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Proof step 10 from proof pathex-addobj (previous step)

fis .keys = instfields(class), is_obj(r, addobj(r, class, fis, st)), validFields(r, fis, addobj(r, class, fis, st)), newref(r, st), validref(str, r, mkclasstype(class), addobj(r, class, fis, st)), fs ' × refval(r0) ∈ fis, fs ' ∈ instfields(class), validrefs(str, r0 ' + refs0, mkclasstype(`java.lang.Object' .class), st), class+∃(str, class), validrefs(str, r ' + r0 ' + refs0, mkclasstype(class), addobj(r, class, fis, st)) ⊦ r = jvmref, class = `java.lang.Object' .class, validrefs(str, r ' + r0 ' + refs0, mkclasstype(`java.lang.Object' .class), addobj(r, class, fis, st)), is_abstract(class), class ≤ `java.lang.Object' .class

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 8:
⊦ class∃(str, class) → class ≤ `java.lang.Object' .class
Proof step 9:
¬ class∃(str, class), fis .keys = instfields(class), is_obj(r, addobj(r, class, fis, st)), validFields(r, fis, addobj(r, class, fis, st)), newref(r, st), validref(str, r, mkclasstype(class), addobj(r, class, fis, st)), fs ' × refval(r0) ∈ fis, fs ' ∈ instfields(class), validrefs(str, r0 ' + refs0, mkclasstype(`java.lang.Object' .class), st), class+∃(str, class), validrefs(str, r ' + r0 ' + refs0, mkclasstype(class), addobj(r, class, fis, st)) ⊦ r = jvmref, class = `java.lang.Object' .class, validrefs(str, r ' + r0 ' + refs0, mkclasstype(`java.lang.Object' .class), addobj(r, class, fis, st)), is_abstract(class), class ≤ `java.lang.Object' .class

Rule argument

[speclemmaarg: ,class∃(str, class) → class ≤ `java.lang.Object' .class ,[str, class] → [str, class] ,F ,typefuns , ,classex-object ]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (str, class)]]