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Proof step 35 from proof junkref-addobj-01 (previous step)

fis .keys = instfields(class), fis[mkfs(class0, ty, fieldvar) '] = refval(r0), is_array(str, r0, st), mkfs(class0, ty, fieldvar) ' ∈ fis, junkrefs(str, r0 ' + refs, ty, addobj(r, class, fis, st)), mkfs(class0, ty, fieldvar) ' ∈ instfields(class), validfieldinits(fis, st), class+∃(str, class), newref(r, st) ⊦ r = jvmref, r0 = jvmref, is_abstract(class), junkrefs(str, r0 ' + refs, st[r0 -- _type] .type, st), st[r0 -- _type] .type ≤ ty

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 33:
⊦ validfieldinits(fis, st) ↔ (∀ sk, val. sk × val ∈ fis → is_fskey(sk) ∧ oktype(val, sk .fs .type, st) ∧ ( is_referencevalue(val) → val .refval = jvmref ∨ val .refval -- _type ∈ st ∧ is_typevalue(st[val .refval -- _type]) ∧ st[val .refval -- _type] .type ≤ sk .fs .type))
Proof step 34:
fis .keys = instfields(class), fis[mkfs(class0, ty, fieldvar) '] = refval(r0), is_array(str, r0, st), mkfs(class0, ty, fieldvar) ' ∈ fis, junkrefs(str, r0 ' + refs, ty, addobj(r, class, fis, st)), mkfs(class0, ty, fieldvar) ' ∈ instfields(class), ∀ sk, val. sk × val ∈ fis → is_fskey(sk) ∧ oktype(val, sk .fs .type, st) ∧ ( is_referencevalue(val) → val .refval = jvmref ∨ val .refval -- _type ∈ st ∧ is_typevalue(st[val .refval -- _type]) ∧ st[val .refval -- _type] .type ≤ sk .fs .type), class+∃(str, class), newref(r, st) ⊦ r = jvmref, r0 = jvmref, is_abstract(class), junkrefs(str, r0 ' + refs, st[r0 -- _type] .type, st), st[r0 -- _type] .type ≤ ty

Rule argument

[speclemmaarg: , validfieldinits(fis, st) ↔ (∀ sk, val. sk × val ∈ fis → is_fskey(sk) ∧ oktype(val, sk .fs .type, st) ∧ ( is_referencevalue(val) → val .refval = jvmref ∨ val .refval -- _type ∈ st ∧ is_typevalue(st[val .refval -- _type]) ∧ st[val .refval -- _type] .type ≤ sk .fs .type)) ,[st, fis] → [st, fis] ,F ,addfuns , ,validfieldinits-all ]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (st, fis)]]