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Proof step 2 from proof sw-del-add-01 (previous step)

r0 ∈ H1 ⊦ r = null, ((H -- r0) ++ r)[r, o] = (H ++ r)[r, o] -- r0, r ∈ H, r ∈ H1

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 1:
r ≠ null ∧ ¬ r ∈ H ⊦ r0 ≠ r → ((H -- r0) ++ r)[r, o] = (H ++ r)[r, o] -- r0

Rule argument

[x0lemmaarg: spec-name: instance-name: lemma-name: sw-del-add antecedent: r ≠ null ∧ ¬ r ∈ H succedent: r0 ≠ r → ((H -- r0) ++ r)[r, o] = (H ++ r)[r, o] -- r0 substlist: [o, r, r0, H] → [o, r, r0, H] add preconditions?: F is rewrite lemma?: T current spec?: T rotate lemma?: F replace all?: T paths: ((1, 0, 1, 1, 0)) dummy: () ]

Additional information

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