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Proof step 255 from proof refine-rmdir (previous step)

fs0[ri0[inodekey(m4)]] = inodenode(key2, md3, true, 1, m12, m10), fs0[ri0[dentrykey(m, str)]] = dentrynode(key, m4), fs0[ri0[inodekey(m)]] = inodenode(key0, md1, true, m3, m0 + 1, m1 + 1), abs-children(m4, fs0, ri0) = ∅, dentrykeys(inodekey(m4), ri0) = ∅, links(m4, fs0, ri0) = ∅ ++ dentrykey(m, str), orphans(fs0, ri0).inodes?, fo.inodes?, afs-cons(abs-dirs(fs0, ri0), abs-files(fs0, ri0)), afs-cons(abs-dirs(fs0, ri0)[m, mkdir(m1, md, m3, m0, abs-children(m, fs0, ri0) -- str)][m4, mkdir(m10, md0, 0, m12, ∅)], abs-files(fs0, ri0)), file-node-cons(fs0, ri0), file-node-cons (fs0[adr1, inodenode(inodekey(m), md, true, m3, m0, m1)][adr2, dentrynode(dentrykey(m, str), 0)] [adr3, inodenode(inodekey(m4), md0, true, 0, m12, m10) ], (ri0[inodekey(m), adr1] -- dentrykey(m, str))[inodekey(m4), adr3]), log-cons(log0, fs0), log-cons (log0, fs0[adr1, inodenode(inodekey(m), md, true, m3, m0, m1)][adr2, dentrynode(dentrykey(m, str), 0)] [adr3, inodenode(inodekey(m4), md0, true, 0, m12, m10) ]), orphans-cons(fs0, ri0, orphans(fs0, ri0)), orphans-cons (fs0[adr1, inodenode(inodekey(m), md, true, m3, m0, m1)][adr2, dentrynode(dentrykey(m, str), 0)] [adr3, inodenode(inodekey(m4), md0, true, 0, m12, m10) ], (ri0[inodekey(m), adr1] -- dentrykey(m, str))[inodekey(m4), adr3], orphans(fs0, ri0) ++ inodekey(m4)), replay-cons-strong(fs0, ri0, orphans(fs0, ri0), fi, fo, log0), replay-cons-strong (fs0[adr1, inodenode(inodekey(m), md, true, m3, m0, m1)][adr2, dentrynode(dentrykey(m, str), 0)] [adr3, inodenode(inodekey(m4), md0, true, 0, m12, m10) ], (ri0[inodekey(m), adr1] -- dentrykey(m, str))[inodekey(m4), adr3], orphans(fs0, ri0) ++ inodekey(m4), 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(m4), adr3]), ubifs-cons(fs0, ri0, orphans(fs0, ri0), fi, fo, log0), ubifs-cons (fs0[adr1, inodenode(inodekey(m), md, true, m3, m0, m1)][adr2, dentrynode(dentrykey(m, str), 0)] [adr3, inodenode(inodekey(m4), md0, true, 0, m12, m10) ], (ri0[inodekey(m), adr1] -- dentrykey(m, str))[inodekey(m4), adr3], orphans(fs0, ri0) ++ inodekey(m4), fi, fo, ((log0 + adr1 ') + adr2 ') + adr3 '), inodekey(m) ∈ ri0, ri0[inodekey(m)] ∈ fs0, ri0[inodekey(m4)] ∈ fs0, inodekey(m4) ∈ ri0, ri0[dentrykey(m, str)] ∈ fs0, dentrykey(m, str) ∈ ri0, inodekey(ino) ∈ ri0, asynced0 → boolvar0, links(m, abs-dirs(fs0, ri0)) ≠ ∅ ∨ m = ROOT_INO, m3 ≠ 0 ∨ m = ROOT_INO ⊦ fs0[ri0[inodekey(ino)]].directory ↔ inodekey(ino) ∈ (ri0[inodekey(m), adr1] -- dentrykey(m, str))[inodekey(m4), adr3] ∧ (adr1 = ri0[inodekey(ino)] ⊃ inodenode(inodekey(m), md, true, m3, m0, m1);fs0[ri0[inodekey(ino)]]).directory, adr1 = adr3, adr1 = adr2, adr2 = ri0[inodekey(ino)], adr2 = adr3, adr3 = ri0[inodekey(ino)], ino = m4, m = ino, m = 0, m4 = m, m4 = 0, m4 = ROOT_INO, adr1 ∈ fs0, adr2 ∈ fs0, adr3 ∈ fs0, m3 = 0 ∧ m ≠ ROOT_INO

Heuristic nonsplitting cut applied rule cut formula

And closed the goal!

Rule argument

fma: adr1 = ri0[inodekey(ino)]

Additional information

Used simplifier rules: ⊦ key ∈ ri[key0, adr] ↔ key = key0 ∨ key ∈ ri; (ws)% ⊦ inodekey(m) = inodekey(m0) ↔ m = m0; (s)% ⊦ key ∈ ri -- key0 ↔ key ≠ key0 ∧ key ∈ ri; (s)% ⊦ inodekey(m) ≠ dentrykey(m0, str); (s)% ⊦ ¬ adr ∈ fs → fs[adr] = (∅)[adr]; (s)% ⊦ inodenode(key, md, boolvar, m, m0, m1).directory ↔ boolvar; (s)% ⊦ key ∈ ri ∧ ri-cons(ri, fs) → ri[key] ∈ fs; (ss) Used formulas: adr1 = ri0[inodekey(ino)]