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Proof step 16 from proof sw-del-add (previous step)

r1 ∈ H, r1 ∈ H -- r0 ⊦ (H -- r0)[r1] = (H ++ r)[r1], r = null, r0 = r, r1 = r0, r1 = r, r ∈ H, r ∈ H -- r0

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 17:
r1 ∈ H ⊦ H[r1] = (H ++ r)[r1], r = null, r0 = r, r1 = r0, r ∈ H

Rule argument

Additional information

Used simplifier rules: at-del: r ∈ H ⊦ r ≠ r0 → (H -- r0)[r] = H[r];%in-del: ⊦ r ∈ H -- r0 ↔ r ≠ r0 ∧ r ∈ H;