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Proof step 3 from proof nonnullrefs-one (previous step)

⊦ r = jvmref, refval(r) ' .nonnullrefs = r '

User applied rule insert lemma

And obtained the following new goals

Proof step 1:
⊦ is_referencevalue(val) ∧ val .refval ≠ jvmref → (val ' + vals) .nonnullrefs = val .refval + vals .nonnullrefs
Proof step 2:
⊦ (vals + vals0) .nonnullrefs = vals .nonnullrefs + vals0 .nonnullrefs

Rule argument

[x0lemmaarg: spec-name: instance-name: lemma-name: nonnullrefs-yes antecedent: succedent: is_referencevalue(val) ∧ val .refval ≠ jvmref → (val ' + vals) .nonnullrefs = val .refval + vals .nonnullrefs substlist: [val, vals] → [refval(r), refval(r) '] add preconditions?: F is rewrite lemma?: F current spec?: T rotate lemma?: F replace all?: F paths: () dummy: () ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPNAMEDSEQ : javavalue, , test-19, ⊦ is_referencevalue(refval(r))], [CSIMPNAMEDSEQ : javavalue, , sel-09, ⊦ refval(r) .refval = r], [CSIMPNAMEDSEQ : list, javavalues, a, ⊦ (vals + vals0) + vals1 = vals + vals0 + vals1], [CSIMPNAMEDSEQ : list, references, c, ⊦ r + refs = r ' + refs], [CSIMPNAMEDSEQ : list, references, app-03, ⊦ refs + refs0 = refs1 + refs0 ↔ refs = refs1], [CSIMPNAMEDSEQ : list, references, a, ⊦ (refs + refs0) + refs1 = refs + refs0 + refs1])], [EXTRATERMS : (refval(r), refval(r) ')]]