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Proof step 284 from proof refine-rename-new-reparent (previous step)

boolvar0 ↔ false, boolvar ↔ false, fs0[ri0[inodekey(m3)]] = inodenode(key0, md2, true, m4, n0 + (boolvar1 ⊃ 1;0), m11 + 1), fs0[ri0[dentrykey(m3, str)]] = dentrynode(key2, m), fs0[ri0[inodekey(m7)]] = inodenode(key1, md3, true, m5, m6, m8), dirs = dirs0[old_ino, dirs0[old_ino].size:= (dirs0[old_ino].size - 1)], dirs0 = abs-dirs(fs0, ri0)[old_ino, abs-dirs(fs0, ri0)[old_ino].entries:= (abs-dirs(fs0, ri0)[old_ino].entries -- str)], new_ino = m7, old_dent = mkdentry(str, m), old_ino = m3, old_dent.dentry?, orphans(fs0, ri0).inodes?, fo.inodes?, afs-cons(abs-dirs(fs0, ri0), abs-files(fs0, ri0)), file-node-cons(fs0, ri0), file-node-cons (fs0[adr1, dentrynode(dentrykey(m3, str), 0)][adr2, dentrynode(dentrykey(m7, str0), m)][adr3, inodenode(inodekey(m3), md0, true, m4, n0, m11)] [adr4, inodenode(inodekey(m7), md1, true, m5, m6 + (boolvar1 ⊃ 1;0), m8 + 1) ], (ri0 -- dentrykey(m3, str))[dentrykey(m7, str0), adr2][inodekey(m3), adr3][inodekey(m7), adr4]), log-cons(log0, fs0), log-cons (log0, fs0[adr1, dentrynode(dentrykey(m3, str), 0)][adr2, dentrynode(dentrykey(m7, str0), m)][adr3, inodenode(inodekey(m3), md0, true, m4, n0, m11)] [adr4, inodenode(inodekey(m7), md1, true, m5, m6 + (boolvar1 ⊃ 1;0), m8 + 1) ]), orphans-cons(fs0, ri0, orphans(fs0, ri0)), orphans-cons (fs0[adr1, dentrynode(dentrykey(m3, str), 0)][adr2, dentrynode(dentrykey(m7, str0), m)][adr3, inodenode(inodekey(m3), md0, true, m4, n0, m11)] [adr4, inodenode(inodekey(m7), md1, true, m5, m6 + (boolvar1 ⊃ 1;0), m8 + 1) ], (ri0 -- dentrykey(m3, str))[dentrykey(m7, str0), adr2][inodekey(m3), adr3][inodekey(m7), adr4], orphans(fs0, ri0)), replay-cons-strong(fs0, ri0, orphans(fs0, ri0), fi, fo, log0), replay-cons-strong (fs0[adr1, dentrynode(dentrykey(m3, str), 0)][adr2, dentrynode(dentrykey(m7, str0), m)][adr3, inodenode(inodekey(m3), md0, true, m4, n0, m11)] [adr4, inodenode(inodekey(m7), md1, true, m5, m6 + (boolvar1 ⊃ 1;0), m8 + 1) ], (ri0 -- dentrykey(m3, str))[dentrykey(m7, str0), adr2][inodekey(m3), adr3][inodekey(m7), adr4], orphans(fs0, ri0), fi, fo, (((log0 + adr1 ') + adr2 ') + adr3 ') + adr4 '), ri-inj(ri0), ri-inj(fi), ri-inj((ri0 -- dentrykey(m3, str))[dentrykey(m7, str0), adr2][inodekey(m3), adr3][inodekey(m7), adr4]), ubifs-cons(fs0, ri0, orphans(fs0, ri0), fi, fo, log0), ubifs-cons (fs0[adr1, dentrynode(dentrykey(m3, str), 0)][adr2, dentrynode(dentrykey(m7, str0), m)][adr3, inodenode(inodekey(m3), md0, true, m4, n0, m11)] [adr4, inodenode(inodekey(m7), md1, true, m5, m6 + (boolvar1 ⊃ 1;0), m8 + 1) ], (ri0 -- dentrykey(m3, str))[dentrykey(m7, str0), adr2][inodekey(m3), adr3][inodekey(m7), adr4], orphans(fs0, ri0), fi, fo, (((log0 + adr1 ') + adr2 ') + adr3 ') + adr4 '), old_dent.ino ∈ dirs, ri0[dentrykey(m3, str)] ∈ fs0, ri0[inodekey(m3)] ∈ fs0, ri0[inodekey(m7)] ∈ fs0, inodekey(m3) ∈ ri0, inodekey(m) ∈ ri0, dentrykey(m3, str) ∈ ri0, inodekey(m7) ∈ ri0, dirs0[old_ino].size ≥ 1, dirs[old_ino].nsubdirs ≥ 1, boolvar3 → boolvar4, m4 ≠ 0 ∨ m3 = ROOT_INO, m5 ≠ 0 ∨ m7 = ROOT_INO, links(m3, abs-dirs(fs0, ri0)) ≠ ∅ ∨ m3 = ROOT_INO, links(m7, abs-dirs(fs0, ri0)) ≠ ∅ ∨ m7 = ROOT_INO, ¬ fs0[ri0[inodekey(m)]].directory ∧ ¬ boolvar1 ∧ m0 = fs0[ri0[inodekey(m)]].nlink ∧ m1 = fs0[ri0[inodekey(m)]].nsubdirs ∨ fs0[ri0[inodekey(m)]].directory ∧ boolvar1 ∧ m0 = fs0[ri0[inodekey(m)]].nlink ∧ m1 = fs0[ri0[inodekey(m)]].nsubdirs ∧ m2 = fs0[ri0[inodekey(m)]].size, fs0[ri0[inodekey(m)]].directory ∧ m0 = fs0[ri0[inodekey(m)]].nlink ∧ m2 = fs0[ri0[inodekey(m)]].size ∧ m1 = fs0[ri0[inodekey(m)]].nsubdirs ∧ boolvar1 ∨ ¬ fs0[ri0[inodekey(m)]].directory ∧ m0 = fs0[ri0[inodekey(m)]].nlink ∧ m1 = 0 ∧ ¬ boolvar1 ⊦ adr1 = adr2, adr1 = adr3, adr1 = adr4, adr2 = adr3, adr2 = adr4, adr3 = adr4, m3 = m7, m3 = 0, m7 = 0, adr4 ∈ (ri0 -- dentrykey(m3, str))[dentrykey(m7, str0), adr2][inodekey(m3), adr3], adr2 ∈ ri0 -- dentrykey(m3, str), adr4 ∈ fs0, adr3 ∈ fs0, adr2 ∈ fs0, adr1 ∈ fs0, dentrykey(m7, str0) ∈ ri0, adr3 ∈ (ri0 -- dentrykey(m3, str))[dentrykey(m7, str0), adr2], m5 = 0 ∧ m7 ≠ ROOT_INO, m4 = 0 ∧ m3 ≠ ROOT_INO, dirs[old_ino].nsubdirs ≥ 1 ∧ dirs[old_ino].nsubdirs ≥ 1 ∧ dirs[old_ino].nsubdirs ≥ 1 ∧ old_dent.dentry?

