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Proof step 43 from proof validrefnotnull-union-at-right (previous step)

is_fskey(sk), sk ∈ instfields(class), st0[r -- _type] .type ≤ mkclasstype(class) ⊦ r = jvmref, st[r -- sk] = noval, is_classtype(st0[r -- _type] .type), r -- sk ∈ st0, junkref(str, r, st0), st0[r -- _type] .type = mkclasstype(st0[r -- _type] .type .class) ∧ (∃ fs. fs ' ∈ instfields(st0[r -- _type] .type .class) ∧ (is_reftype(fs .type) ∨ fs .type = abstract_type) ∧ st0[r -- fs '] .refval ≠ jvmref ∧ (¬ is_referencevalue(st0[r -- fs ']) ∨ ¬ st0[r -- (fs ' ' + _type ')] .type ≤ fs .type ∨ ¬ validref(str, st0[r -- fs '] .refval, fs .type, st0)))

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 42:
⊦ class ≠ `java.lang.Object' .class → (ty ≤ mkclasstype(class) ↔ is_classtype(ty) ∧ ty .class ≤ class)

Rule argument

[speclemmaarg: , class ≠ `java.lang.Object' .class → (ty ≤ mkclasstype(class) ↔ is_classtype(ty) ∧ ty .class ≤ class) ,[class, ty] → [class, st0[r -- _type] .type] ,F ,typefuns , ,subclass-01 ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ instfields (`java.lang.Object' .class) = []], [CSIMPSEQ : ⊦ ¬ sk ∈ []])], [EXTRATERMS : (class, st0[r -- _type] .type)]]