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Proof step 3 from proof sw-delswr (previous step)

r ∈ H ⊦ H[r, o] \ rs = (H \ rs)[r, o], r ∈ rs

User applied rule structural induction

And obtained the following new goals

Proof step 4:
r ∈ H, ∀ r, H, o. r ∈ H → H[r, o] \ rs0 = (H \ rs0)[r, o] ∨ r ∈ rs0 ⊦ H[r, o] \ (rs0 ++ r0) = (H \ (rs0 ++ r0))[r, o], r ∈ rs0 ++ r0

Rule argument

indvar: rs

Additional information

Used simplifier rules: diffs-emp: ⊦ H0 \ ∅ = H0;%refset generated by ∅, ++;;