[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 232 from proof inv-rename-overwrite-keep-parent (previous step)

¬ boolvar1 ↔ ¬ boolvar0, fs0[ri0[dentrykey(m, str0)]] = dentrynode(key4, m1), fs0[ri0[dentrykey(m, str)]] = dentrynode(key0, m2), fs0[ri0[inodekey(m2)]] = inodenode(key1, md0, boolvar0, m5, m9, m10), fs0[ri0[inodekey(m1)]] = inodenode(key3, md3, boolvar1, 1, m11, m12), boolvar2, links(m1, fs0, ri0) = ∅ ++ dentrykey(m, str0), replay-log(log0, fs0, fi ⊖ fo) = ri0 ⊖ ro, 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), replay-safe(log0, fs0, fi ⊖ fo), ri-cons(ri0, fs0), ri-inj(fi), ri-inj(ri0), ubifs-cons(fs0, ri0, ro, fi, fo, log0), dentrykey(m, str) ∈ ri0, inodekey(m2) ∈ ri0, dentrykey(m, str0) ∈ ri0, inodekey(m1) ∈ ri0, ri0[dentrykey(m, str)] ∈ fs0, ri0[inodekey(m2)] ∈ fs0, inodekey(m) ∈ ri0, ri0[dentrykey(m, str0)] ∈ fs0, ri0[inodekey(m1)] ∈ fs0, ri0[inodekey(m)] ∈ fs0, key ∈ (boolvar2 ⊃ ((ri0 ⊖ ro) -- dentrykey(m, str))[dentrykey(m, str0), adr2][inodekey(m), adr3] -- inodekey(m1) ;((ri0 ⊖ ro) -- dentrykey(m, str))[dentrykey(m, str0), adr2][inodekey(m), adr3] ⊖ inodekey(m1) ), boolvar1 → dentrykeys(inodekey(m1), ri0) = ∅, m4 ≠ 0 ∨ m = ROOT_INO, ¬ boolvar0 ∧ ¬ boolvar3 ∨ boolvar0 ∧ boolvar3 ∧ m3 = m10, ¬ boolvar0 ∧ ¬ boolvar2 ∨ boolvar1 ∧ boolvar2 ∧ m6 = m12 ⊦ (((ri0 ⊖ ro) -- dentrykey(m, str))[dentrykey(m, str0), adr2][inodekey(m), adr3] -- inodekey(m1))[key] = ((ri0 -- dentrykey(m, str))[dentrykey(m, str0), adr2][inodekey(m), adr3][inodekey(m1), adr4] ⊖ (ro ++ inodekey(m1)))[key], adr1 = adr4, adr1 = adr3, adr1 = adr2, adr2 = adr4, adr2 = adr3, adr3 = adr4, key = dentrykey(m, str0), m = 0, m1 = 0, m1 = ROOT_INO, m2 = 0, mkdentry(str, m2) = mkdentry(str0, m1), adr1 ∈ log0, adr2 ∈ log0, adr3 ∈ log0, adr4 ∈ log0, adr3 ∈ (ri0 -- dentrykey(m, str))[dentrykey(m, str0), adr2], inodekey(m) ∈ ro, adr1 ∈ fs0, adr2 ∈ fs0, adr3 ∈ fs0, adr4 ∈ fs0, adr2 ∈ ri0 -- dentrykey(m, str), adr4 ∈ (ri0 -- dentrykey(m, str))[dentrykey(m, str0), adr2][inodekey(m), adr3], (key = inodekey(m) ∨ key ≠ dentrykey(m, str) ∧ key ∈ ri0) ∧ key ≠ inodekey(m1) ∧ ¬ key ∈ ro ∧ ¬ key.data?

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 233:
fs0[ri0[dentrykey(m, str0)]] = dentrynode(key4, m1), fs0[ri0[dentrykey(m, str)]] = dentrynode(key0, m2), fs0[ri0[inodekey(m2)]] = inodenode(key1, md0, true, m5, m9, m10), fs0[ri0[inodekey(m1)]] = inodenode(key3, md3, true, 1, m11, m12), dentrykeys(inodekey(m1), ri0) = ∅, links(m1, fs0, ri0) = ∅ ++ dentrykey(m, str0), replay-log(log0, fs0, fi ⊖ fo) = ri0 ⊖ ro, 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), replay-safe(log0, fs0, fi ⊖ fo), ri-cons(ri0, fs0), ri-inj(fi), ri-inj(ri0), ubifs-cons(fs0, ri0, ro, fi, fo, log0), dentrykey(m, str) ∈ ri0, inodekey(m2) ∈ ri0, dentrykey(m, str0) ∈ ri0, inodekey(m1) ∈ ri0, ri0[dentrykey(m, str)] ∈ fs0, ri0[inodekey(m2)] ∈ fs0, inodekey(m) ∈ ri0, ri0[dentrykey(m, str0)] ∈ fs0, ri0[inodekey(m1)] ∈ fs0, ri0[inodekey(m)] ∈ fs0, m4 ≠ 0 ∨ m = ROOT_INO, key = inodekey(m) ∨ key ≠ dentrykey(m, str) ∧ key ∈ ri0 ⊖ ro ⊦ (inodekey(m) = key ⊃ adr3;(dentrykey(m, str) = key ⊃ (∅)[dentrykey(m, str)];(ri0 ⊖ ro)[key])) = ((ri0 -- dentrykey(m, str))[dentrykey(m, str0), adr2][inodekey(m), adr3][inodekey(m1), adr4] ⊖ (ro ++ inodekey(m1)))[key], adr1 = adr4, adr1 = adr3, adr1 = adr2, adr2 = adr4, adr2 = adr3, adr3 = adr4, key = dentrykey(m, str0), key = inodekey(m1), m = 0, m1 = 0, m1 = ROOT_INO, m2 = 0, mkdentry(str, m2) = mkdentry(str0, m1), adr1 ∈ log0, adr2 ∈ log0, adr3 ∈ log0, adr4 ∈ log0, adr3 ∈ (ri0 -- dentrykey(m, str))[dentrykey(m, str0), adr2], inodekey(m) ∈ ro, adr1 ∈ fs0, adr2 ∈ fs0, adr3 ∈ fs0, adr4 ∈ fs0, adr2 ∈ ri0 -- dentrykey(m, str), adr4 ∈ (ri0 -- dentrykey(m, str))[dentrykey(m, str0), adr2][inodekey(m), adr3], (key = inodekey(m) ∨ key ≠ dentrykey(m, str) ∧ key ∈ ri0) ∧ ¬ key ∈ ro ∧ ¬ key.data?

Rule argument

Additional information

Used simplifier rules: at-del-ri: ⊦ (ri -- key0)[key1] = (key0 = key1 ⊃ (∅)[key0];ri[key1]);%at-ri: ⊦ ri[key0, adr][key1] = (key0 = key1 ⊃ adr;ri[key1]);%in-ri: ⊦ key0 ∈ ri[key1, adr] ↔ key0 = key1 ∨ key0 ∈ ri;% ⊦ key ≠ key0 → (key ∈ ri[key0, adr] ↔ key ∈ ri); (s)% ⊦ key ∈ ri -- key0 ↔ key ≠ key0 ∧ key ∈ ri; (s)% ⊦ key ≠ key0 → ri[key0, adr][key] = ri[key]; (s)