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Proof step 27 from proof validrefnotnull-union-at-right (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 11:
⊦ is_obj(str, r, st) → ( junkref(str, r, st) ↔ (∃ fs. fs ' ∈ instfields(st[r -- _type] .type .class) ∧ is_referencevalue(st[r -- fs ']) ∧ st[r -- fs '] .refval ≠ jvmref ∧ (¬ st[st[r -- fs '] .refval -- _type] .type ≤ fs .type ∨ junkref(str, st[r -- fs '] .refval, st))))
Proof step 26:
is_obj(str, r, st0), st0[r -- _type] .type = mkclasstype(class0), mkfs(class1, ty, fieldvar) ' ∈ instfields(class), class0 ≤ class, is_valid_ref(str, r, st0) ⊦ r = jvmref, st[r -- mkfs(class1, ty, fieldvar) '] = noval, ∃ fs. fs ' ∈ instfields(st0[r -- _type] .type .class) ∧ is_referencevalue(st0[r -- fs ']) ∧ st0[r -- fs '] .refval ≠ jvmref ∧ (¬ st0[st0[r -- fs '] .refval -- _type] .type ≤ fs .type ∨ junkref(str, st0[r -- fs '] .refval, st0)), r -- mkfs(class1, ty, fieldvar) ' ∈ st0, (is_reftype(ty) ∨ ty = abstract_type) ∧ noval .refval ≠ jvmref

Rule argument

[crewrite-arg: junkref-class, F, [st, r, str] → [st0, r, str]]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ ¬ is_obj(str, r, st) → ( is_valid_ref(str, r, st) ↔ is_array(str, r, st))], [CSIMPSEQ : ⊦ st[r -- _type] .type = mkclasstype(class) → ¬ is_array(str, r, st)])], [EXTRATERMS : (st0, r, str)]]