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Proof step 15 from proof replay-nonorphans-trunc (previous step)

datakey(m, m0) ∈ ri, ¬ key.inode? ∨ m ≠ key.ino ∨ ¬ n ≤ m0 * VFS_PAGE_SIZE ⊦ (ri ⊖ ro)[datakey(m, m0)] = ((ri \ datakeys(key, n, ri)) ⊖ ro)[datakey(m, m0)], inodekey(m) ∈ ro, datakey(m, m0) ∈ ro, key ∈ ro, datakey(m, m0) ∈ datakeys(key, n, ri)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 16:
datakey(m, m0) ∈ ri, ¬ key.inode? ∨ m ≠ key.ino ∨ ¬ n ≤ m0 * VFS_PAGE_SIZE ⊦ ri[datakey(m, m0)] = ((ri \ datakeys(key, n, ri)) ⊖ ro)[datakey(m, m0)], key ∈ ro, datakey(m, m0) ∈ ro, inodekey(m) ∈ ro, key.inode? ∧ m = key.ino ∧ n ≤ m0 * VFS_PAGE_SIZE

Rule argument

Additional information

Used simplifier rules: ⊦ datakey(m, m0).part = m0; (s)% ⊦ datakey(m, m0).ino = m; (s)% ⊦ datakey(m, m0).data?; (s)%⊦ key ∈ datakeys(key0, ri) ↔ key ∈ ri ∧ key.data? ∧ key0.inode? ∧ key.ino = key0.ino; (s)%⊦ key ∈ datakeys(key0, n, ri) ↔ key ∈ datakeys(key0, ri) ∧ n ≤ key.part * VFS_PAGE_SIZE; (s)%⊦ datakey(ino, n) ∈ ri ∧ ¬ datakey(ino, n) ∈ ks ∧ ¬ inodekey(ino) ∈ ks → (ri ⊖ ks)[datakey(ino, n)] = ri[datakey(ino, n)]; (s)