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Proof step 8 from proof replay-drop-data (previous step)

inodekey(ino) ∈ ro ⊦ # ro = 0, ro = ∅, (key ∈ ri[datakey(ino, n), adr] ∧ ¬ key ∈ ro ∧ (key.data? → ¬ inodekey(key.ino) ∈ ro) ↔ key ∈ ri ⊖ ro) ∧ (key ∈ ri[datakey(ino, n), adr] ∧ ¬ key ∈ ro ∧ (key.data? → ¬ inodekey(key.ino) ∈ ro) → (ri[datakey(ino, n), adr] ⊖ ro)[key] = (ri ⊖ ro)[key])

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 9:
⊦ key ∈ ri[key0, adr] ↔ key = key0 ∨ key ∈ ri
Proof step 10:
inodekey(ino) ∈ ro ⊦ # ro = 0, ro = ∅, ((key = datakey(ino, n) ∨ key ∈ ri) ∧ ¬ key ∈ ro ∧ (key.data? → ¬ inodekey(key.ino) ∈ ro) ↔ key ∈ ri ⊖ ro) ∧ ((key = datakey(ino, n) ∨ key ∈ ri) ∧ ¬ key ∈ ro ∧ (key.data? → ¬ inodekey(key.ino) ∈ ro) → (ri[datakey(ino, n), adr] ⊖ ro)[key] = (ri ⊖ ro)[key])

Rule argument

spec: store, inst: node-index name: In-insert seq: ⊦ key ∈ ri[key0, adr] ↔ key = key0 ∨ key ∈ ri subst: [adr, key0, ri, key] → [adr, datakey(ino, n), ri, key] flags: <all paths>

Additional information

Used terms: adr, datakey(ino, n), ri, key