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Proof step 11 from proof replay-cons-add-page (previous step)

log-cons(log, fs), replay-safe(log, fs, fi ⊖ fo) ⊦ ri ⊖ (ro ++ datakey(ino, n)) = (ri -- datakey(ino, n)) ⊖ ro

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 12:
⊦ ri = ri0 ↔ (∀ key. (key ∈ ri ↔ key ∈ ri0) ∧ (key ∈ ri → ri[key] = ri0[key]))
Proof step 13:
log-cons(log, fs), replay-safe(log, fs, fi ⊖ fo) ⊦ ∀ key. (key ∈ ri ⊖ (ro ++ datakey(ino, n)) ↔ key ∈ (ri -- datakey(ino, n)) ⊖ ro) ∧ (key ∈ ri ⊖ (ro ++ datakey(ino, n)) → (ri ⊖ (ro ++ datakey(ino, n)))[key] = ((ri -- datakey(ino, n)) ⊖ ro)[key])

Rule argument

spec: store, inst: node-index name: k-Extension seq: ⊦ ri = ri0 ↔ (∀ key. (key ∈ ri ↔ key ∈ ri0) ∧ (key ∈ ri → ri[key] = ri0[key])) subst: [ri0, ri] → [(ri -- datakey(ino, n)) ⊖ ro, ri ⊖ (ro ++ datakey(ino, n))] flags: <all paths>

Additional information

Used terms: (ri -- datakey(ino, n)) ⊖ ro, ri ⊖ (ro ++ datakey(ino, n))