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Proof step 7 from proof validrefnotnull-union-at-right (previous step)

st0[r -- _type] .type = mkclasstype(class0), validref(str, r, mkclasstype(class), st0), mkfs(class1, ty, fieldvar) ' ∈ instfields(class) ⊦ st[r -- mkfs(class1, ty, fieldvar) '] = noval, r = jvmref, r -- mkfs(class1, ty, fieldvar) ' ∈ st0, class0 ≤ class, mkfs(class1, ty, fieldvar) ' ∈ instfields(class0) ∧ (is_reftype(ty) ∨ ty = abstract_type) ∧ noval .refval ≠ jvmref

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 6:
⊦ validref(str, r, ty, st) ↔ r = jvmref ∨ st[r -- _type] .type ≤ ty ∧ ¬ junkref(str, r, st)

Rule argument

[crewrite-arg: validref-def , F , [st, ty, r, str] → [st0, mkclasstype(class), r, str] ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ mkclasstype(class1) ≤ mkclasstype(class2) ↔ class1 ≤ class2], [CSIMPSEQ : ⊦ fs ' ∈ instfields(class) ∧ class0 ≤ class → fs ' ∈ instfields(class0)])], [EXTRATERMS : (st0, mkclasstype(class), r, str)]]