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Proof step 12 from proof del-commute-dels (previous step)

key0 = datakey(m, m0), key0.data?, key0 ∈ ri ⊦ ((ri ⊖ key) ⊖ ks)[key0] = ((ri ⊖ ks) ⊖ key)[key0], inodekey(m) = key, key0 = key, inodekey(m) ∈ ks, key0 ∈ ks, key ∈ ks

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 13:
datakey(m, m0) ∈ ri ⊦ ((ri ⊖ key) ⊖ ks)[datakey(m, m0)] = ((ri ⊖ ks) ⊖ key)[datakey(m, m0)], datakey(m, m0) = key, inodekey(m) = key, key ∈ ks, datakey(m, m0) ∈ ks, inodekey(m) ∈ ks

Rule argument

Additional information

Used simplifier rules: ⊦ datakey(m, m0).data?; (s)