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Proof step 24 from proof del-merge-dels (previous step)

key0 ∈ ri, key ∈ ks, key0 ∈ ri ⊖ key, key0.data? → inodekey(key0.ino) ≠ key, key0.data? → ¬ inodekey(key0.ino) ∈ ks ⊦ # ks = 0, (ri ⊖ key)[key0] = (ri ⊖ ks)[key0], ks = ∅, key0.data?, key0 ∈ ks

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 25:
key ∈ ks, key0 ∈ ri ⊦ # ks = 0, (ri ⊖ key)[key0] = ri[key0], ks = ∅, key0.data?, key0 ∈ ks

Rule argument

Additional information

Used simplifier rules: at-dels-ro-nodata: ⊦ key ∈ ri ∧ ¬ key ∈ ks ∧ ¬ key.data? → (ri ⊖ ks)[key] = ri[key];%in-del-ro: ⊦ key ∈ ri ⊖ key0 ↔ key ∈ ri ∧ key ≠ key0 ∧ (key.data? → inodekey(key.ino) ≠ key0);