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Proof step 179 from proof inv-rmdir (previous step)

fs0[ri0[inodekey(ino)]].nlink = 0 ↔ inodekey(ino) ∈ ro, fs0[ri0[inodekey(m)]] = inodenode(key0, md1, true, 1, m2, m3), fs0[ri0[dentrykey(m0, str)]] = dentrynode(key, m), fs0[ri0[inodekey(m0)]] = inodenode(key1, md2, true, m1, m4, m5), dentrykeys(inodekey(m), ri0) = ∅, links(m, fs0, ri0) = ∅ ++ dentrykey(m0, str), 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-cons(ri0, fs0), ri-inj(fi), ri-inj(ri0), ubifs-cons(fs0, ri0, ro, fi, fo, log0), ri0[inodekey(m0)] ∈ fs0, ri0[inodekey(m)] ∈ fs0, ri0[dentrykey(m0, str)] ∈ fs0, inodekey(m0) ∈ ri0, inodekey(m) ∈ ri0, dentrykey(m0, str) ∈ ri0, inodekey(ino) ∈ ri0, 1 ≤ m4, 1 ≤ m5, m1 ≠ 0 ∨ m0 = ROOT_INO ⊦ (adr2 = (m = ino ⊃ adr3;ri0[inodekey(ino)]) ⊃ dentrynode(dentrykey(m0, str), 0);fs0[(m = ino ⊃ adr3;ri0[inodekey(ino)])]).nlink = 0 ↔ ino = m ∨ inodekey(ino) ∈ ro, adr1 = (m = ino ⊃ adr3;ri0[inodekey(ino)]), adr1 = adr2, adr1 = adr3, adr2 = adr3, adr3 = (m = ino ⊃ adr3;ri0[inodekey(ino)]), ino = ROOT_INO, m = ROOT_INO, m = 0, m0 = ino, m0 = 0, m4 = 0, m5 = 0, adr3 ∈ fs0, adr2 ∈ fs0, adr1 ∈ fs0, inodekey(m0) ∈ ro, inodekey(m) ∈ ro

Heuristic if-then-else split applied rule case distinction

And obtained the following new goals

Proof step 180:
fs0[ri0[inodekey(ino)]].nlink = 0 ↔ inodekey(ino) ∈ ro, fs0[ri0[inodekey(m0)]] = inodenode(key1, md2, true, m1, m4, m5), fs0[ri0[dentrykey(m0, str)]] = dentrynode(key, m), fs0[ri0[inodekey(m)]] = inodenode(key0, md1, true, 1, m2, m3), dentrykeys(inodekey(m), ri0) = ∅, links(m, fs0, ri0) = ∅ ++ dentrykey(m0, str), 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-cons(ri0, fs0), ri-inj(ri0), ri-inj(fi), ubifs-cons(fs0, ri0, ro, fi, fo, log0), inodekey(ino) ∈ ri0, dentrykey(m0, str) ∈ ri0, inodekey(m) ∈ ri0, inodekey(m0) ∈ ri0, ri0[dentrykey(m0, str)] ∈ fs0, ri0[inodekey(m)] ∈ fs0, ri0[inodekey(m0)] ∈ fs0, 1 ≤ m5, 1 ≤ m4, m1 ≠ 0 ∨ m0 = ROOT_INO ⊦ (adr2 = (m = ino ⊃ adr3;ri0[inodekey(ino)]) ⊃ dentrynode(dentrykey(m0, str), 0);fs0[(m = ino ⊃ adr3;ri0[inodekey(ino)])]).nlink = 0 ↔ ino = m ∨ inodekey(ino) ∈ ro, adr1 = adr3, adr1 = adr2, adr1 = ri0[inodekey(ino)], adr2 = adr3, adr3 = (m = ino ⊃ adr3;ri0[inodekey(ino)]), ino = ROOT_INO, m = 0, m = ROOT_INO, m = ino, m0 = 0, m0 = ino, m4 = 0, m5 = 0, inodekey(m) ∈ ro, inodekey(m0) ∈ ro, adr1 ∈ fs0, adr2 ∈ fs0, adr3 ∈ fs0

Rule argument

pos: right 2

Additional information

Used simplifier rules: ubifs-cons-dentry-target-not-in-orphans: ⊦ ubifs-cons(fs, ri, ro, fi, fo, log) ∧ dentrykey(ino, str) ∈ ri ∧ fs[ri[dentrykey(ino, str)]] = dentrynode(key, m) → ¬ inodekey(m) ∈ ro;