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Proof step 77 from proof refine-unlink (previous step)

0 = fs[ri[inodekey(fs[ri[dentrykey(m, str)]].ino)]].nsubdirs, dent = mkdentry(str, fs[ri[dentrykey(m, str)]].ino), dirs = abs-dirs(fs, ri), files = abs-files(fs, ri), m0 = fs[ri[inodekey(m)]].nlink, m1 = fs[ri[inodekey(m)]].nsubdirs, m2 = fs[ri[inodekey(m)]].size, m3 = fs[ri[dentrykey(m, str)]].ino, m4 = fs[ri[inodekey(fs[ri[dentrykey(m, str)]].ino)]].nlink, m4 = m5 + 1, ro = orphans(fs, ri), fs[ri[inodekey(m)]].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(m) ∈ ri, inodekey(fs[ri[dentrykey(m, str)]].ino) ∈ ri, dentrykey(m, str) ∈ ri, 1 ≤ fs[ri[inodekey(fs[ri[dentrykey(m, str)]].ino)]].nlink, 1 ≤ fs[ri[inodekey(m)]].size, fs[ri[inodekey(fs[ri[dentrykey(m, str)]].ino)]].nlink = 1 → links(fs[ri[dentrykey(m, str)]].ino, fs, ri) = ∅ ++ dentrykey(m, str), asynced → boolvar, fs[ri[inodekey(m)]].nlink ≠ 0 ∨ m = ROOT_INO, links(m, abs-dirs(fs, ri)) ≠ ∅ ∨ m = ROOT_INO ⊦ [aubifs_core_journal_add3# (inodenode(inodekey(m), md, true, m0, m1, m2 - 1), dentrynode(dentrykey(m, dent.name), 0), inodenode(inodekey(m3), md0, false, m5, 0, m6), ri, fi, orphans(fs, ri), fo ; adr1, adr0, adr, fs, log ; boolvar, err); nd1 := inodenode(inodekey(m), md, true, m0, m1, m2 - 1); nd := inodenode(inodekey(m3), md0, false, m5, 0, m6); ino := m3; p_inode := mkinode(m, md, true, m0, m1, m2); c_inode := mkinode(m3, md0, false, m4, 0, m6); if err = ESUCCESS then {aubifs_core_index_store#(inodekey(m), adr1, fi, ro, fo, fs, log, boolvar; ri); aubifs_core_index_remove#(dentrykey(m, dent.name), fi, ro, fo, fs, log, boolvar; ri); aubifs_core_index_store#(inodekey(m3), adr, fi, ro, fo, fs, log, boolvar; ri); if m4 = 1 then aubifs_core_orphans_insert#(inodekey(m3), ri, fi, fo, fs, log, boolvar; ro); dent := negdentry(dent.name); p_inode := mkinode(p_inode.ino, nd1.meta, nd1.directory, nd1.nlink, nd1.nsubdirs, nd1.size); c_inode := mkinode(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 := mkdentry(str, m3); p_inode0 := mkinode(m, md, true, m0, m1, m2); p_inode1 := mkinode(m3, md0, false, m4, 0, m6); afs_unlink#(; 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(ro) ∧ (asynced → boolvar) ∧ p_inode = p_inode0 ∧ c_inode = p_inode1 ∧ dent = old_dent ∧ err = err0)), fs[ri[dentrykey(m, str)]].ino = ROOT_INO, fs[ri[inodekey(fs[ri[dentrykey(m, str)]].ino)]].nlink = 0, fs[ri[inodekey(m)]].size = 0, m4 = 0, fs[ri[inodekey(fs[ri[dentrykey(m, str)]].ino)]].directory

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)