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Proof step 341 from proof refine-rmdir (previous step)

fs0[ri0[dentrykey(m, str)]] = dentrynode(key, m), fs0[ri0[inodekey(m)]] = inodenode(key2, md6, true, 1, m12 + 1, m10 + 1), dentrykeys(inodekey(m), ri0) = ∅, links(m, fs0, ri0) = ∅ ++ dentrykey(m, str), orphans(fs0, ri0).inodes?, fo.inodes?, afs-cons(abs-dirs(fs0, ri0)[m, mkdir(m10, md0, 0, m12, ∅)], abs-files(fs0, ri0)), afs-cons(abs-dirs(fs0, ri0), abs-files(fs0, ri0)), file-node-cons(fs0, ri0), file-node-cons (fs0[adr1, inodenode(inodekey(m), md, true, 1, m12, m10)][adr2, dentrynode(dentrykey(m, str), 0)] [adr3, inodenode(inodekey(m), md0, true, 0, m12 + 1, m10 + 1) ], (ri0[inodekey(m), adr1] -- dentrykey(m, str))[inodekey(m), adr3]), log-cons(log0, fs0), log-cons (log0, fs0[adr1, inodenode(inodekey(m), md, true, 1, m12, m10)][adr2, dentrynode(dentrykey(m, str), 0)] [adr3, inodenode(inodekey(m), md0, true, 0, m12 + 1, m10 + 1) ]), orphans-cons(fs0, ri0, orphans(fs0, ri0)), orphans-cons (fs0[adr1, inodenode(inodekey(m), md, true, 1, m12, m10)][adr2, dentrynode(dentrykey(m, str), 0)] [adr3, inodenode(inodekey(m), md0, true, 0, m12 + 1, m10 + 1) ], (ri0[inodekey(m), adr1] -- dentrykey(m, str))[inodekey(m), adr3], orphans(fs0, ri0) ++ inodekey(m)), replay-cons-strong(fs0, ri0, orphans(fs0, ri0), fi, fo, log0), replay-cons-strong (fs0[adr1, inodenode(inodekey(m), md, true, 1, m12, m10)][adr2, dentrynode(dentrykey(m, str), 0)] [adr3, inodenode(inodekey(m), md0, true, 0, m12 + 1, m10 + 1) ], (ri0[inodekey(m), adr1] -- dentrykey(m, str))[inodekey(m), adr3], orphans(fs0, ri0) ++ inodekey(m), fi, fo, ((log0 + adr1 ') + adr2 ') + adr3 '), ri-cons(ri0, fs0), ri-inj(ri0), ri-inj(fi), ri-inj((ri0[inodekey(m), adr1] -- dentrykey(m, str))[inodekey(m), adr3]), ubifs-cons(fs0, ri0, orphans(fs0, ri0), fi, fo, log0), ubifs-cons (fs0[adr1, inodenode(inodekey(m), md, true, 1, m12, m10)][adr2, dentrynode(dentrykey(m, str), 0)] [adr3, inodenode(inodekey(m), md0, true, 0, m12 + 1, m10 + 1) ], (ri0[inodekey(m), adr1] -- dentrykey(m, str))[inodekey(m), adr3], orphans(fs0, ri0) ++ inodekey(m), fi, fo, ((log0 + adr1 ') + adr2 ') + adr3 '), ri0[inodekey(m)] ∈ fs0, inodekey(m) ∈ ri0, ri0[dentrykey(m, str)] ∈ fs0, dentrykey(m, str) ∈ ri0, asynced0 → boolvar0, ∀ str0. ¬ dentrykey(m, str0) ∈ ri0 ∧ abs-children(m, fs0, ri0)[str0] = (∅)[str0] ⊦ # links(m, abs-dirs(fs0, ri0)) = 0, adr1 = adr3, adr1 = adr2, adr2 = adr3, links(m, abs-dirs(fs0, ri0)) = ∅, m = ROOT_INO, m = 0, mkinode(m, md0, true, 0, m12 + 1, m10 + 1) = mkinode(m, md0, true, 0, m12, m10), adr1 ∈ fs0, adr2 ∈ fs0, adr3 ∈ fs0

Proof step 341 from proof refine-rmdir (previous step)

Heuristic quantifier closing applied rule all left

And closed the goal!

Rule argument

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