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Proof step 19 from proof inv-rmdir (previous step)

1 = fs[ri[inodekey(fs[ri[dentrykey(m0, str)]].ino)]].nlink, dentrykeys(inodekey(fs[ri[dentrykey(m0, str)]].ino), ri) = ∅, links(fs[ri[dentrykey(m0, str)]].ino, fs, ri) = ∅ ++ dentrykey(m0, str), m = fs[ri[dentrykey(m0, str)]].ino, m1 = fs[ri[inodekey(fs[ri[dentrykey(m0, str)]].ino)]].nsubdirs, m2 = fs[ri[inodekey(fs[ri[dentrykey(m0, str)]].ino)]].size, m3 = fs[ri[inodekey(m0)]].nlink, m4 = fs[ri[inodekey(m0)]].nsubdirs, m5 = fs[ri[inodekey(m0)]].size, fs[ri[dentrykey(m0, str)]].ino ≠ ROOT_INO, fs[ri[inodekey(m0)]].nsubdirs ≠ 0, fs[ri[inodekey(m0)]].size ≠ 0, fs[ri[inodekey(fs[ri[dentrykey(m0, str)]].ino)]].directory, fs[ri[inodekey(m0)]].directory, 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(fs[ri[dentrykey(m0, str)]].ino) ∈ ri, dentrykey(m0, str) ∈ ri, inodekey(m0) ∈ ri, 1 ≤ fs[ri[inodekey(m0)]].nsubdirs, 1 ≤ fs[ri[inodekey(m0)]].size, ¬ inodekey(m0) ∈ ro, ¬ inodekey(fs[ri[dentrykey(m0, str)]].ino) ∈ ro, fs[ri[inodekey(m0)]].nlink ≠ 0 ∨ m0 = ROOT_INO ⊦ ⟪aubifs_core_journal_add3# (inodenode(inodekey(m0), md0, true, m3, m4 - 1, m5 - 1), dentrynode(dentrykey(m0, str), 0), inodenode(inodekey(m), md, true, 0, m1, m2), ri, fi, ro, fo ; adr1, adr0, adr, fs, log ; boolvar, err); if err = ESUCCESS then {aubifs_core_index_store#(inodekey(m0), adr1, fi, ro, fo, fs, log, boolvar; ri); aubifs_core_index_remove#(dentrykey(m0, str), fi, ro, fo, fs, log, boolvar; ri); aubifs_core_index_store#(inodekey(m), adr, fi, ro, fo, fs, log, boolvar; ri); aubifs_core_orphans_insert#(inodekey(m), ri, fi, fo, fs, log, boolvar; ro); dent := negdentry(str); p_inode0 := mkinode (m0, inodenode(inodekey(m0), md0, true, m3, m4 - 1, m5 - 1).meta, inodenode(inodekey(m0), md0, true, m3, m4 - 1, m5 - 1).directory, inodenode(inodekey(m0), md0, true, m3, m4 - 1, m5 - 1).nlink, inodenode(inodekey(m0), md0, true, m3, m4 - 1, m5 - 1).nsubdirs, inodenode(inodekey(m0), md0, true, m3, m4 - 1, m5 - 1).size); c_inode0 := mkinode (m, inodenode(inodekey(m), md, true, 0, m1, m2).meta, inodenode(inodekey(m), md, true, 0, m1, m2).directory, inodenode(inodekey(m), md, true, 0, m1, m2).nlink, inodenode(inodekey(m), md, true, 0, m1, m2).nsubdirs, inodenode(inodekey(m), md, true, 0, m1, m2).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))

