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Proof step 109 from proof inv-create (previous step)

fs1[ri1[inodekey(m)]].directory, fs1[ri1[inodekey(m)]].inode?, fo.inodes?, ro.inodes?, file-node-cons(fs1, ri1), log-cons(log0, fs1), log-cons (log0, fs1[adr1, inodenode(inodekey(m), md0, true, fs1[ri1[inodekey(m)]].nlink, fs1[ri1[inodekey(m)]].nsubdirs, fs1[ri1[inodekey(m)]].size + 1)] [adr2, dentrynode(dentrykey(m, str), n) ]), orphans-cons(fs1, ri1, ro), replay-cons-strong (fs1[adr1, inodenode(inodekey(m), md0, true, fs1[ri1[inodekey(m)]].nlink, fs1[ri1[inodekey(m)]].nsubdirs, fs1[ri1[inodekey(m)]].size + 1)] [adr2, dentrynode(dentrykey(m, str), n) ], ri1[inodekey(m), adr1][dentrykey(m, str), adr2], ro, fi, fo, (log0 + adr1 ') + adr2 '), replay-cons-strong(fs1, ri1, ro, fi, fo, log0), ri-cons (ri1[inodekey(m), adr1][dentrykey(m, str), adr2], fs1[adr1, inodenode(inodekey(m), md0, true, fs1[ri1[inodekey(m)]].nlink, fs1[ri1[inodekey(m)]].nsubdirs, fs1[ri1[inodekey(m)]].size + 1)] [adr2, dentrynode(dentrykey(m, str), n) ]), ri-inj(fi), ri-inj(ri1), ubifs-cons(fs1, ri1, ro, fi, fo, log0), ri1[inodekey(m)] ∈ fs1, inodekey(m) ∈ ri1, fs1[ri1[inodekey(m)]].nlink ≠ 0 ∨ m = ROOT_INO ⊦ (ri1[inodekey(m), adr1][dentrykey(m, str), adr2] ⊖ ro)[inodekey(n), adr3] = ri1[inodekey(m), adr1][dentrykey(m, str), adr2][inodekey(n), adr3] ⊖ ro, adr1 = adr3, adr1 = adr2, adr2 = adr3, m = 0, n = 0, inodekey(m) ∈ ro, dentrykey(m, str) ∈ ri1, inodekey(n) ∈ fo, inodekey(n) ∈ ri1, adr1 ∈ fs1, adr2 ∈ fs1, adr3 ∈ fs1

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: aubifs-replay name: replay-orphans-inode seq: ⊦ ¬ inodekey(ino) ∈ ro → (ri ⊖ ro)[inodekey(ino), adr] = ri[inodekey(ino), adr] ⊖ ro subst: [adr, ino, ro, ri] → [adr3, n, ro, ri1[inodekey(m), adr1][dentrykey(m, str), adr2]] flags: <all paths>

Additional information

Used simplifier rules: ⊦ inodekey(m) ∈ ks → ri[inodekey(m), adr] ⊖ ks = ri ⊖ ks; (s)% ⊦ ubifs-cons(fs, ri, ro, fi, fo, log) ∧ key ∈ ro → key ∈ ri; (ss) Used terms: adr3, n, ro, ri1[inodekey(m), adr1][dentrykey(m, str), adr2]