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Rule argument

Additional information

Used simplifier rules: ⊦ m ≤ m + n; (s)% ⊦ mkdir(m, md, m0, m1, entries).nsubdirs = m1; (s)% ⊦ n + 0 = n; (s)% ⊦ n ≤ m → m + n0 - n = (m - n) + n0; (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)% ⊦ inodenode(key, md, boolvar, m, m0, m1).nsubdirs = m0; (s)% ⊦ inodenode(key, md, boolvar, m, m0, m1).nlink = m; (s)% ⊦ inodenode(key, md, boolvar, m, m0, m1).meta = md; (s)% ⊦ inodenode(key, md, boolvar, m, m0, m1).size = m1; (s)% ⊦ inodenode(key, md, boolvar, m, m0, m1).directory ↔ boolvar; (s)%not-zero: 0 < n ⊦ (* n) ≤ m → m ≠ 0; (forward) from specification nat% ⊦ m < 1 ↔ m = 0; (s)% ⊦ m ≤ n ↔ ¬ n < m; (ss)% ⊦ (ad.entries:= entries).nsubdirs = ad.nsubdirs; (s)% ⊦ (ad.size:= m).nsubdirs = ad.nsubdirs; (s)% ⊦ (ad.entries:= entries).size = ad.size; (s)%⊦ dentrykey(ino, str) ∈ ri ∧ ubifs-cons(fs, ri, ro, fi, fo, log) → fs[ri[inodekey(ino)]].directory; (ss)% ⊦ mkdentry(str, m).dentry?; (s)% ⊦ ino ∈ dirs[ino0, ad] ↔ ino ∈ dirs; (s)% ⊦ mkdentry(str, m).ino = m; (s)% ⊦ n ≥ m ↔ m ≤ n; (s)%⊦ mkdir(m, md, m0, m1, entries).size:= m2 = mkdir(m2, md, m0, m1, entries); (s)% ⊦ mkdir(m, md, m0, m1, entries).size = m; (s)% ⊦ dirs[ino, ad][ino, ad0] = dirs[ino, ad0]; (s)%⊦ mkdir(m, md, m0, m1, entries).entries:= entries0 = mkdir(m, md, m0, m1, entries0); (s)% ⊦ mkdir(m, md, m0, m1, entries).entries = entries; (s)%⊦ abs-dir(ino, fs, ri) = mkdir (fs[ri[inodekey(ino)]].size, fs[ri[inodekey(ino)]].meta, fs[ri[inodekey(ino)]].nlink, fs[ri[inodekey(ino)]].nsubdirs, abs-children(ino, fs, ri)); (s)%⊦ inodekey(ino) ∈ ri ∧ fs[ri[inodekey(ino)]].directory → abs-dirs(fs, ri)[ino] = abs-dir(ino, fs, ri); (s)%⊦ ino ∈ abs-dirs(fs, ri) ↔ inodekey(ino) ∈ ri ∧ fs[ri[inodekey(ino)]].directory; (s)% ⊦ dirs[ino, ad][ino0] = (ino0 = ino ∧ ino ∈ dirs ⊃ ad;dirs[ino0]); (s)