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Proof step 5 from proof delswr (previous step)

r ∈ H, r ∈ rs0, ∀ r1, H0, o0. r1 ∈ rs0 ∧ r1 ∈ H0 → H0[r1, o0] \ rs0 = H0 \ rs0 ⊦ # rs0 = 0, #(rs0 ++ r0) = 0, (H[r, o] -- r0) \ rs0 = (H -- r0) \ rs0, r = r0, rs0 = ∅

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 6:
⊦ (H -- r) \ rs = (H \ rs) -- r
Proof step 7:
r ∈ rs0, r ∈ H, ∀ r1, H0, o0. r1 ∈ rs0 ∧ r1 ∈ H0 → H0[r1, o0] \ rs0 = H0 \ rs0 ⊦ #(rs0 ++ r0) = 0, # rs0 = 0, (H[r, o] \ rs0) -- r0 = (H -- r0) \ rs0, r = r0, rs0 = ∅

Rule argument

spec: <toplevel> name: diffs-sw seq: ⊦ (H -- r) \ rs = (H \ rs) -- r subst: [rs, r, H] → [rs0, r0, H[r, o]] flags: <all paths>

Additional information

Used terms: rs0, r0, H[r, o]