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Proof step 254 from proof refine-rename-new-reparent (previous step)

fs0[ri0[dentrykey(m3, str)]] = dentrynode(key2, m), fs0[ri0[inodekey(m7)]] = inodenode(key1, md3, true, m5, m6, m8), fs0[ri0[inodekey(m3)]] = inodenode(key0, md2, true, m4, n0 + 1, m11 + 1), fs0[ri0[inodekey(m)]].directory, key.inode?, orphans(fs0, ri0).inodes?, fo.inodes?, afs-cons(abs-dirs(fs0, ri0), abs-files(fs0, ri0)), afs-cons (abs-dirs(fs0, ri0)[m3, mkdir(m11, md0, m4, n0, abs-children(m3, fs0, ri0) -- str)] [m7, mkdir(m8 + 1, md1, m5, m6 + 1, abs-children(m7, fs0, ri0)[str0, m]) ], 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 + 1, 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 + 1, 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 + 1, 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 + 1, 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 + 1, 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 '), 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, 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 ⊦ key.ino = ROOT_INO, key ∈ ri0 ∧ fs0[ri0[key]].nlink = 0 ↔ key ∈ (ri0 -- dentrykey(m3, str))[dentrykey(m7, str0), adr2][inodekey(m3), adr3][inodekey(m7), adr4] ∧ (adr4 = (inodekey(m7) = key ⊃ adr4;(inodekey(m3) = key ⊃ adr3;(dentrykey(m7, str0) = key ⊃ adr2;ri0[key]))) ⊃ inodenode(inodekey(m7), md1, true, m5, m6 + 1, m8 + 1) ;(adr3 = (inodekey(m7) = key ⊃ adr4;(inodekey(m3) = key ⊃ adr3;(dentrykey(m7, str0) = key ⊃ adr2;ri0[key]))) ⊃ inodenode(inodekey(m3), md0, true, m4, n0, m11) ;(adr2 = (inodekey(m7) = key ⊃ adr4;(inodekey(m3) = key ⊃ adr3;(dentrykey(m7, str0) = key ⊃ adr2;ri0[key]))) ⊃ dentrynode(dentrykey(m7, str0), m) ;(adr1 = (inodekey(m7) = key ⊃ adr4;(inodekey(m3) = key ⊃ adr3;(dentrykey(m7, str0) = key ⊃ adr2;ri0[key]))) ⊃ dentrynode(dentrykey(m3, str), 0) ;fs0[(inodekey(m7) = key ⊃ adr4;(inodekey(m3) = key ⊃ adr3;(dentrykey(m7, str0) = key ⊃ adr2;ri0[key])))] ) ) ) ) .nlink = 0, 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

