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Proof step 40 from proof replay-one-update (previous step)

fs[ri[dentrykey(ino, str)]] = dentrynode(dentrykey(ino, str), m), ro.inodes?, orphans-cons(fs, ri, ro), dentrykey(ino, str) ∈ ri, ri[dentrykey(ino, str)] ∈ 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) ⊦ (m ≠ 0 ⊃ (ri ⊖ ro)[dentrykey(ino, str), adr];(ri ⊖ ro) -- dentrykey(ino, str)) = ri[dentrykey(ino, str), adr] ⊖ ro

User applied rule all left

And obtained the following new goals

Proof step 41:
fs[ri[dentrykey(ino, str)]] = dentrynode(dentrykey(ino, str), m), ro.inodes?, orphans-cons(fs, ri, ro), ri[dentrykey(ino, str)] ∈ fs, dentrykey(ino, str) ∈ ri, dentrykey(ino, str) ∈ ri → ri[dentrykey(ino, str)] ∈ fs ∧ node-closed(fs[ri[dentrykey(ino, str)]], ri, fs, ro), ∀ key. key ∈ ri → ri[key] ∈ fs ∧ key-cons(key, fs[ri[key]]) ⊦ (m ≠ 0 ⊃ (ri ⊖ ro)[dentrykey(ino, str), adr];(ri ⊖ ro) -- dentrykey(ino, str)) = ri[dentrykey(ino, str), adr] ⊖ ro

Rule argument

pos: left 7 terms: dentrykey(ino, str) abort: F discard: T computed: T

Additional information

Used terms: dentrykey(ino, str)