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Proof step 8 from proof replay-orphans-trunc (previous step)

key ∈ ro, key0 ∈ ri, key0.data? → ¬ inodekey(key0.ino) ∈ ro, ¬ key0.data? ∨ ¬ 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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 9:
⊦ key ∈ ri ∧ ¬ key ∈ ks ∧ ¬ key.data? → (ri ⊖ ks)[key] = ri[key]
Proof step 10:
key0 ∈ ri, key ∈ ro, key0.data? → ¬ inodekey(key0.ino) ∈ ro, ¬ key0.data? ∨ ¬ 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, key0 ∈ ri \ datakeys(key, n, ri) ∧ ¬ key0 ∈ ro ∧ ¬ key0.data?
Proof step 18:
key0 ∈ ri, key ∈ ro, key0 ∈ ri \ datakeys(key, n, ri), key0.data? → ¬ inodekey(key0.ino) ∈ ro, ¬ key0.data? ∨ ¬ key.inode? ∨ key0.ino ≠ key.ino ∨ ¬ n ≤ key0.part * VFS_PAGE_SIZE ⊦ # ro = 0, (ri \ datakeys(key, n, ri))[key0] = (ri ⊖ ro)[key0], ro = ∅, key0.data?, key0 ∈ ro

Rule argument

spec: aubifs-base name: at-dels-ro-nodata seq: ⊦ key ∈ ri ∧ ¬ key ∈ ks ∧ ¬ key.data? → (ri ⊖ ks)[key] = ri[key] subst: [key, ks, ri] → [key0, ro, ri \ datakeys(key, n, ri)] flags: <all paths>

Additional information

Used terms: key0, ro, ri \ datakeys(key, n, ri)