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Proof step 3 from proof delswr (previous step)

r ∈ rs, r ∈ H ⊦ # rs = 0, H[r, o] \ rs = H \ rs, rs = ∅

User applied rule structural induction

And obtained the following new goals

Proof step 4:
r ∈ H, r ∈ rs0 ++ r0, ∀ r, H, o. r ∈ rs0 ∧ r ∈ H → # rs0 = 0 ∨ H[r, o] \ rs0 = H \ rs0 ∨ rs0 = ∅ ⊦ #(rs0 ++ r0) = 0, rs0 ++ r0 = ∅, H[r, o] \ (rs0 ++ r0) = H \ (rs0 ++ r0)

Rule argument

indvar: rs

Additional information

Used simplifier rules: refset generated by ∅, ++;;