Heuristic unfold applied rule call right

And obtained the following new goals

Proof step 20:
1 = fs[ri[inodekey(fs[ri[dentrykey(m0, str)]].ino)]].nlink, adr4 = adr1, dentrykeys(inodekey(fs[ri[dentrykey(m0, str)]].ino), ri) = ∅, links(fs[ri[dentrykey(m0, str)]].ino, fs, ri) = ∅ ++ dentrykey(m0, str), m = fs[ri[dentrykey(m0, str)]].ino, m1 = fs[ri[inodekey(fs[ri[dentrykey(m0, str)]].ino)]].nsubdirs, m2 = fs[ri[inodekey(fs[ri[dentrykey(m0, str)]].ino)]].size, m3 = fs[ri[inodekey(m0)]].nlink, m4 = fs[ri[inodekey(m0)]].nsubdirs, m5 = fs[ri[inodekey(m0)]].size, nd = inodenode(inodekey(m), md, true, 0, m1, m2), nd0 = dentrynode(dentrykey(m0, str), 0), nd1 = inodenode(inodekey(m0), md0, true, m3, m4 - 1, m5 - 1), fs[ri[inodekey(m0)]].directory, fs[ri[inodekey(fs[ri[dentrykey(m0, str)]].ino)]].directory, ro.inodes?, fo.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(ri), ri-inj(fi), ubifs-cons(fs, ri, ro, fi, fo, log), inodekey(m0) ∈ ri, dentrykey(m0, str) ∈ ri, inodekey(fs[ri[dentrykey(m0, str)]].ino) ∈ ri, 1 ≤ fs[ri[inodekey(m0)]].size, 1 ≤ fs[ri[inodekey(m0)]].nsubdirs, m4 ≥ 1, m5 ≥ 1, fs[ri[inodekey(m0)]].nlink ≠ 0 ∨ m0 = ROOT_INO ⊦ ⟪if ri-cons(ri, fs) ∧ node-cons(nd1.key, nd1) ∧ node-cons(nd0.key, nd0) ∧ node-cons(nd.key, nd) then { choose adr1, adr2, adr3 with new(adr1 ' + (adr2 ' + adr3), fs) ∧ ¬ dups(adr1 ' + adr2 ' + adr3 ') in {adr4 := adr1, adr0 := adr2, adr := adr3; fs := fs[adr4, nd1][adr0, nd0][adr, nd], log := ((log + adr4) + adr0) + adr, err := ESUCCESS} ifnone err := ENOSPC or {fail#(; ; err); adr4 := ?, adr0 := ?, adr := ?}; boolvar := ?} else abort; if err = ESUCCESS then {aubifs_core_index_store#(inodekey(m0), adr4, fi, ro, fo, fs, log, boolvar; ri); aubifs_core_index_remove#(dentrykey(m0, str), fi, ro, fo, fs, log, boolvar; ri); aubifs_core_index_store#(inodekey(m), adr, fi, ro, fo, fs, log, boolvar; ri); aubifs_core_orphans_insert#(inodekey(m), ri, fi, fo, fs, log, boolvar; ro); dent := negdentry(str); p_inode0 := mkinode (m0, inodenode(inodekey(m0), md0, true, m3, m4 - 1, m5 - 1).meta, inodenode(inodekey(m0), md0, true, m3, m4 - 1, m5 - 1).directory, inodenode(inodekey(m0), md0, true, m3, m4 - 1, m5 - 1).nlink, inodenode(inodekey(m0), md0, true, m3, m4 - 1, m5 - 1).nsubdirs, inodenode(inodekey(m0), md0, true, m3, m4 - 1, m5 - 1).size); c_inode0 := mkinode (m, inodenode(inodekey(m), md, true, 0, m1, m2).meta, inodenode(inodekey(m), md, true, 0, m1, m2).directory, inodenode(inodekey(m), md, true, 0, m1, m2).nlink, inodenode(inodekey(m), md, true, 0, m1, m2).nsubdirs, inodenode(inodekey(m), md, true, 0, m1, m2).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(m0, str)]].ino = ROOT_INO, fs[ri[inodekey(m0)]].nsubdirs = 0, fs[ri[inodekey(m0)]].size = 0, inodekey(m0) ∈ ro, inodekey(fs[ri[dentrykey(m0, str)]].ino) ∈ ro

Rule argument

pos: right 1

Additional information

Used simplifier rules: aubifs_core_journal_add3# (ND1, ND2, ND3, RI, FI, RO, FO ; ADR1, ADR2, ADR3, FS, LOG ; CSYNCED, ERR ) {if ri-cons(RI, FS) ∧ node-cons(ND1.key, ND1) ∧ node-cons(ND2.key, ND2) ∧ node-cons(ND3.key, ND3) then { choose adr1, adr2, adr3 with new(adr1 ' + (adr2 ' + adr3), FS) ∧ ¬ dups(adr1 ' + adr2 ' + adr3 ') in {ADR1 := adr1, ADR2 := adr2, ADR3 := adr3; FS := FS[ADR1, ND1][ADR2, ND2][ADR3, ND3], LOG := ((LOG + ADR1) + ADR2) + ADR3, ERR := ESUCCESS} ifnone ERR := ENOSPC or {fail#(; ; ERR); ADR1 := ?, ADR2 := ?, ADR3 := ?}; CSYNCED := ?} else abort };% ⊦ n ≥ m ↔ m ≤ n; (s)