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Proof step 18 from proof inv-unlink (previous step)

m = fs[ri[dentrykey(m1, str)]].ino, m0 = fs[ri[inodekey(fs[ri[dentrykey(m1, str)]].ino)]].nlink, m0 = m3 + 1, nd1 = inodenode(inodekey(m1), md0, true, fs[ri[inodekey(m1)]].nlink, fs[ri[inodekey(m1)]].nsubdirs, fs[ri[inodekey(m1)]].size - 1), fs[ri[inodekey(m1)]].directory, fs[ri[inodekey(m1)]].inode?, fo.inodes?, ro.inodes?, file-node-cons(fs, ri), log-cons(log, fs), orphans-cons(fs, ri, ro), replay-cons-strong(fs, ri, ro, fi, fo, log), ri-inj(fi), ri-inj(ri), ubifs-cons(fs, ri, ro, fi, fo, log), inodekey(m1) ∈ ri, ri[inodekey(m1)] ∈ fs, inodekey(fs[ri[dentrykey(m1, str)]].ino) ∈ ri, dentrykey(m1, str) ∈ ri, 1 ≤ fs[ri[inodekey(m1)]].size, fs[ri[inodekey(m1)]].size ≥ 1, fs[ri[inodekey(fs[ri[dentrykey(m1, str)]].ino)]].nlink = 1 → links(fs[ri[dentrykey(m1, str)]].ino, fs, ri) = ∅ ++ dentrykey(m1, str), fs[ri[inodekey(m1)]].trunc? ∨ fs[ri[inodekey(m1)]].inode?, fs[ri[inodekey(m1)]].nlink ≠ 0 ∨ m1 = ROOT_INO ⊦ ⟪nd0 := dentrynode(dentrykey(m1, str), 0); nd := inodenode(inodekey(m), md, false, m3, fs[ri[inodekey(m)]].nsubdirs, m2); aubifs_core_journal_add3#(nd1, nd0, nd, ri, fi, ro, fo; adr1, adr0, adr, fs, log; boolvar, err); if err = ESUCCESS then {aubifs_core_index_store#(inodekey(m1), adr1, fi, ro, fo, fs, log, boolvar; ri); aubifs_core_index_remove#(dentrykey(m1, str), fi, ro, fo, fs, log, boolvar; ri); aubifs_core_index_store#(inodekey(m), adr, fi, ro, fo, fs, log, boolvar; ri); if m0 = 1 then aubifs_core_orphans_insert#(inodekey(m), ri, fi, fo, fs, log, boolvar; ro); dent := negdentry(str); p_inode := mkinode(m1, nd1.meta, nd1.directory, nd1.nlink, nd1.nsubdirs, nd1.size); c_inode0 := mkinode(m, 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)), fs[ri[dentrykey(m1, str)]].ino = ROOT_INO, fs[ri[inodekey(fs[ri[dentrykey(m1, str)]].ino)]].nlink = 0, fs[ri[inodekey(m1)]].size = 0, m0 = 0, fs[ri[inodekey(fs[ri[dentrykey(m1, str)]].ino)]].directory, inodekey(fs[ri[dentrykey(m1, str)]].ino) ∈ ro, inodekey(m1) ∈ ro

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 19:
m3 + 1 = fs[ri[inodekey(fs[ri[dentrykey(m1, str)]].ino)]].nlink, m = fs[ri[dentrykey(m1, str)]].ino, nd1 = inodenode(inodekey(m1), md0, true, fs[ri[inodekey(m1)]].nlink, fs[ri[inodekey(m1)]].nsubdirs, fs[ri[inodekey(m1)]].size - 1), fs[ri[dentrykey(m1, str)]].ino ≠ ROOT_INO, fs[ri[inodekey(m1)]].size ≠ 0, fs[ri[inodekey(m1)]].directory, fs[ri[inodekey(m1)]].inode?, fo.inodes?, ro.inodes?, file-node-cons(fs, ri), log-cons(log, fs), orphans-cons(fs, ri, ro), replay-cons-strong(fs, ri, ro, fi, fo, log), ri-inj(fi), ri-inj(ri), ubifs-cons(fs, ri, ro, fi, fo, log), inodekey(m1) ∈ ri, ri[inodekey(m1)] ∈ fs, inodekey(fs[ri[dentrykey(m1, str)]].ino) ∈ ri, dentrykey(m1, str) ∈ ri, 1 ≤ fs[ri[inodekey(m1)]].size, ¬ fs[ri[inodekey(fs[ri[dentrykey(m1, str)]].ino)]].directory, ¬ inodekey(fs[ri[dentrykey(m1, str)]].ino) ∈ ro, ¬ inodekey(m1) ∈ ro, m3 = 0 → links(fs[ri[dentrykey(m1, str)]].ino, fs, ri) = ∅ ++ dentrykey(m1, str), fs[ri[inodekey(m1)]].nlink ≠ 0 ∨ m1 = ROOT_INO ⊦ ⟪nd0 := dentrynode(dentrykey(m1, str), 0); nd := inodenode(inodekey(m), md, false, m3, fs[ri[inodekey(m)]].nsubdirs, m2); aubifs_core_journal_add3#(nd1, nd0, nd, ri, fi, ro, fo; adr1, adr0, adr, fs, log; boolvar, err); if err = ESUCCESS then {aubifs_core_index_store#(inodekey(m1), adr1, fi, ro, fo, fs, log, boolvar; ri); aubifs_core_index_remove#(dentrykey(m1, str), fi, ro, fo, fs, log, boolvar; ri); aubifs_core_index_store#(inodekey(m), adr, fi, ro, fo, fs, log, boolvar; ri); if m3 = 0 then aubifs_core_orphans_insert#(inodekey(m), ri, fi, fo, fs, log, boolvar; ro); dent := negdentry(str); p_inode := mkinode(m1, nd1.meta, nd1.directory, nd1.nlink, nd1.nsubdirs, nd1.size); c_inode0 := mkinode(m, 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))

Rule argument

Additional information

Used simplifier rules: ⊦ 1 = m + 1 ↔ m = 0; (s)% ⊦ n ≥ m ↔ m ≤ n; (s)%c: ⊦ m + n = n + m; from specification nat-basic%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic% ⊦ m + 1 ≠ 0; (s)