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Proof step 29 from proof sw-del-add (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 1:
⊦ H0 = H1 ↔ (∀ r. (r ∈ H0 ↔ r ∈ H1) ∧ (r ∈ H0 → H0[r] = H1[r]))

Rule argument

[x0lemmaarg: spec-name: instance-name: lemma-name: ext antecedent: succedent: H0 = H1 ↔ (∀ r. (r ∈ H0 ↔ r ∈ H1) ∧ (r ∈ H0 → H0[r] = H1[r])) substlist: [H1, H0] → [(H ++ r)[r, o] -- r0, ((H -- r0) ++ r)[r, o]] add preconditions?: F is rewrite lemma?: T current spec?: T rotate lemma?: F replace all?: T paths: ((1, 0, 2)) dummy: () ]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : ((H ++ r)[r, o] -- r0, ((H -- r0) ++ r)[r, o])]]