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Proof step 270 from proof inv-rename-overwrite-reparent (previous step)

¬ fs0[ri0[inodekey(m8)]].directory ↔ ¬ fs0[ri0[inodekey(m5)]].directory, 1 = fs0[ri0[inodekey(m8)]].nlink, fs0[ri0[dentrykey(m, str)]] = dentrynode(key1, m5), fs0[ri0[inodekey(m0)]] = inodenode(key0, md1, true, m9, m12, m13), fs0[ri0[dentrykey(m0, str0)]] = dentrynode(key3, m8), links(m8, fs0, ri0) = ∅ ++ dentrykey(m0, str0), ro.inodes?, fo.inodes?, file-node-cons(fs0, ri0), log-cons(log0, fs0), replay-cons-strong(fs0, ri0, ro, fi, fo, log0), ri-cons(ri0, fs0), ri-inj(ri0), ri-inj(fi), ubifs-cons(fs0, ri0, ro, fi, fo, log0), ri0[inodekey(m)] ∈ fs0, ri0[dentrykey(m0, str0)] ∈ fs0, inodekey(m0) ∈ ri0, inodekey(m) ∈ ri0, ri0[dentrykey(m, str)] ∈ fs0, inodekey(m8) ∈ ri0, dentrykey(m0, str0) ∈ ri0, inodekey(m5) ∈ ri0, dentrykey(m, str) ∈ ri0, ri0[inodekey(m0)] ∈ fs0, fs0[ri0[inodekey(m8)]].directory → dentrykeys(inodekey(m8), ri0) = ∅, m9 ≠ 0 ∨ m0 = ROOT_INO, m10 ≠ 0 ∨ m = ROOT_INO, ¬ fs0[ri0[inodekey(m5)]].directory ∧ ¬ boolvar3 ∧ m3 = fs0[ri0[inodekey(m5)]].nsubdirs ∨ fs0[ri0[inodekey(m5)]].directory ∧ boolvar3 ∧ m3 = fs0[ri0[inodekey(m5)]].nsubdirs ∧ m4 = fs0[ri0[inodekey(m5)]].size, ¬ fs0[ri0[inodekey(m5)]].directory ∧ ¬ boolvar1 ∨ fs0[ri0[inodekey(m8)]].directory ∧ boolvar1 ∧ m7 = fs0[ri0[inodekey(m8)]].size ⊦ adr1 = adr2, adr1 = adr3, adr1 = adr4, adr1 = adr5, adr2 = adr3, adr2 = adr4, adr2 = adr5, adr3 = adr4, adr3 = adr5, adr4 = adr5, m = 0, m0 = m, m0 = 0, m8 = ROOT_INO, m8 = 0, file-node-cons (fs0[adr1, dentrynode(dentrykey(m, str), 0)][adr2, dentrynode(dentrykey(m0, str0), m5)][adr3, inodenode(inodekey(m), md, true, m10, n0, m1)] [adr4, inodenode(inodekey(m0), md0, true, m9, m12, m13) ] [adr5, inodenode(inodekey(m8), md2, boolvar1, 0, fs0[ri0[inodekey(m8)]].nsubdirs, m7) ], (ri0 -- dentrykey(m, str))[dentrykey(m0, str0), adr2][inodekey(m), adr3][inodekey(m0), adr4][inodekey(m8), adr5]), adr4 ∈ (ri0 -- dentrykey(m, str))[dentrykey(m0, str0), adr2][inodekey(m), adr3], adr2 ∈ ri0 -- dentrykey(m, str), adr5 ∈ fs0, adr4 ∈ fs0, adr3 ∈ fs0, adr2 ∈ fs0, adr1 ∈ fs0, inodekey(m) ∈ ro, inodekey(m0) ∈ ro, adr3 ∈ (ri0 -- dentrykey(m, str))[dentrykey(m0, str0), adr2], adr5 ∈ (ri0 -- dentrykey(m, str))[dentrykey(m0, str0), adr2][inodekey(m), adr3][inodekey(m0), adr4]

