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Proof step 25 from proof replay-orphans-inode (previous step)

datakey(m, m0) ∈ ri ⊦ ri[datakey(m, m0)] = (ri[inodekey(ino), adr] ⊖ ro)[datakey(m, m0)], inodekey(ino) ∈ ro, datakey(m, m0) ∈ ro, inodekey(m) ∈ ro

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 26:
⊦ datakey(ino, n) ∈ ri ∧ ¬ datakey(ino, n) ∈ ks ∧ ¬ inodekey(ino) ∈ ks → (ri ⊖ ks)[datakey(ino, n)] = ri[datakey(ino, n)]
Proof step 27:
datakey(m, m0) ∈ ri, datakey(m, m0) ∈ ri[inodekey(ino), adr] ⊦ ri[datakey(m, m0)] = ri[inodekey(ino), adr][datakey(m, m0)], inodekey(ino) ∈ ro, inodekey(m) ∈ ro, datakey(m, m0) ∈ ro

Rule argument

spec: aubifs-base name: at-dels-ro-data seq: ⊦ datakey(ino, n) ∈ ri ∧ ¬ datakey(ino, n) ∈ ks ∧ ¬ inodekey(ino) ∈ ks → (ri ⊖ ks)[datakey(ino, n)] = ri[datakey(ino, n)] subst: [n, ino, ks, ri] → [m0, m, ro, ri[inodekey(ino), adr]] flags: <all paths>

Additional information

Used simplifier rules: ⊦ key ∈ ri[key0, adr] ↔ key = key0 ∨ key ∈ ri; (ws)% ⊦ inodekey(m) ≠ datakey(m0, m1); (s) Used terms: m0, m, ro, ri[inodekey(ino), adr]