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Proof step 12 from proof nonnullrefs-append (previous step)

∀ vals0. (vals1 + vals0) .nonnullrefs = vals1 .nonnullrefs + vals0 .nonnullrefs ⊦ ((val ' + vals1) + vals0) .nonnullrefs = (val ' + vals1) .nonnullrefs + vals0 .nonnullrefs

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 2:
⊦ ¬ is_referencevalue(val) ∨ val .refval = jvmref → (val ' + vals) .nonnullrefs = vals .nonnullrefs
Proof step 7:
¬ (¬ is_referencevalue(val) ∨ val .refval = jvmref), ∀ vals0. (vals1 + vals0) .nonnullrefs = vals1 .nonnullrefs + vals0 .nonnullrefs ⊦ ((val ' + vals1) + vals0) .nonnullrefs = (val ' + vals1) .nonnullrefs + vals0 .nonnullrefs
Proof step 11:
¬ is_referencevalue(val) ∨ val .refval = jvmref, ∀ vals0. (vals1 + vals0) .nonnullrefs = vals1 .nonnullrefs + vals0 .nonnullrefs ⊦ (vals1 + vals0) .nonnullrefs = (val ' + vals1) .nonnullrefs + vals0 .nonnullrefs

Rule argument

[x0lemmaarg: spec-name: instance-name: lemma-name: nonnullrefs-no antecedent: succedent: ¬ is_referencevalue(val) ∨ val .refval = jvmref → (val ' + vals) .nonnullrefs = vals .nonnullrefs substlist: [vals, val] → [vals1 + vals0, val] add preconditions?: F is rewrite lemma?: T current spec?: T rotate lemma?: F replace all?: T paths: ((1, 0, 0, 1, 0)) dummy: () ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPNAMEDSEQ : list, javavalues, a, ⊦ (vals + vals0) + vals1 = vals + vals0 + vals1])], [EXTRATERMS : (vals1 + vals0, val)]]