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Proof step 12 from proof del-del-again (previous step)

key = datakey(m0, m1), key.data?, key ∈ ri, inodekey(m) ∈ ks ⊦ # ks = 0, ((ri ⊖ ks) ⊖ inodekey(m))[key] = (ri ⊖ ks)[key], ks = ∅, inodekey(m0) ∈ ks, key ∈ ks

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 13:
inodekey(m) ∈ ks, datakey(m0, m1) ∈ ri ⊦ # ks = 0, ((ri ⊖ ks) ⊖ inodekey(m))[datakey(m0, m1)] = ri[datakey(m0, m1)], ks = ∅, datakey(m0, m1) ∈ ks, inodekey(m0) ∈ 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)