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Proof step 3 from proof split-union (previous step)

R0(H0, H1), R1(H2, H3), H0 ⊥ H2, H1 ⊥ H3 ⊦ (R0 * R1)(H0 ∪ H2, H1 ∪ H3)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 1:
⊦ (R0 * R1)(H0, H1) ↔ (∃ H2, H3, H4, H5. H2 ⊥ H3 ∧ H4 ⊥ H5 ∧ H2 ∪ H3 = H0 ∧ H4 ∪ H5 = H1 ∧ R0(H2, H4) ∧ R1(H3, H5))

Rule argument

[x0lemmaarg: spec-name: instance-name: lemma-name: sep antecedent: succedent: (R0 * R1)(H0, H1) ↔ (∃ H2, H3, H4, H5. H2 ⊥ H3 ∧ H4 ⊥ H5 ∧ H2 ∪ H3 = H0 ∧ H4 ∪ H5 = H1 ∧ R0(H2, H4) ∧ R1(H3, H5)) substlist: [H1, H0, R1, R0] → [H1 ∪ H3, H0 ∪ H2, R1, R0] add preconditions?: F is rewrite lemma?: T current spec?: T rotate lemma?: F replace all?: T paths: ((1, 0, 0)) dummy: () ]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (H1 ∪ H3, H0 ∪ H2, R1, R0)]]