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Proof step 3 from proof replay-drop-data (previous step)

inodekey(ino) ∈ ro ⊦ # ro = 0, ro = ∅, ri[datakey(ino, n), adr] ⊖ ro = ri ⊖ ro

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 4:
⊦ ri = ri0 ↔ (∀ key. (key ∈ ri ↔ key ∈ ri0) ∧ (key ∈ ri → ri[key] = ri0[key]))
Proof step 5:
inodekey(ino) ∈ ro ⊦ # ro = 0, ro = ∅, ∀ key. (key ∈ ri[datakey(ino, n), adr] ⊖ ro ↔ key ∈ ri ⊖ ro) ∧ (key ∈ ri[datakey(ino, n), adr] ⊖ ro → (ri[datakey(ino, n), adr] ⊖ ro)[key] = (ri ⊖ 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 ⊖ ro, ri[datakey(ino, n), adr] ⊖ ro] flags: <all paths>

Additional information

Used terms: ri ⊖ ro, ri[datakey(ino, n), adr] ⊖ ro