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Proof step 15 from proof del-merge-dels (previous step)

key0 = datakey(m, m0), key0.data?, key0 ∈ ri, key ∈ ks ⊦ # ks = 0, ((ri ⊖ key) ⊖ ks)[key0] = (ri ⊖ ks)[key0], ks = ∅, inodekey(m) ∈ ks, key0 ∈ ks

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 16:
key ∈ ks, datakey(m, m0) ∈ ri ⊦ # ks = 0, ((ri ⊖ key) ⊖ ks)[datakey(m, m0)] = ri[datakey(m, m0)], ks = ∅, datakey(m, m0) ∈ ks, inodekey(m) ∈ ks

Rule argument

Additional information

Used simplifier rules: at-dels-ro-data: ⊦ datakey(ino, n) ∈ ri ∧ ¬ datakey(ino, n) ∈ ks ∧ ¬ inodekey(ino) ∈ ks → (ri ⊖ ks)[datakey(ino, n)] = ri[datakey(ino, n)];% ⊦ datakey(m, m0).data?; (s)