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 255:
fs0[ri0[inodekey(m3)]] = inodenode(key0, md2, true, m4, n0 + 1, m11 + 1), fs0[ri0[inodekey(m7)]] = inodenode(key1, md3, true, m5, m6, m8), fs0[ri0[dentrykey(m3, str)]] = dentrynode(key2, m), key = inodekey(m0), fs0[ri0[inodekey(m)]].directory, key.inode?, fo.inodes?, orphans(fs0, ri0).inodes?, afs-cons (abs-dirs(fs0, ri0)[m3, mkdir(m11, md0, m4, n0, abs-children(m3, fs0, ri0) -- str)] [m7, mkdir(m8 + 1, md1, m5, m6 + 1, abs-children(m7, fs0, ri0)[str0, m]) ], abs-files(fs0, ri0)), afs-cons(abs-dirs(fs0, ri0), abs-files(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 + 1, m8 + 1) ], (ri0 -- dentrykey(m3, str))[dentrykey(m7, str0), adr2][inodekey(m3), adr3][inodekey(m7), adr4]), file-node-cons(fs0, ri0), 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 + 1, m8 + 1) ]), log-cons(log0, fs0), 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 + 1, m8 + 1) ], (ri0 -- dentrykey(m3, str))[dentrykey(m7, str0), adr2][inodekey(m3), adr3][inodekey(m7), adr4], orphans(fs0, ri0)), orphans-cons(fs0, ri0, orphans(fs0, ri0)), 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 + 1, 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 '), replay-cons-strong(fs0, ri0, orphans(fs0, ri0), fi, fo, log0), ri-inj((ri0 -- dentrykey(m3, str))[dentrykey(m7, str0), adr2][inodekey(m3), adr3][inodekey(m7), adr4]), ri-inj(fi), ri-inj(ri0), 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 + 1, 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 '), ubifs-cons(fs0, ri0, orphans(fs0, ri0), fi, fo, log0), inodekey(m7) ∈ ri0, dentrykey(m3, str) ∈ ri0, inodekey(m) ∈ ri0, inodekey(m3) ∈ ri0, ri0[inodekey(m7)] ∈ fs0, ri0[inodekey(m3)] ∈ fs0, ri0[dentrykey(m3, str)] ∈ fs0, boolvar3 → boolvar4, links(m7, abs-dirs(fs0, ri0)) ≠ ∅ ∨ m7 = ROOT_INO, links(m3, abs-dirs(fs0, ri0)) ≠ ∅ ∨ m3 = ROOT_INO, m5 ≠ 0 ∨ m7 = ROOT_INO, m4 ≠ 0 ∨ m3 = ROOT_INO ⊦ key ∈ ri0 ∧ fs0[ri0[key]].nlink = 0 ↔ key ∈ (ri0 -- dentrykey(m3, str))[dentrykey(m7, str0), adr2][inodekey(m3), adr3][inodekey(m7), adr4] ∧ (adr4 = (inodekey(m7) = key ⊃ adr4;(inodekey(m3) = key ⊃ adr3;(dentrykey(m7, str0) = key ⊃ adr2;ri0[key]))) ⊃ inodenode(inodekey(m7), md1, true, m5, m6 + 1, m8 + 1) ;(adr3 = (inodekey(m7) = key ⊃ adr4;(inodekey(m3) = key ⊃ adr3;(dentrykey(m7, str0) = key ⊃ adr2;ri0[key]))) ⊃ inodenode(inodekey(m3), md0, true, m4, n0, m11) ;(adr2 = (inodekey(m7) = key ⊃ adr4;(inodekey(m3) = key ⊃ adr3;(dentrykey(m7, str0) = key ⊃ adr2;ri0[key]))) ⊃ dentrynode(dentrykey(m7, str0), m) ;(adr1 = (inodekey(m7) = key ⊃ adr4;(inodekey(m3) = key ⊃ adr3;(dentrykey(m7, str0) = key ⊃ adr2;ri0[key]))) ⊃ dentrynode(dentrykey(m3, str), 0) ;fs0[(inodekey(m7) = key ⊃ adr4;(inodekey(m3) = key ⊃ adr3;(dentrykey(m7, str0) = key ⊃ adr2;ri0[key])))] ) ) ) ) .nlink = 0, adr1 = adr4, adr1 = adr3, adr1 = adr2, adr2 = adr4, adr2 = adr3, adr3 = adr4, m0 = ROOT_INO, m3 = 0, m3 = m7, m7 = 0, adr3 ∈ (ri0 -- dentrykey(m3, str))[dentrykey(m7, str0), adr2], dentrykey(m7, str0) ∈ ri0, adr1 ∈ fs0, adr2 ∈ fs0, adr3 ∈ fs0, adr4 ∈ fs0, adr2 ∈ ri0 -- dentrykey(m3, str), adr4 ∈ (ri0 -- dentrykey(m3, str))[dentrykey(m7, str0), adr2][inodekey(m3), adr3], m4 = 0 ∧ m3 ≠ ROOT_INO, m5 = 0 ∧ m7 ≠ ROOT_INO

Rule argument

spec: key name: elim-01 seq: ⊦ key.inode? → (m = key.ino ↔ key = inodekey(m)) subst: [key, m] → [key, m0]

Additional information

Used simplifier rules: ⊦ key.inode? → (m = key.ino ↔ key = inodekey(m)); (elim) Used terms: key, m0