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Proof step 11 from proof replay-orphans-trunc (previous step)

key0.data?, key ∈ ro, key0 ∈ ri, ¬ key.inode? ∨ key0.ino ≠ key.ino ∨ ¬ n ≤ key0.part * VFS_PAGE_SIZE ⊦ # ro = 0, ((ri \ datakeys(key, n, ri)) ⊖ ro)[key0] = (ri ⊖ ro)[key0], ro = ∅, key0 ∈ ro, inodekey(key0.ino) ∈ ro

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 12:
key0 = datakey(m, m0), key0.data?, key0 ∈ ri, key ∈ ro, ¬ key.inode? ∨ m ≠ key.ino ∨ ¬ n ≤ m0 * VFS_PAGE_SIZE ⊦ # ro = 0, ((ri \ datakeys(key, n, ri)) ⊖ ro)[key0] = (ri ⊖ ro)[key0], ro = ∅, inodekey(m) ∈ ro, key0 ∈ ro

Rule argument

spec: key name: elim-02 seq: ⊦ key.data? → (m = key.ino ∧ m0 = key.part ↔ key = datakey(m, m0)) subst: [key, m, m0] → [key0, m, m0]

Additional information

Used simplifier rules: ⊦ key.data? → (m = key.ino ∧ m0 = key.part ↔ key = datakey(m, m0)); (elim) Used terms: key0, m, m0