrykey(m11, str)]] = dentrynode(key, m), fs0[ri0[inodekey(m7)]] = inodenode(key1, md3, true, m1, m2, m3), abs-children(m0, fs0, ri0) = ∅, dentrykeys(inodekey(m0), ri0) = ∅, ri = (ri0 -- dentrykey(m11, str))[dentrykey(m7, str0), adr2], adr1 ≠ adr5, adr1 ≠ adr4, adr1 ≠ adr3, adr1 ≠ adr2, adr2 ≠ adr5, adr2 ≠ adr4, adr2 ≠ adr3, adr3 ≠ adr5, adr3 ≠ adr4, adr4 ≠ adr5, m0 ≠ 0, m0 ≠ ROOT_INO, m11 ≠ 0, m11 ≠ m7, m7 ≠ 0, fs0[ri0[inodekey(m11)]].directory, fs0[ri0[inodekey(m0)]].directory, fs0[ri0[inodekey(m)]].directory, fs0[ri0[inodekey(m11)]].inode?, fs0[ri0[inodekey(m0)]].inode?, fo.inodes?, orphans(fs0, ri0).inodes?, afs-cons(abs-dirs(fs0, ri0), abs-files(fs0, ri0)), file-node-cons(fs0, ri0), log-cons(log0, fs0), orphans-cons(fs0, ri0, orphans(fs0, ri0)), replay-cons-strong(fs0, ri0, orphans(fs0, ri0), fi, fo, log0), ri-cons(ri0, fs0), ri-inj(fi), ri-inj(ri0), ubifs-cons(fs0, ri0, orphans(fs0, ri0), fi, fo, log0), ri0[dentrykey(m11, str)] ∈ fs0, ri0[inodekey(m11)] ∈ fs0, ri0[inodekey(m7)] ∈ fs0, ri0[inodekey(m0)] ∈ fs0, ri0[dentrykey(m7, str0)] ∈ fs0, inodekey(m11) ∈ ri0, inodekey(m7) ∈ ri0, inodekey(m) ∈ ri0, dentrykey(m11, str) ∈ ri0, inodekey(m0) ∈ ri0, dentrykey(m7, str0) ∈ ri0, ¬ adr1 ∈ fs0, ¬ adr2 ∈ fs0, ¬ adr3 ∈ fs0, ¬ adr4 ∈ fs0, ¬ adr5 ∈ fs0, ¬ adr2 ∈ ri0 -- dentrykey(m11, str), boolvar2 → boolvar0, m14 = 0 → links(m0, fs0, ri0) = ∅ ++ dentrykey(m7, str0), fs0[ri0[inodekey(m11)]].nlink ≠ 0 ∨ m11 = ROOT_INO, m1 ≠ 0 ∨ m7 = ROOT_INO, links(m11, abs-dirs(fs0, ri0)) ≠ ∅ ∨ m11 = ROOT_INO, links(m7, abs-dirs(fs0, ri0)) ≠ ∅ ∨ m7 = ROOT_INO ⊦ [aubifs_core_index_store# (inodekey(m11), adr3, fi, orphans(fs0, ri0), fo, fs0[adr1, dentrynode(dentrykey(m11, str), 0)][adr2, dentrynode(dentrykey(m7, str0), m)] [adr3, inodenode(inodekey(m11), md2, true, fs0[ri0[inodekey(m11)]].nlink, m16, m13) ] [adr4, inodenode(inodekey(m7), md1, true, m1, m2, m3) ] [adr5, inodenode(inodekey(m0), md0, true, m14, fs0[ri0[inodekey(m0)]].nsubdirs, fs0[ri0[inodekey(m0)]].size) ], ((((log0 + adr1 ') + adr2 ') + adr3 ') + adr4 ') + adr5 ', boolvar1 ; ri); aubifs_core_index_store# (inodekey(m7), adr4, fi, orphans(fs0, ri0), fo, fs0[adr1, dentrynode(dentrykey(m11, str), 0)][adr2, dentrynode(dentrykey(m7, str0), m)] [adr3, inodenode(inodekey(m11), md2, true, fs0[ri0[inodekey(m11)]].nlink, m16, m13) ] [adr4, inodenode(inodekey(m7), md1, true, m1, m2, m3) ] [adr5, inodenode(inodekey(m0), md0, true, m14, fs0[ri0[inodekey(m0)]].nsubdirs, fs0[ri0[inodekey(m0)]].size) ], ((((log0 + adr1 ') + adr2 ') + adr3 ') + adr4 ') + adr5 ', boolvar1 ; ri); aubifs_core_index_store# (inodekey(mkdentry(str0, m0).ino), adr5, fi, orphans(fs0, ri0), fo, fs0[adr1, dentrynode(dentrykey(m11, str), 0)][adr2, dentrynode(dentrykey(m7, str0), m)] [adr3, inodenode(inodekey(m11), md2, true, fs0[ri0[inodekey(m11)]].nlink, m16, m13) ] [adr4, inodenode(inodekey(m7), md1, true, m1, m2, m3) ] [adr5, inodenode(inodekey(m0), md0, true, m14, fs0[ri0[inodekey(m0)]].nsubdirs, fs0[ri0[inodekey(m0)]].size) ], ((((log0 + adr1 ') + adr2 ') + adr3 ') + adr4 ') + adr5 ', boolvar1 ; ri); nd := inodenode(inodekey(mkdentry(str0, m0).ino), md0, true, m14, fs0[ri0[inodekey(m0)]].nsubdirs, fs0[ri0[inodekey(m0)]].size); log := ((((log0 + adr1 ') + adr2 ') + adr3 ') + adr4 ') + adr5 '; ro0 := orphans(fs0, ri0); new_dent := mkdentry(str0, m0); fs := fs0[adr1, dentrynode(dentrykey(m11, str), 0)][adr2, dentrynode(dentrykey(m7, str0), m)] [adr3, inodenode(inodekey(m11), md2, true, fs0[ri0[inodekey(m11)]].nlink, m16, m13) ] [adr4, inodenode(inodekey(m7), md1, true, m1, m2, m3) ] [adr5, inodenode(inodekey(m0), md0, true, m14, fs0[ri0[inodekey(m0)]].nsubdirs, fs0[ri0[inodekey(m0)]].size) ]; if nd.nlink = 0 then aubifs_core_orphans_insert#(inodekey(new_dent.ino), ri, fi, fo, fs, log, boolvar1; ro0); new_dent := mkdentry(new_dent.name, mkdentry(str, m).ino); old_dent := negdentry(str); old_parent_inode := mkinode (m11, inodenode(inodekey(m11), md2, true, fs0[ri0[inodekey(m11)]].nlink, m16, m13).meta, inodenode(inodekey(m11), md2, true, fs0[ri0[inodekey(m11)]].nlink, m16, m13).directory, inodenode(inodekey(m11), md2, true, fs0[ri0[inodekey(m11)]].nlink, m16, m13).nlink, inodenode(inodekey(m11), md2, true, fs0[ri0[inodekey(m11)]].nlink, m16, m13).nsubdirs, inodenode(inodekey(m11), md2, true, fs0[ri0[inodekey(m11)]].nlink, m16, m13).size); new_child_inode := mkinode(m0, nd.meta, nd.directory, nd.nlink, nd.nsubdirs, nd.size)] ( ubifs-cons(fs, ri, ro0, fi, fo, log) ∧ replay-cons-strong(fs, ri, ro0, fi, fo, log) ∧ file-node-cons(fs, ri) ∧ orphans-cons(fs, ri, ro0) ∧ ri-inj(ri) ∧ log-cons(log, fs) ∧ ro0.inodes? → ⟨old_dent_inode0 := mkinode(m, md, true, fs0[ri0[inodekey(m)]].nlink, fs0[ri0[inodekey(m)]].nsubdirs, fs0[ri0[inodekey(m)]].size); old_dent0 := mkdentry(str, m); old_dent1 := mkdentry(str0, m0); old_dent_inode := mkinode(m, md, true, fs0[ri0[inodekey(m)]].nlink, fs0[ri0[inodekey(m)]].nsubdirs, fs0[ri0[inodekey(m)]].size); new_dent_inode := mkinode(m0, md0, true, m14 + 1, fs0[ri0[inodekey(m0)]].nsubdirs, fs0[ri0[inodekey(m0)]].size); new_inode := mkinode(m7, md1, true, m1, m2, m3); old_inode := mkinode(m11, md2, true, fs0[ri0[inodekey(m11)]].nlink, m16 + 1, m13 + 1); files := abs-files(fs0, ri0); dirs := abs-dirs(fs0, ri0); 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(ro0) ∧ (boolvar2 → boolvar1) ∧ old_parent_inode = old_inode ∧ mkinode(m7, md1, true, m1, m2, m3) = new_inode ∧ old_dent_inode0 = old_dent_inode ∧ new_child_inode = new_dent_inode ∧ old_dent = old_dent0 ∧ new_dent = old_dent1 ∧ ESUCCESS = err0)), m1 = 0 ∧ m7 ≠ ROOT_INO, fs0[ri0[inodekey(m11)]].nlink = 0 ∧ m11 ≠ ROOT_INO

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 74:
m14 + 1 = fs0[ri0[inodekey(m0)]].nlink, m13 + 1 = m6, m16 + 1 = m5, fs0[ri0[inodekey(m7)]] = inodenode(key1, md3, true, m1, m2, m3), fs0[ri0[dentrykey(m11, str)]] = dentrynode(key, m), fs0[ri0[dentrykey(m7, str0)]] = dentrynode(key0, m0), fs0[ri0[inodekey(m11)]] = inodenode(key2, md4, boolvar, m4, m5, m6), abs-children(m0, fs0, ri0) = ∅, boolvar, dentrykeys(inodekey(m0), ri0) = ∅, ri = (ri0 -- dentrykey(m11, str))[dentrykey(m7, str0), adr2], fs0[ri0[inodekey(m)]].directory, fs0[ri0[inodekey(m0)]].directory, fs0[ri0[inodekey(m0)]].inode?, fs0[ri0[inodekey(m11)]].inode?, orphans(fs0, ri0).inodes?, fo.inodes?, afs-cons(abs-dirs(fs0, ri0), abs-files(fs0, ri0)), file-node-cons(fs0, ri0), log-cons(log0, fs0), orphans-cons(fs0, ri0, orphans(fs0, ri0)), replay-cons-strong(fs0, ri0, orphans(fs0, ri0), fi, fo, log0), ri-cons(ri0, fs0), ri-inj(ri0), ri-inj(fi), ubifs-cons(fs0, ri0, orphans(fs0, ri0), fi, fo, log0), dentrykey(m7, str0) ∈ ri0, inodekey(m0) ∈ ri0, dentrykey(m11, str) ∈ ri0, inodekey(m) ∈ ri0, inodekey(m7) ∈ ri0, inodekey(m11) ∈ ri0, ri0[dentrykey(m7, str0)] ∈ fs0, ri0[inodekey(m0)] ∈ fs0, ri0[inodekey(m7)] ∈ fs0, ri0[inodekey(m11)] ∈ fs0, ri0[dentrykey(m11, str)] ∈ fs0, m14 = 0 → links(m0, fs0, ri0) = ∅ ++ dentrykey(m7, str0), boolvar2 → boolvar0, links(m7, abs-dirs(fs0, ri0)) ≠ ∅ ∨ m7 = ROOT_INO, links(m11, abs-dirs(fs0, ri0)) ≠ ∅ ∨ m11 = ROOT_INO, m1 ≠ 0 ∨ m7 = ROOT_INO, m4 ≠ 0 ∨ m11 = ROOT_INO ⊦ [aubifs_core_index_store# (inodekey(m11), adr3, fi, orphans(fs0, ri0), fo, fs0[adr1, dentrynode(dentrykey(m11, str), 0)][adr2, dentrynode(dentrykey(m7, str0), m)][adr3, inodenode(inodekey(m11), md2, true, m4, m16, m13)] [adr4, inodenode(inodekey(m7), md1, true, m1, m2, m3) ] [adr5, inodenode(inodekey(m0), md0, true, m14, fs0[ri0[inodekey(m0)]].nsubdirs, fs0[ri0[inodekey(m0)]].size) ], ((((log0 + adr1 ') + adr2 ') + adr3 ') + adr4 ') + adr5 ', boolvar1 ; ri); aubifs_core_index_store# (inodekey(m7), adr4, fi, orphans(fs0, ri0), fo, fs0[adr1, dentrynode(dentrykey(m11, str), 0)][adr2, dentrynode(dentrykey(m7, str0), m)][adr3, inodenode(inodekey(m11), md2, true, m4, m16, m13)] [adr4, inodenode(inodekey(m7), md1, true, m1, m2, m3) ] [adr5, inodenode(inodekey(m0), md0, true, m14, fs0[ri0[inodekey(m0)]].nsubdirs, fs0[ri0[inodekey(m0)]].size) ], ((((log0 + adr1 ') + adr2 ') + adr3 ') + adr4 ') + adr5 ', boolvar1 ; ri); aubifs_core_index_store# (inodekey(mkdentry(str0, m0).ino), adr5, fi, orphans(fs0, ri0), fo, fs0[adr1, dentrynode(dentrykey(m11, str), 0)][adr2, dentrynode(dentrykey(m7, str0), m)][adr3, inodenode(inodekey(m11), md2, true, m4, m16, m13)] [adr4, inodenode(inodekey(m7), md1, true, m1, m2, m3) ] [adr5, inodenode(inodekey(m0), md0, true, m14, fs0[ri0[inodekey(m0)]].nsubdirs, fs0[ri0[inodekey(m0)]].size) ], ((((log0 + adr1 ') + adr2 ') + adr3 ') + adr4 ') + adr5 ', boolvar1 ; ri); nd := inodenode(inodekey(mkdentry(str0, m0).ino), md0, true, m14, fs0[ri0[inodekey(m0)]].nsubdirs, fs0[ri0[inodekey(m0)]].size); log := ((((log0 + adr1 ') + adr2 ') + adr3 ') + adr4 ') + adr5 '; ro0 := orphans(fs0, ri0); new_dent := mkdentry(str0, m0); fs := fs0[adr1, dentrynode(dentrykey(m11, str), 