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 271:
¬ fs0[ri0[inodekey(m8)]].directory ↔ ¬ fs0[ri0[inodekey(m5)]].directory, 1 = fs0[ri0[inodekey(m8)]].nlink, fs0[ri0[dentrykey(m0, str0)]] = dentrynode(key3, m8), fs0[ri0[inodekey(m0)]] = inodenode(key0, md1, true, m9, m12, m13), fs0[ri0[dentrykey(m, str)]] = dentrynode(key1, m5), links(m8, fs0, ri0) = ∅ ++ dentrykey(m0, str0), fo.inodes?, ro.inodes?, file-node-cons(fs0, ri0), log-cons(log0, fs0), replay-cons-strong(fs0, ri0, ro, fi, fo, log0), ri-cons(ri0, fs0), ri-inj(fi), ri-inj(ri0), ubifs-cons(fs0, ri0, ro, fi, fo, log0), ri0[inodekey(m0)] ∈ fs0, dentrykey(m, str) ∈ ri0, inodekey(m5) ∈ ri0, dentrykey(m0, str0) ∈ ri0, inodekey(m8) ∈ ri0, ri0[dentrykey(m, str)] ∈ fs0, inodekey(m) ∈ ri0, inodekey(m0) ∈ ri0, ri0[dentrykey(m0, str0)] ∈ fs0, ri0[inodekey(m)] ∈ fs0, inodekey(ino) ∈ ri0, fs0[ri0[inodekey(m8)]].directory → dentrykeys(inodekey(m8), ri0) = ∅, ¬ fs0[ri0[inodekey(ino)]].directory → fs0[ri0[inodekey(ino)]].nsubdirs = 0, ¬ fs0[ri0[inodekey(m5)]].directory ∧ ¬ boolvar1 ∨ fs0[ri0[inodekey(m8)]].directory ∧ boolvar1 ∧ m7 = fs0[ri0[inodekey(m8)]].size, ¬ fs0[ri0[inodekey(m5)]].directory ∧ ¬ boolvar3 ∧ m3 = fs0[ri0[inodekey(m5)]].nsubdirs ∨ fs0[ri0[inodekey(m5)]].directory ∧ boolvar3 ∧ m3 = fs0[ri0[inodekey(m5)]].nsubdirs ∧ m4 = fs0[ri0[inodekey(m5)]].size, m10 ≠ 0 ∨ m = ROOT_INO, m9 ≠ 0 ∨ m0 = ROOT_INO ⊦ (adr5 = (m8 = ino ⊃ adr5;(m0 = ino ⊃ adr4;(m = ino ⊃ adr3;ri0[inodekey(ino)]))) ⊃ inodenode(inodekey(m8), md2, boolvar1, 0, fs0[ri0[inodekey(m8)]].nsubdirs, m7) ;(adr4 = (m8 = ino ⊃ adr5;(m0 = ino ⊃ adr4;(m = ino ⊃ adr3;ri0[inodekey(ino)]))) ⊃ inodenode(inodekey(m0), md0, true, m9, m12, m13) ;(adr3 = (m8 = ino ⊃ adr5;(m0 = ino ⊃ adr4;(m = ino ⊃ adr3;ri0[inodekey(ino)]))) ⊃ inodenode(inodekey(m), md, true, m10, n0, m1) ;(adr2 = (m8 = ino ⊃ adr5;(m0 = ino ⊃ adr4;(m = ino ⊃ adr3;ri0[inodekey(ino)]))) ⊃ dentrynode(dentrykey(m0, str0), m5) ;(adr1 = (m8 = ino ⊃ adr5;(m0 = ino ⊃ adr4;(m = ino ⊃ adr3;ri0[inodekey(ino)]))) ⊃ dentrynode(dentrykey(m, str), 0) ;fs0[(m8 = ino ⊃ adr5;(m0 = ino ⊃ adr4;(m = ino ⊃ adr3;ri0[inodekey(ino)])))] ) ) ) ) ) .nsubdirs = 0, adr1 = adr5, adr1 = adr4, adr1 = adr3, adr1 = adr2, adr2 = adr5, adr2 = adr4, adr2 = adr3, adr3 = adr5, adr3 = adr4, adr4 = adr5, m = 0, m0 = 0, m0 = m, m8 = 0, m8 = ROOT_INO, (adr5 = (m8 = ino ⊃ adr5;(m0 = ino ⊃ adr4;(m = ino ⊃ adr3;ri0[inodekey(ino)]))) ⊃ inodenode(inodekey(m8), md2, boolvar1, 0, fs0[ri0[inodekey(m8)]].nsubdirs, m7) ;(adr4 = (m8 = ino ⊃ adr5;(m0 = ino ⊃ adr4;(m = ino ⊃ adr3;ri0[inodekey(ino)]))) ⊃ inodenode(inodekey(m0), md0, true, m9, m12, m13) ;(adr3 = (m8 = ino ⊃ adr5;(m0 = ino ⊃ adr4;(m = ino ⊃ adr3;ri0[inodekey(ino)]))) ⊃ inodenode(inodekey(m), md, true, m10, n0, m1) ;(adr2 = (m8 = ino ⊃ adr5;(m0 = ino ⊃ adr4;(m = ino ⊃ adr3;ri0[inodekey(ino)]))) ⊃ dentrynode(dentrykey(m0, str0), m5) ;(adr1 = (m8 = ino ⊃ adr5;(m0 = ino ⊃ adr4;(m = ino ⊃ adr3;ri0[inodekey(ino)]))) ⊃ dentrynode(dentrykey(m, str), 0) ;fs0[(m8 = ino ⊃ adr5;(m0 = ino ⊃ adr4;(m = ino ⊃ adr3;ri0[inodekey(ino)])))] ) ) ) ) ) .directory, adr5 ∈ (ri0 -- dentrykey(m, str))[dentrykey(m0, str0), adr2][inodekey(m), adr3][inodekey(m0), adr4], adr3 ∈ (ri0 -- dentrykey(m, str))[dentrykey(m0, str0), adr2], inodekey(m0) ∈ ro, inodekey(m) ∈ ro, adr1 ∈ fs0, adr2 ∈ fs0, adr3 ∈ fs0, adr4 ∈ fs0, adr5 ∈ fs0, adr2 ∈ ri0 -- dentrykey(m, str), adr4 ∈ (ri0 -- dentrykey(m, str))[dentrykey(m0, str0), adr2][inodekey(m), adr3]

