[Imprint][Data Privacy Statement][E-Mail]

View long theorem info. View the proof. Back to main index. View the specification. View theorem base summary, View theorem base listing, the used properties by spec, the dependency list, the symbol table,

Proof step 573 from proof inv-rename-overwrite-keep-parent (previous step)

fs0[ri0[dentrykey(ino, str)]].key = dentrykey(ino, str), fs0[ri0[inodekey(m8)]] = inodenode(key1, md0, boolvar0, m0, m9, m10), fs0[ri0[dentrykey(m, str0)]] = dentrynode(key0, m8), fs0[ri0[inodekey(m)]] = inodenode(key2, md2, true, m1, m2, m4), fs0[ri0[dentrykey(ino, str)]].dentry?, fs0[ri0[inodekey(ino)]].directory, fo.inodes?, ro.inodes?, file-node-cons(fs0, ri0), log-cons(log0, fs0), orphans-cons(fs0, ri0, ro), replay-cons-strong(fs0, ri0, ro, fi, fo, log0), ri-inj(fi), ri-inj(ri0), ubifs-cons(fs0, ri0, ro, fi, fo, log0), ri0[inodekey(m)] ∈ fs0, inodekey(m) ∈ ri0, dentrykey(m, str0) ∈ ri0, inodekey(m8) ∈ ri0, ri0[dentrykey(m, str0)] ∈ fs0, ri0[inodekey(m8)] ∈ fs0, ri0[dentrykey(ino, str)] ∈ fs0, dentrykey(ino, str) ∈ ri0, inodekey(fs0[ri0[dentrykey(ino, str)]].ino) ∈ ri0, inodekey(ino) ∈ ri0, 1 ≤ m4, boolvar3 → 1 ≤ m2, m0 = 1 → links(m8, fs0, ri0) = ∅ ++ dentrykey(m, str0), boolvar0 → dentrykeys(inodekey(m8), ri0) = ∅, m1 ≠ 0 ∨ m = ROOT_INO, ¬ boolvar0 ∧ ¬ boolvar3 ∨ boolvar0 ∧ boolvar3 ∧ m3 = m10, ¬ boolvar0 ∧ ¬ boolvar2 ∨ boolvar0 ∧ boolvar2 ∧ m6 = m10 ⊦ 0 = m, 0 = m8, adr1 = adr4, adr1 = adr3, adr1 = adr2, adr2 = adr4, adr2 = adr3, adr3 = adr4, m0 = 0, m4 = 0, m8 = ROOT_INO, inodekey(m) ∈ ro, adr1 ∈ fs0, adr2 ∈ fs0, adr3 ∈ fs0, adr4 ∈ fs0, adr2 ∈ ri0 -- dentrykey(m, str0), inodekey(fs0[ri0[dentrykey(ino, str)]].ino) ∈ ro, inodekey(ino) ∈ ro, (adr4 = (dentrykey(m, str0) = dentrykey(ino, str) ⊃ adr2;ri0[dentrykey(ino, str)]) ⊃ inodenode(inodekey(m8), md1, boolvar2, m0, m9, m6) ;(adr3 = (dentrykey(m, str0) = dentrykey(ino, str) ⊃ adr2;ri0[dentrykey(ino, str)]) ⊃ inodenode(inodekey(m), md, true, m1, m2, m4) ;(adr2 = (dentrykey(m, str0) = dentrykey(ino, str) ⊃ adr2;ri0[dentrykey(ino, str)]) ⊃ dentrynode(dentrykey(m, str0), m8) ;(adr1 = (dentrykey(m, str0) = dentrykey(ino, str) ⊃ adr2;ri0[dentrykey(ino, str)]) ⊃ dentrynode(dentrykey(m, str0), 0) ;fs0[(dentrykey(m, str0) = dentrykey(ino, str) ⊃ adr2;ri0[dentrykey(ino, str)])] ) ) ) ) .dentry? ∧ ( (adr4 = (dentrykey(m, str0) = dentrykey(ino, str) ⊃ adr2;ri0[dentrykey(ino, str)]) ⊃ inodenode(inodekey(m8), md1, boolvar2, m0, m9, m6) ;(adr3 = (dentrykey(m, str0) = dentrykey(ino, str) ⊃ adr2;ri0[dentrykey(ino, str)]) ⊃ inodenode(inodekey(m), md, true, m1, m2, m4) ;(adr2 = (dentrykey(m, str0) = dentrykey(ino, str) ⊃ adr2;ri0[dentrykey(ino, str)]) ⊃ dentrynode(dentrykey(m, str0), m8) ;(adr1 = (dentrykey(m, str0) = dentrykey(ino, str) ⊃ adr2;ri0[dentrykey(ino, str)]) ⊃ dentrynode(dentrykey(m, str0), 0) ;fs0[(dentrykey(m, str0) = dentrykey(ino, str) ⊃ adr2;ri0[dentrykey(ino, str)])] ) ) ) ) .ino = m8 ∨ (adr4 = (dentrykey(m, str0) = dentrykey(ino, str) ⊃ adr2;ri0[dentrykey(ino, str)]) ⊃ inodenode(inodekey(m8), md1, boolvar2, m0, m9, m6) ;(adr3 = (dentrykey(m, str0) = dentrykey(ino, str) ⊃ adr2;ri0[dentrykey(ino, str)]) ⊃ inodenode(inodekey(m), md, true, m1, m2, m4) ;(adr2 = (dentrykey(m, str0) = dentrykey(ino, str) ⊃ adr2;ri0[dentrykey(ino, str)]) ⊃ dentrynode(dentrykey(m, str0), m8) ;(adr1 = (dentrykey(m, str0) = dentrykey(ino, str) ⊃ adr2;ri0[dentrykey(ino, str)]) ⊃ dentrynode(dentrykey(m, str0), 0) ;fs0[(dentrykey(m, str0) = dentrykey(ino, str) ⊃ adr2;ri0[dentrykey(ino, str)])] ) ) ) ) .ino = m ∨ inodekey ((adr4 = (dentrykey(m, str0) = dentrykey(ino, str) ⊃ adr2;ri0[dentrykey(ino, str)]) ⊃ inodenode(inodekey(m8), md1, boolvar2, m0, m9, m6) ;(adr3 = (dentrykey(m, str0) = dentrykey(ino, str) ⊃ adr2;ri0[dentrykey(ino, str)]) ⊃ inodenode(inodekey(m), md, true, m1, m2, m4) ;(adr2 = (dentrykey(m, str0) = dentrykey(ino, str) ⊃ adr2;ri0[dentrykey(ino, str)]) ⊃ dentrynode(dentrykey(m, str0), m8) ;(adr1 = (dentrykey(m, str0) = dentrykey(ino, str) ⊃ adr2;ri0[dentrykey(ino, str)]) ⊃ dentrynode(dentrykey(m, str0), 0) ;fs0[(dentrykey(m, str0) = dentrykey(ino, str) ⊃ adr2;ri0[dentrykey(ino, str)])] ) ) ) ) .ino) ∈ ri0) ∧ ¬ inodekey ((adr4 = (dentrykey(m, str0) = dentrykey(ino, str) ⊃ adr2;ri0[dentrykey(ino, str)]) ⊃ inodenode(inodekey(m8), md1, boolvar2, m0, m9, m6) ;(adr3 = (dentrykey(m, str0) = dentrykey(ino, str) ⊃ adr2;ri0[dentrykey(ino, str)]) ⊃ inodenode(inodekey(m), md, true, m1, m2, m4) ;(adr2 = (dentrykey(m, str0) = dentrykey(ino, str) ⊃ adr2;ri0[dentrykey(ino, str)]) ⊃ dentrynode(dentrykey(m, str0), m8) ;(adr1 = (dentrykey(m, str0) = dentrykey(ino, str) ⊃ adr2;ri0[dentrykey(ino, str)]) ⊃ dentrynode(dentrykey(m, str0), 0) ;fs0[(dentrykey(m, str0) = dentrykey(ino, str) ⊃ adr2;ri0[dentrykey(ino, str)])] ) ) ) ) .ino) ∈ ro ∧ (adr4 = (m8 = ino ⊃ adr4;(m = ino ⊃ adr3;ri0[inodekey(ino)])) ⊃ inodenode(inodekey(m8), md1, boolvar2, m0, m9, m6) ;(adr3 = (m8 = ino ⊃ adr4;(m = ino ⊃ adr3;ri0[inodekey(ino)])) ⊃ inodenode(inodekey(m), md, true, m1, m2, m4) ;(adr2 = (m8 = ino ⊃ adr4;(m = ino ⊃ adr3;ri0[inodekey(ino)])) ⊃ dentrynode(dentrykey(m, str0), m8) ;(adr1 = (m8 = ino ⊃ adr4;(m = ino ⊃ adr3;ri0[inodekey(ino)])) ⊃ dentrynode(dentrykey(m, str0), 0) ;fs0[(m8 = ino ⊃ adr4;(m = ino ⊃ adr3;ri0[inodekey(ino)]))] ) ) ) ) .directory

