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Proof step 5 from proof data-ubifs-cons (previous step)

ro.inodes?, fo.inodes?, log-cons(log, fs), ri-closed(ri, fs, ro), ri-cons(ri, fs), inodekey(ino) ∈ ri, datakey(ino, n) ∈ ri, ri[datakey(ino, n)] ∈ fs, ro ⊆ dom ri, fo ⊆ dom fi ⊦ fs[ri[datakey(ino, n)]].data?, fs[ri[inodekey(ino)]].directory, dups(log), inodekey(0) ∈ ri

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 6:
⊦ ri-cons(ri, fs) ↔ (∀ key. key ∈ ri → ri[key] ∈ fs ∧ key-cons(key, fs[ri[key]]))
Proof step 7:
fo.inodes?, ro.inodes?, log-cons(log, fs), ri-closed(ri, fs, ro), ri[datakey(ino, n)] ∈ fs, datakey(ino, n) ∈ ri, inodekey(ino) ∈ ri, fo ⊆ dom fi, ro ⊆ dom ri, ∀ key. key ∈ ri → ri[key] ∈ fs ∧ key-cons(key, fs[ri[key]]) ⊦ fs[ri[datakey(ino, n)]].data?, fs[ri[inodekey(ino)]].directory, dups(log), inodekey(0) ∈ ri

Rule argument

spec: aubifs-inv name: ri-cons seq: ⊦ ri-cons(ri, fs) ↔ (∀ key. key ∈ ri → ri[key] ∈ fs ∧ key-cons(key, fs[ri[key]])) subst: [fs, ri] → [fs, ri] flags: <all paths>

Additional information

Used terms: fs, ri