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Proof step 44 from proof replay-one-update (previous step)

fs[ri[dentrykey(ino, str)]] = dentrynode(dentrykey(ino, str), m), fs[ri[inodekey(ino)]].directory, ro.inodes?, orphans-cons(fs, ri, ro), ri[dentrykey(ino, str)] ∈ fs, dentrykey(ino, str) ∈ ri, inodekey(ino) ∈ ri, inodekey(m) ∈ ri, ∀ key. key ∈ ri → ri[key] ∈ fs ∧ key-cons(key, fs[ri[key]]) ⊦ (ri ⊖ ro)[dentrykey(ino, str), adr] = ri[dentrykey(ino, str), adr] ⊖ ro, m = 0, inodekey(m) ∈ ro, inodekey(ino) ∈ ro

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: <toplevel> name: replay-orphans-dentry seq: ⊦ ¬ dentrykey(ino, str) ∈ ro → (ri ⊖ ro)[dentrykey(ino, str), adr] = ri[dentrykey(ino, str), adr] ⊖ ro subst: [adr, str, ino, ro, ri] → [adr, str, ino, ro, ri] flags: <all paths>

Additional information

Used simplifier rules: ⊦ ks.inodes? → ¬ dentrykey(ino, str) ∈ ks; (s) Used terms: adr, str, ino, ro, ri