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 574:
fs0[ri0[inodekey(m)]] = inodenode(key2, md2, true, m1, m2, m4), fs0[ri0[dentrykey(m, str0)]] = dentrynode(key0, m8), fs0[ri0[inodekey(m8)]] = inodenode(key1, md0, boolvar0, m0, m9, m10), fs0[ri0[dentrykey(ino, str)]] = dentrynode(key, m5), key = dentrykey(ino, str), fs0[ri0[dentrykey(ino, str)]].dentry?, fs0[ri0[inodekey(ino)]].directory, ro.inodes?, fo.inodes?, file-node-cons(fs0, ri0), log-cons(log0, fs0), orphans-cons(fs0, ri0, ro), replay-cons-strong(fs0, ri0, ro, fi, fo, log0), ri-inj(ri0), ri-inj(fi), ubifs-cons(fs0, ri0, ro, fi, fo, log0), inodekey(ino) ∈ ri0, inodekey(m5) ∈ ri0, dentrykey(ino, str) ∈ ri0, ri0[dentrykey(ino, str)] ∈ fs0, ri0[inodekey(m8)] ∈ fs0, ri0[dentrykey(m, str0)] ∈ fs0, inodekey(m8) ∈ ri0, dentrykey(m, str0) ∈ ri0, inodekey(m) ∈ ri0, ri0[inodekey(m)] ∈ fs0, 1 ≤ m4, boolvar0 → dentrykeys(inodekey(m8), ri0) = ∅, m0 = 1 → links(m8, fs0, ri0) = ∅ ++ dentrykey(m, str0), boolvar3 → 1 ≤ m2, ¬ boolvar0 ∧ ¬ boolvar2 ∨ boolvar0 ∧ boolvar2 ∧ m6 = m10, ¬ boolvar0 ∧ ¬ boolvar3 ∨ boolvar0 ∧ boolvar3 ∧ m3 = m10, m1 ≠ 0 ∨ m = ROOT_INO ⊦ 0 = m8, 0 = m, adr1 = adr2, adr1 = adr3, adr1 = adr4, adr2 = adr3, adr2 = adr4, adr3 = adr4, m0 = 0, m4 = 0, m8 = ROOT_INO, inodekey(ino) ∈ ro, inodekey(m5) ∈ ro, adr2 ∈ ri0 -- dentrykey(m, str0), adr4 ∈ fs0, adr3 ∈ fs0, adr2 ∈ fs0, adr1 ∈ fs0, inodekey(m) ∈ ro, (adr4 = (dentrykey(m, str0) = dentrykey(ino, str) ⊃ adr2;ri0[dentrykey(ino, str)]) ⊃ inodenode(inodekey(m8), md1, boolvar2, m0, m9, m6) ;(adr3 = (dentrykey(m, str0) = dentrykey(ino, str) ⊃ adr2;ri0[dentrykey(ino, str)]) ⊃ inodenode(inodekey(m), md, true, m1, m2, m4) ;(adr2 = (dentrykey(m, str0) = dentrykey(ino, str) ⊃ adr2;ri0[dentrykey(ino, str)]) ⊃ dentrynode(dentrykey(m, str0), m8) ;(adr1 = (dentrykey(m, str0) = dentrykey(ino, str) ⊃ adr2;ri0[dentrykey(ino, str)]) ⊃ dentrynode(dentrykey(m, str0), 0) ;fs0[(dentrykey(m, str0) = dentrykey(ino, str) ⊃ adr2;ri0[dentrykey(ino, str)])] ) ) ) ) .dentry? ∧ ( (adr4 = (dentrykey(m, str0) = dentrykey(ino, str) ⊃ adr2;ri0[dentrykey(ino, str)]) ⊃ inodenode(inodekey(m8), md1, boolvar2, m0, m9, m6) ;(adr3 = (dentrykey(m, str0) = dentrykey(ino, str) ⊃ adr2;ri0[dentrykey(ino, str)]) ⊃ inodenode(inodekey(m), md, true, m1, m2, m4) ;(adr2 = (dentrykey(m, str0) = dentrykey(ino, str) ⊃ adr2;ri0[dentrykey(ino, str)]) ⊃ dentrynode(dentrykey(m, str0), m8) ;(adr1 = (dentrykey(m, str0) = dentrykey(ino, str) ⊃ adr2;ri0[dentrykey(ino, str)]) ⊃ dentrynode(dentrykey(m, str0), 0) ;fs0[(dentrykey(m, str0) = dentrykey(ino, str) ⊃ adr2;ri0[dentrykey(ino, str)])] ) ) ) ) .ino = m8 ∨ (adr4 = (dentrykey(m, str0) = dentrykey(ino, str) ⊃ adr2;ri0[dentrykey(ino, str)]) ⊃ inodenode(inodekey(m8), md1, boolvar2, m0, m9, m6) ;(adr3 = (dentrykey(m, str0) = dentrykey(ino, str) ⊃ adr2;ri0[dentrykey(ino, str)]) ⊃ inodenode(inodekey(m), md, true, m1, m2, m4) ;(adr2 = (dentrykey(m, str0) = dentrykey(ino, str) ⊃ adr2;ri0[dentrykey(ino, str)]) ⊃ dentrynode(dentrykey(m, str0), m8) ;(adr1 = (dentrykey(m, str0) = dentrykey(ino, str) ⊃ adr2;ri0[dentrykey(ino, str)]) ⊃ dentrynode(dentrykey(m, str0), 0) ;fs0[(dentrykey(m, str0) = dentrykey(ino, str) ⊃ adr2;ri0[dentrykey(ino, str)])] ) ) ) ) .ino = m ∨ inodekey ((adr4 = (dentrykey(m, str0) = dentrykey(ino, str) ⊃ adr2;ri0[dentrykey(ino, str)]) ⊃ inodenode(inodekey(m8), md1, boolvar2, m0, m9, m6) ;(adr3 = (dentrykey(m, str0) = dentrykey(ino, str) ⊃ adr2;ri0[dentrykey(ino, str)]) ⊃ inodenode(inodekey(m), md, true, m1, m2, m4) ;(adr2 = (dentrykey(m, str0) = dentrykey(ino, str) ⊃ adr2;ri0[dentrykey(ino, str)]) ⊃ dentrynode(dentrykey(m, str0), m8) ;(adr1 = (dentrykey(m, str0) = dentrykey(ino, str) ⊃ adr2;ri0[dentrykey(ino, str)]) ⊃ dentrynode(dentrykey(m, str0), 0) ;fs0[(dentrykey(m, str0) = dentrykey(ino, str) ⊃ adr2;ri0[dentrykey(ino, str)])] ) ) ) ) .ino) ∈ ri0) ∧ ¬ inodekey ((adr4 = (dentrykey(m, str0) = dentrykey(ino, str) ⊃ adr2;ri0[dentrykey(ino, str)]) ⊃ inodenode(inodekey(m8), md1, boolvar2, m0, m9, m6) ;(adr3 = (dentrykey(m, str0) = dentrykey(ino, str) ⊃ adr2;ri0[dentrykey(ino, str)]) ⊃ inodenode(inodekey(m), md, true, m1, m2, m4) ;(adr2 = (dentrykey(m, str0) = dentrykey(ino, str) ⊃ adr2;ri0[dentrykey(ino, str)]) ⊃ dentrynode(dentrykey(m, str0), m8) ;(adr1 = (dentrykey(m, str0) = dentrykey(ino, str) ⊃ adr2;ri0[dentrykey(ino, str)]) ⊃ dentrynode(dentrykey(m, str0), 0) ;fs0[(dentrykey(m, str0) = dentrykey(ino, str) ⊃ adr2;ri0[dentrykey(ino, str)])] ) ) ) ) .ino) ∈ ro ∧ (adr4 = (m8 = ino ⊃ adr4;(m = ino ⊃ adr3;ri0[inodekey(ino)])) ⊃ inodenode(inodekey(m8), md1, boolvar2, m0, m9, m6) ;(adr3 = (m8 = ino ⊃ adr4;(m = ino ⊃ adr3;ri0[inodekey(ino)])) ⊃ inodenode(inodekey(m), md, true, m1, m2, m4) ;(adr2 = (m8 = ino ⊃ adr4;(m = ino ⊃ adr3;ri0[inodekey(ino)])) ⊃ dentrynode(dentrykey(m, str0), m8) ;(adr1 = (m8 = ino ⊃ adr4;(m = ino ⊃ adr3;ri0[inodekey(ino)])) ⊃ dentrynode(dentrykey(m, str0), 0) ;fs0[(m8 = ino ⊃ adr4;(m = ino ⊃ adr3;ri0[inodekey(ino)]))] ) ) ) ) .directory

Rule argument

spec: node name: elim-02 seq: ⊦ nd.dentry? → (key = nd.key ∧ m = nd.ino ↔ nd = dentrynode(key, m)) subst: [nd, key, m] → [fs0[ri0[dentrykey(ino, str)]], key, m5]

Additional information

Used simplifier rules: ⊦ nd.dentry? → (key = nd.key ∧ m = nd.ino ↔ nd = dentrynode(key, m)); (elim) Used terms: fs0[ri0[dentrykey(ino, str)]], key, m5