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Proof step 5 from proof sw-delswr (previous step)

r ∈ H, ∀ r, H, o. r ∈ H → H[r, o] \ rs0 = (H \ rs0)[r, o] ∨ r ∈ rs0 ⊦ (H[r, o] -- r0) \ rs0 = ((H -- r0) \ rs0)[r, o], r = r0, r ∈ rs0

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 6:
r ∈ H ⊦ r ≠ r0 → H[r, o] -- r0 = (H -- r0)[r, o]
Proof step 7:
r ∈ H, ∀ r, H, o. r ∈ H → H[r, o] \ rs0 = (H \ rs0)[r, o] ∨ r ∈ rs0 ⊦ (H -- r0)[r, o] \ rs0 = ((H -- r0) \ rs0)[r, o], r = r0, r ∈ rs0

Rule argument

spec: <toplevel> name: sw-delwr seq: r ∈ H ⊦ r ≠ r0 → H[r, o] -- r0 = (H -- r0)[r, o] subst: [r0, o, r, H] → [r0, o, r, H] flags: <all paths>

Additional information

Used terms: r0, o, r, H