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Proof step 69 from proof validrefs-addobj-01 (previous step)

fis .keys = instfields(class), unique_al(fis), validrefs(str, r0 ' + refs0, ty, st), mkfs(class0, ty0, fieldvar) ' ∈ instfields(class), mkfs(class0, ty0, fieldvar) ' × refval(r0) ∈ fis, validref(str, r, mkclasstype(class), addobj(r, class, fis, st)), newref(r, st), validFields(r, fis, addobj(r, class, fis, st)), class+∃(str, class), ∀ sk. sk ∈ instfields(class) → goodfieldandtype(r, sk, addobj(r, class, fis, st)) ⊦ r0 ' + refs0 = jvmref ', r = jvmref, is_reftype(ty0), is_abstract(class)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 60:
⊦ is_predefined_class(class) → instfields(class) = []
Proof step 68:
¬ is_predefined_class(class), fis .keys = instfields(class), unique_al(fis), validrefs(str, r0 ' + refs0, ty, st), mkfs(class0, ty0, fieldvar) ' ∈ instfields(class), mkfs(class0, ty0, fieldvar) ' × refval(r0) ∈ fis, validref(str, r, mkclasstype(class), addobj(r, class, fis, st)), newref(r, st), validFields(r, fis, addobj(r, class, fis, st)), class+∃(str, class), ∀ sk. sk ∈ instfields(class) → goodfieldandtype(r, sk, addobj(r, class, fis, st)) ⊦ r0 ' + refs0 = jvmref ', r = jvmref, is_reftype(ty0), is_abstract(class)

Rule argument

[speclemmaarg: ,is_predefined_class(class) → instfields(class) = [] ,[class] → [class] ,F ,addfuns , ,instfields-predef ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ fis .keys = [] ↔ fis = []], [CSIMPSEQ : ⊦ ¬ sk ∈ []])], [EXTRATERMS : (class)]]