Rule argument

Additional information

Used simplifier rules: in-ri: ⊦ key0 ∈ ri[key1, adr] ↔ key0 = key1 ∨ key0 ∈ ri;%at-ri: ⊦ ri[key0, adr][key1] = (key0 = key1 ⊃ adr;ri[key1]);%at-del-ri: ⊦ (ri -- key0)[key1] = (key0 = key1 ⊃ (∅)[key0];ri[key1]);%at-fs: ⊦ fs[adr0, nd][adr1] = (adr0 = adr1 ⊃ nd;fs[adr1]);% ⊦ key ∈ ri -- key0 ↔ key ≠ key0 ∧ key ∈ ri; (s)% ⊦ inodekey(m) ≠ dentrykey(m0, str); (s)% ⊦ inodekey(m) = inodekey(m0) ↔ m = m0; (s)%⊦ file-node-cons(fs, ri) → ( file-node-cons(fs0, ri0) ↔ (∀ ino. ( inodekey(ino) ∈ ri ∧ ¬ fs[ri[inodekey(ino)]].directory → fs[ri[inodekey(ino)]].nsubdirs = 0) → inodekey(ino) ∈ ri0 ∧ ¬ fs0[ri0[inodekey(ino)]].directory → fs0[ri0[inodekey(ino)]].nsubdirs = 0)); (ss)