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Proof step 18 from proof pathex-addobj (previous step)

fis .keys = instfields(class), 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) ∧ ¬ is_abstract(class) → validrefs(str, r ' + r0 ' + refs0, mkclasstype(class), addobj(r, class, fis, st)) ⊦ r = jvmref, validrefs(str, r ' + r0 ' + refs0, mkclasstype(`java.lang.Object' .class), addobj(r, class, fis, st))

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 4:
⊦ ty ≤ ty0 ∧ st[r -- _type] = typeval(ty) ∧ ¬ validrefs(str, r ' + refs, ty, st) → ¬ validrefs(str, r ' + refs, ty0, st)
Proof step 17:
¬ ( mkclasstype(`java.lang.Object' .class) ≤ mkclasstype(class) ∧ (addobj(r, class, fis, st)[r -- _type]) = typeval(mkclasstype(`java.lang.Object' .class)) ∧ ¬ validrefs(str, r ' + r0 ' + refs0, mkclasstype(`java.lang.Object' .class), addobj(r, class, fis, st))), fis .keys = instfields(class), 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) ∧ ¬ is_abstract(class) → validrefs(str, r ' + r0 ' + refs0, mkclasstype(class), addobj(r, class, fis, st)) ⊦ r = jvmref, validrefs(str, r ' + r0 ' + refs0, mkclasstype(`java.lang.Object' .class), addobj(r, class, fis, st))

Rule argument

[crewrite-arg: validrefs-subtype , F , [ty, ty0, st, r, str, refs] → [mkclasstype(`java.lang.Object' .class), mkclasstype(class), addobj(r, class, fis, st), r, str, r0 ' + refs0] ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ fis .keys = instfields(class) → ¬ _type ∈ fis], [CSIMPSEQ : ¬ _type ∈ fis ⊦ (addobj(r, class1, fis, st) [r -- _type ] ) = typeval(mkclasstype(class1))], [CSIMPSEQ : ⊦ typeval(ty) = typeval(ty0) ↔ ty = ty0], [CSIMPSEQ : ⊦ mkclasstype(class) = mkclasstype(class0) ↔ class = class0], [CSIMPSEQ : ⊦ mkclasstype(class1) ≤ mkclasstype(class2) ↔ class1 ≤ class2], [CSIMPSEQ : ⊦ `java.lang.Object' .class ≤ class ↔ class = `java.lang.Object' .class], [CSIMPSEQ : ⊦ instfields (`java.lang.Object' .class) = []], [CSIMPSEQ : ⊦ fis .keys = [] ↔ fis = []], [CSIMPSEQ : ⊦ ¬ sk ∈ []], [CSIMPSEQ : ⊦ (refs + refs0) + refs1 = refs + refs0 + refs1])], [EXTRATERMS : (mkclasstype(`java.lang.Object' .class), mkclasstype(class), addobj(r, class, fis, st), r, str, r0 ' + refs0)]]