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Proof step 47 from proof replay-one-update (previous step)

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

User applied rule all left

And closed the goal!

Rule argument

pos: left 9 terms: inodekey(0) abort: F discard: F computed: T

Additional information

Used simplifier rules: ⊦ key-cons(inodekey(ino), nd) ↔ nd.inode? ∧ nd.key = inodekey(ino) ∧ ino ≠ 0; (s) Used terms: inodekey(0)