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Proof step 43 from proof refine-create (previous step)

fs0 = fs, nd1 = inodenode(inodekey(m3), md0, true, fs[ri[inodekey(m3)]].nlink, fs[ri[inodekey(m3)]].nsubdirs, fs[ri[inodekey(m3)]].size + 1), n ≠ 0, fs[ri[inodekey(m3)]].directory, fs[ri[inodekey(m3)]].inode?, 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), ri[inodekey(m3)] ∈ fs, inodekey(m3) ∈ ri, ¬ inodekey(n) ∈ ri, ¬ inodekey(n) ∈ fo, ¬ dentrykey(m3, str) ∈ ri, asynced → boolvar, links(m3, abs-dirs(fs, ri)) ≠ ∅ ∨ m3 = ROOT_INO, fs[ri[inodekey(m3)]].nlink ≠ 0 ∨ m3 = ROOT_INO ⊦ [aubifs_core_journal_add3# (nd1, dentrynode(dentrykey(m3, str), n), inodenode(inodekey(n), md, false, 1, 0, 0), ri, fi, orphans(fs, ri), fo ; adr1, adr0, adr, fs, log ; boolvar, err); ro0 := orphans(fs0, ri); p_inode := mkinode(m3, md0, true, fs0[ri[inodekey(m3)]].nlink, fs0[ri[inodekey(m3)]].nsubdirs, fs0[ri[inodekey(m3)]].size); m2 := fs0[ri[inodekey(m3)]].size; m1 := fs0[ri[inodekey(m3)]].nsubdirs; m0 := fs0[ri[inodekey(m3)]].nlink; files := abs-files(fs0, ri); dirs := abs-dirs(fs0, ri); dent := negdentry(str); c_inode := p_inode1; if err = ESUCCESS then {ri0 := ri; aubifs_core_index_store#(inodekey(p_inode.ino), adr1, fi, orphans(fs0, ri), fo, fs, log, boolvar; ri); aubifs_core_index_store#(dentrykey(p_inode.ino, dent.name), adr0, fi, orphans(fs0, ri0), fo, fs, log, boolvar; ri); aubifs_core_index_store#(inodekey(n), adr, fi, orphans(fs0, ri0), fo, fs, log, boolvar; ri); dent := mkdentry(dent.name, n); p_inode := mkinode(p_inode.ino, nd1.meta, nd1.directory, nd1.nlink, nd1.nsubdirs, nd1.size); c_inode := mkinode (n, inodenode(inodekey(n), md, false, 1, 0, 0).meta, inodenode(inodekey(n), md, false, 1, 0, 0).directory, inodenode(inodekey(n), md, false, 1, 0, 0).nlink, inodenode(inodekey(n), md, false, 1, 0, 0).nsubdirs, inodenode(inodekey(n), md, false, 1, 0, 0).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) → ⟨old_dent := negdentry(str); p_inode0 := mkinode(m3, md0, true, m0, m1, m2); afs_create#(md; p_inode0, p_inode1, old_dent, err0, dirs, files; asynced)⟩ ( dirs = abs-dirs(fs, ri) ∧ files = abs-files(fs, ri) ∧ orphans(abs-dirs(fs, ri), abs-files(fs, ri)) = abs-keys(ro0) ∧ (asynced → boolvar) ∧ p_inode = p_inode0 ∧ c_inode = p_inode1 ∧ dent = old_dent ∧ err = err0)), fs[ri[inodekey(m3)]].nlink = 0 ∧ m3 ≠ ROOT_INO

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 44:
fs[ri[inodekey(m3)]] = inodenode(key, md1, boolvar0, m, m4, m5), boolvar0, fs0 = fs, nd1 = inodenode(inodekey(m3), md0, true, m, m4, m5 + 1), fs[ri[inodekey(m3)]].inode?, fo.inodes?, orphans(fs, ri).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(fi), ri-inj(ri), ubifs-cons(fs, ri, orphans(fs, ri), fi, fo, log), inodekey(m3) ∈ ri, ri[inodekey(m3)] ∈ fs, asynced → boolvar, m ≠ 0 ∨ m3 = ROOT_INO, links(m3, abs-dirs(fs, ri)) ≠ ∅ ∨ m3 = ROOT_INO ⊦ [aubifs_core_journal_add3# (nd1, dentrynode(dentrykey(m3, str), n), inodenode(inodekey(n), md, false, 1, 0, 0), ri, fi, orphans(fs, ri), fo ; adr1, adr0, adr, fs, log ; boolvar, err); ro0 := orphans(fs0, ri); p_inode := mkinode(m3, md0, true, fs0[ri[inodekey(m3)]].nlink, fs0[ri[inodekey(m3)]].nsubdirs, fs0[ri[inodekey(m3)]].size); m2 := fs0[ri[inodekey(m3)]].size; m1 := fs0[ri[inodekey(m3)]].nsubdirs; m0 := fs0[ri[inodekey(m3)]].nlink; files := abs-files(fs0, ri); dirs := abs-dirs(fs0, ri); dent := negdentry(str); c_inode := p_inode1; if err = ESUCCESS then {ri0 := ri; aubifs_core_index_store#(inodekey(p_inode.ino), adr1, fi, orphans(fs0, ri), fo, fs, log, boolvar; ri); aubifs_core_index_store#(dentrykey(p_inode.ino, dent.name), adr0, fi, orphans(fs0, ri0), fo, fs, log, boolvar; ri); aubifs_core_index_store#(inodekey(n), adr, fi, orphans(fs0, ri0), fo, fs, log, boolvar; ri); dent := mkdentry(dent.name, n); p_inode := mkinode(p_inode.ino, nd1.meta, nd1.directory, nd1.nlink, nd1.nsubdirs, nd1.size); c_inode := mkinode (n, inodenode(inodekey(n), md, false, 1, 0, 0).meta, inodenode(inodekey(n), md, false, 1, 0, 0).directory, inodenode(inodekey(n), md, false, 1, 0, 0).nlink, inodenode(inodekey(n), md, false, 1, 0, 0).nsubdirs, inodenode(inodekey(n), md, false, 1, 0, 0).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) → ⟨old_dent := negdentry(str); p_inode0 := mkinode(m3, md0, true, m0, m1, m2); afs_create#(md; p_inode0, p_inode1, old_dent, err0, dirs, files; asynced)⟩ ( dirs = abs-dirs(fs, ri) ∧ files = abs-files(fs, ri) ∧ orphans(abs-dirs(fs, ri), abs-files(fs, ri)) = abs-keys(ro0) ∧ (asynced → boolvar) ∧ p_inode = p_inode0 ∧ c_inode = p_inode1 ∧ dent = old_dent ∧ err = err0)), n = 0, inodekey(n) ∈ ri, inodekey(n) ∈ fo, dentrykey(m3, str) ∈ ri, m = 0 ∧ m3 ≠ 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] → [fs[ri[inodekey(m3)]], key, md1, boolvar0, m, m4, m5]

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: fs[ri[inodekey(m3)]], key, md1, boolvar0, m, m4, m5