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Proof step 470 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), p_ino = m, 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, abs-dirs(fs0, ri0)[p_ino, abs-dirs(fs0, ri0)[p_ino].entries:= (abs-dirs(fs0, ri0)[p_ino].entries -- str)][p_ino].size ≥ 1, asynced → boolvar0, links(m, abs-dirs(fs0, ri0)) ≠ ∅ ∨ m = ROOT_INO, m2 ≠ 0 ∨ m = ROOT_INO ⊦ adr1 = adr2, adr1 = adr3, adr2 = adr3, m = 0, m1 = ROOT_INO, m1 = 0, m5 = 0, mkdentry(str, m1).dentry?, fs0[ri0[inodekey(m1)]].directory, adr3 ∈ fs0, adr2 ∈ fs0, adr1 ∈ fs0

Heuristic simplifier applied rule simplifier

And closed the goal!

Rule argument

Additional information

Used simplifier rules: ⊦ mkdentry(str, m).dentry?; (s)% ⊦ n ≥ m ↔ m ≤ n; (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)