0)][adr2, dentrynode(dentrykey(m7, str0), m)][adr3, inodenode(inodekey(m11), md2, true, m4, m16, m13)] [adr4, inodenode(inodekey(m7), md1, true, m1, m2, m3) ] [adr5, inodenode(inodekey(m0), md0, true, m14, fs0[ri0[inodekey(m0)]].nsubdirs, fs0[ri0[inodekey(m0)]].size) ]; if nd.nlink = 0 then aubifs_core_orphans_insert#(inodekey(new_dent.ino), ri, fi, fo, fs, log, boolvar1; ro0); new_dent := mkdentry(new_dent.name, mkdentry(str, m).ino); old_dent := negdentry(str); old_parent_inode := mkinode (m11, inodenode(inodekey(m11), md2, true, m4, m16, m13).meta, inodenode(inodekey(m11), md2, true, m4, m16, m13).directory, inodenode(inodekey(m11), md2, true, m4, m16, m13).nlink, inodenode(inodekey(m11), md2, true, m4, m16, m13).nsubdirs, inodenode(inodekey(m11), md2, true, m4, m16, m13).size); new_child_inode := mkinode(m0, nd.meta, nd.directory, nd.nlink, nd.nsubdirs, nd.size)] ( ubifs-cons(fs, ri, ro0, fi, fo, log) ∧ replay-cons-strong(fs, ri, ro0, fi, fo, log) ∧ file-node-cons(fs, ri) ∧ orphans-cons(fs, ri, ro0) ∧ ri-inj(ri) ∧ log-cons(log, fs) ∧ ro0.inodes? → ⟨old_dent_inode0 := mkinode(m, md, true, fs0[ri0[inodekey(m)]].nlink, fs0[ri0[inodekey(m)]].nsubdirs, fs0[ri0[inodekey(m)]].size); old_dent0 := mkdentry(str, m); old_dent1 := mkdentry(str0, m0); old_dent_inode := mkinode(m, md, true, fs0[ri0[inodekey(m)]].nlink, fs0[ri0[inodekey(m)]].nsubdirs, fs0[ri0[inodekey(m)]].size); new_dent_inode := mkinode(m0, md0, true, m14 + 1, fs0[ri0[inodekey(m0)]].nsubdirs, fs0[ri0[inodekey(m0)]].size); new_inode := mkinode(m7, md1, true, m1, m2, m3); old_inode := mkinode(m11, md2, true, m4, m16 + 1, m13 + 1); files := abs-files(fs0, ri0); dirs := abs-dirs(fs0, ri0); 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(ro0) ∧ (boolvar2 → boolvar1) ∧ old_parent_inode = old_inode ∧ mkinode(m7, md1, true, m1, m2, m3) = new_inode ∧ old_dent_inode0 = old_dent_inode ∧ new_child_inode = new_dent_inode ∧ old_dent = old_dent0 ∧ new_dent = old_dent1 ∧ ESUCCESS = err0)), adr1 = adr5, adr1 = adr4, adr1 = adr3, adr1 = adr2, adr2 = adr5, adr2 = adr4, adr2 = adr3, adr3 = adr5, adr3 = adr4, adr4 = adr5, m0 = 0, m0 = ROOT_INO, m11 = 0, m11 = m7, m7 = 0, adr1 ∈ fs0, adr2 ∈ fs0, adr3 ∈ fs0, adr4 ∈ fs0, adr5 ∈ fs0, adr2 ∈ ri0 -- dentrykey(m11, str), m4 = 0 ∧ m11 ≠ ROOT_INO, m1 = 0 ∧ m7 ≠ ROOT_INO

Rule argument

spec: node name: elim-03 seq: ⊦ nd.inode? → ( ( ( ( (key = nd.key ∧ md = nd.meta) ∧ (boolvar ↔ nd.directory)) ∧ m = nd.nlink) ∧ m0 = nd.nsubdirs) ∧ m1 = nd.size ↔ nd = inodenode(key, md, boolvar, m, m0, m1)) subst: [nd, key, md, boolvar, m, m0, m1] → [fs0[ri0[inodekey(m11)]], key2, md4, boolvar, m4, m5, m6]

Additional information

Used simplifier rules: ⊦ nd.inode? → ( ( ( ( (key = nd.key ∧ md = nd.meta) ∧ (boolvar ↔ nd.directory)) ∧ m = nd.nlink) ∧ m0 = nd.nsubdirs) ∧ m1 = nd.size ↔ nd = inodenode(key, md, boolvar, m, m0, m1)); (elim) Used terms: fs0[ri0[inodekey(m11)]], key2, md4, boolvar, m4, m5, m6