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Proof step 303 from proof refine-rename-new-keep-parent (previous step)

fs0[ri0[inodekey(m)]].nsubdirs = 0, fs0[ri0[inodekey(m3)]] = inodenode(key0, md1, true, m4, m5, m0 + 1), fs0[ri0[dentrykey(m3, str)]] = dentrynode(key1, m), fo.inodes?, orphans(fs0, ri0).inodes?, afs-cons(abs-dirs(fs0, ri0)[m3, mkdir(m0 + 1, md0, m4, m5, (abs-children(m3, fs0, ri0) -- str)[str0, m])], abs-files(fs0, ri0)), afs-cons(abs-dirs(fs0, ri0), abs-files(fs0, ri0)), file-node-cons(fs0, ri0), file-node-cons (fs0[adr1, dentrynode(dentrykey(m3, str), 0)][adr2, dentrynode(dentrykey(m3, str0), m)][adr3, inodenode(inodekey(m3), md0, true, m4, m5, m0 + 1)], (ri0 -- dentrykey(m3, str))[dentrykey(m3, str0), adr2][inodekey(m3), adr3]), log-cons(log0, fs0), log-cons (log0, fs0[adr1, dentrynode(dentrykey(m3, str), 0)][adr2, dentrynode(dentrykey(m3, str0), m)][adr3, inodenode(inodekey(m3), md0, true, m4, m5, m0 + 1)]), orphans-cons(fs0, ri0, orphans(fs0, ri0)), orphans-cons (fs0[adr1, dentrynode(dentrykey(m3, str), 0)][adr2, dentrynode(dentrykey(m3, str0), m)][adr3, inodenode(inodekey(m3), md0, true, m4, m5, m0 + 1)], (ri0 -- dentrykey(m3, str))[dentrykey(m3, str0), adr2][inodekey(m3), adr3], 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(m3, str0), m)][adr3, inodenode(inodekey(m3), md0, true, m4, m5, m0 + 1)], (ri0 -- dentrykey(m3, str))[dentrykey(m3, str0), adr2][inodekey(m3), adr3], orphans(fs0, ri0), fi, fo, ((log0 + adr1 ') + adr2 ') + adr3 '), ri-inj(fi), ri-inj(ri0), ri-inj((ri0 -- dentrykey(m3, str))[dentrykey(m3, str0), adr2][inodekey(m3), adr3]), ubifs-cons(fs0, ri0, orphans(fs0, ri0), fi, fo, log0), ubifs-cons (fs0[adr1, dentrynode(dentrykey(m3, str), 0)][adr2, dentrynode(dentrykey(m3, str0), m)][adr3, inodenode(inodekey(m3), md0, true, m4, m5, m0 + 1)], (ri0 -- dentrykey(m3, str))[dentrykey(m3, str0), adr2][inodekey(m3), adr3], orphans(fs0, ri0), fi, fo, ((log0 + adr1 ') + adr2 ') + adr3 '), inodekey(m3) ∈ ri0, ri0[dentrykey(m3, str)] ∈ fs0, ri0[inodekey(m3)] ∈ fs0, dentrykey(m3, str) ∈ ri0, inodekey(m) ∈ ri0, boolvar3 → boolvar4, links(m3, abs-dirs(fs0, ri0)) ≠ ∅ ∨ m3 = ROOT_INO, m4 ≠ 0 ∨ m3 = ROOT_INO ⊦ str1 ≠ str ∧ dentrykey(m3, str1) ∈ ri0 ↔ dentrykey(m3, str1) ∈ (ri0 -- dentrykey(m3, str))[dentrykey(m3, str0), adr2][inodekey(m3), adr3], adr1 = adr3, adr1 = adr2, adr2 = adr3, dentrykey(m3, str0) = dentrykey(m3, str1), m3 = 0, fs0[ri0[inodekey(m)]].directory, adr3 ∈ (ri0 -- dentrykey(m3, str))[dentrykey(m3, str0), adr2], dentrykey(m3, str0) ∈ ri0, adr1 ∈ fs0, adr2 ∈ fs0, adr3 ∈ fs0, adr2 ∈ ri0 -- dentrykey(m3, str), m4 = 0 ∧ m3 ≠ ROOT_INO

Heuristic nonsplitting cut applied rule cut formula

And closed the goal!

Rule argument

fma: dentrykey(m3, str1) ∈ (ri0 -- dentrykey(m3, str))[dentrykey(m3, str0), adr2] [inodekey(m3), adr3 ]

Additional information

Used simplifier rules: in-ri-dentry-inode: ⊦ dentrykey(ino, str) ∈ ri[inodekey(ino), adr] ↔ dentrykey(ino, str) ∈ ri;% ⊦ key ∈ ri[key0, adr] ↔ key = key0 ∨ key ∈ ri; (ws)% ⊦ inodekey(m) ≠ dentrykey(m0, str); (s)% ⊦ key ≠ key0 → (key ∈ ri[key0, adr] ↔ key ∈ ri); (s)% ⊦ key ∈ ri -- key0 ↔ key ≠ key0 ∧ key ∈ ri; (s)% ⊦ dentrykey(m, str) = dentrykey(m0, str0) ↔ m = m0 ∧ str = str0; (ws) Used formulas: dentrykey(m3, str1) ∈ (ri0 -- dentrykey(m3, str))[dentrykey(m3, str0), adr2] [inodekey(m3), adr3 ]