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Proof step 311 from proof refine-unlink (previous step)

m5 + 1 = fs0[ri0[inodekey(m1)]].nlink, 0 = fs0[ri0[inodekey(m1)]].nsubdirs, fs0[ri0[dentrykey(m, str)]] = dentrynode(key, m1), fs0[ri0[inodekey(m)]] = inodenode(key0, md1, true, m2, m3, m0 + 1), dirs = abs-dirs(fs0, ri0), files = abs-files(fs0, ri0), old_dent = mkdentry(str, m1), p_inode0 = mkinode(m, md, true, m2, m3, m0 + 1), p_inode1 = mkinode(m1, md0, false, m5 + 1, 0, m6), adr1 ≠ adr3, adr1 ≠ adr2, adr2 ≠ adr3, m ≠ 0, m1 ≠ 0, m1 ≠ ROOT_INO, m5 ≠ 0, fo.inodes?, orphans(fs0, ri0).inodes?, afs-cons(abs-dirs(fs0, ri0), abs-files(fs0, ri0)), file-node-cons (fs0[adr1, inodenode(inodekey(m), md, true, m2, m3, m0)][adr2, dentrynode(dentrykey(m, str), 0)][adr3, inodenode(inodekey(m1), md0, false, m5, 0, m6)], (ri0[inodekey(m), adr1] -- dentrykey(m, str))[inodekey(m1), adr3]), file-node-cons(fs0, ri0), log-cons(log0, fs0), log-cons (log0, fs0[adr1, inodenode(inodekey(m), md, true, m2, m3, m0)][adr2, dentrynode(dentrykey(m, str), 0)][adr3, inodenode(inodekey(m1), md0, false, m5, 0, m6)]), orphans-cons(fs0, ri0, orphans(fs0, ri0)), orphans-cons (fs0[adr1, inodenode(inodekey(m), md, true, m2, m3, m0)][adr2, dentrynode(dentrykey(m, str), 0)][adr3, inodenode(inodekey(m1), md0, false, m5, 0, m6)], (ri0[inodekey(m), adr1] -- dentrykey(m, str))[inodekey(m1), adr3], orphans(fs0, ri0)), replay-cons-strong(fs0, ri0, orphans(fs0, ri0), fi, fo, log0), replay-cons-strong (fs0[adr1, inodenode(inodekey(m), md, true, m2, m3, m0)][adr2, dentrynode(dentrykey(m, str), 0)][adr3, inodenode(inodekey(m1), md0, false, m5, 0, m6)], (ri0[inodekey(m), adr1] -- dentrykey(m, str))[inodekey(m1), adr3], orphans(fs0, ri0), fi, fo, ((log0 + adr1 ') + adr2 ') + adr3 '), ri-cons(ri0, fs0), ri-inj(fi), ri-inj(ri0), ri-inj((ri0[inodekey(m), adr1] -- dentrykey(m, str))[inodekey(m1), adr3]), ubifs-cons(fs0, ri0, orphans(fs0, ri0), fi, fo, log0), ubifs-cons (fs0[adr1, inodenode(inodekey(m), md, true, m2, m3, m0)][adr2, dentrynode(dentrykey(m, str), 0)][adr3, inodenode(inodekey(m1), md0, false, m5, 0, m6)], (ri0[inodekey(m), adr1] -- dentrykey(m, str))[inodekey(m1), adr3], orphans(fs0, ri0), fi, fo, ((log0 + adr1 ') + adr2 ') + adr3 '), inodekey(m) ∈ ri0, ri0[inodekey(m)] ∈ fs0, inodekey(m1) ∈ ri0, ri0[dentrykey(m, str)] ∈ fs0, dentrykey(m, str) ∈ ri0, ¬ fs0[ri0[inodekey(m1)]].directory, ¬ adr1 ∈ fs0, ¬ adr2 ∈ fs0, ¬ adr3 ∈ fs0, asynced → boolvar0, links(m, abs-dirs(fs0, ri0)) ≠ ∅ ∨ m = ROOT_INO, m2 ≠ 0 ∨ m = ROOT_INO ⊦ ⟨afs_unlink#(; p_inode0, p_inode1, old_dent, err0, dirs, files; asynced)⟩ ( dirs = abs-dirs (fs0[adr1, inodenode(inodekey(m), md, true, m2, m3, m0)][adr2, dentrynode(dentrykey(m, str), 0)] [adr3, inodenode(inodekey(m1), md0, false, m5, 0, m6) ], (ri0[inodekey(m), adr1] -- dentrykey(m, str))[inodekey(m1), adr3]) ∧ files = abs-files (fs0[adr1, inodenode(inodekey(m), md, true, m2, m3, m0)][adr2, dentrynode(dentrykey(m, str), 0)] [adr3, inodenode(inodekey(m1), md0, false, m5, 0, m6) ], (ri0[inodekey(m), adr1] -- dentrykey(m, str))[inodekey(m1), adr3]) ∧ orphans (abs-dirs (fs0[adr1, inodenode(inodekey(m), md, true, m2, m3, m0)][adr2, dentrynode(dentrykey(m, str), 0)] [adr3, inodenode(inodekey(m1), md0, false, m5, 0, m6) ], (ri0[inodekey(m), adr1] -- dentrykey(m, str))[inodekey(m1), adr3]), abs-files (fs0[adr1, inodenode(inodekey(m), md, true, m2, m3, m0)][adr2, dentrynode(dentrykey(m, str), 0)] [adr3, inodenode(inodekey(m1), md0, false, m5, 0, m6) ], (ri0[inodekey(m), adr1] -- dentrykey(m, str))[inodekey(m1), adr3])) = abs-keys(orphans(fs0, ri0)) ∧ (asynced → boolvar) ∧ mkinode(m, md, true, m2, m3, m0) = p_inode0 ∧ mkinode(m1, md0, false, m5, 0, m6) = p_inode1 ∧ negdentry(str) = old_dent ∧ ESUCCESS = err0)

User applied rule insert program lemma

And obtained the following new goals

Rule argument

spec: afs-asm name: inv-unlink seq: afs-cons(dirs, files), pre-unlink(p_inode, c_inode, dent, dirs, files) ⊦ ⟪afs_unlink# (; p_inode, c_inode, dent, err, dirs, files; asynced)⟫ afs-cons(dirs, files) subst: [files, dirs, err, dent, c_inode, p_inode, asynced] → [files, dirs, err0, old_dent, p_inode1, p_inode0, asynced] flags: List([[1,0,0]])

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