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Proof step 29 from proof replay-one-update (previous step)

fs[ri[datakey(ino, ino0)]] = datanode(datakey(ino, ino0), buf), ro.inodes?, orphans-cons(fs, ri, ro), datakey(ino, ino0) ∈ ri, ri[datakey(ino, ino0)] ∈ fs, ∀ key. key ∈ ri → ri[key] ∈ fs ∧ key-cons(key, fs[ri[key]]), ∀ key. key ∈ ri → ri[key] ∈ fs ∧ node-closed(fs[ri[key]], ri, fs, ro) ⊦ (inodekey(ino) ∈ ri ⊖ ro ⊃ (ri ⊖ ro)[datakey(ino, ino0), adr];ri ⊖ ro) = ri[datakey(ino, ino0), adr] ⊖ ro

User applied rule all left

And obtained the following new goals

Proof step 30:
fs[ri[datakey(ino, ino0)]] = datanode(datakey(ino, ino0), buf), ro.inodes?, orphans-cons(fs, ri, ro), ri[datakey(ino, ino0)] ∈ fs, datakey(ino, ino0) ∈ ri, datakey(ino, ino0) ∈ ri → ri[datakey(ino, ino0)] ∈ fs ∧ node-closed(fs[ri[datakey(ino, ino0)]], ri, fs, ro), ∀ key. key ∈ ri → ri[key] ∈ fs ∧ key-cons(key, fs[ri[key]]) ⊦ (inodekey(ino) ∈ ri ⊖ ro ⊃ (ri ⊖ ro)[datakey(ino, ino0), adr];ri ⊖ ro) = ri[datakey(ino, ino0), adr] ⊖ ro

Rule argument

pos: left 7 terms: datakey(ino, ino0) abort: F discard: T computed: T

Additional information

Used terms: datakey(ino, ino0)