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Proof step 48 from proof validfieldinits-def-01 (previous step)

∀ str, st. validfieldinits(str, fis0, st) ↔ validfieldinits(fis0, st) ∧ ¬ junkrefs(str, fis0 .vals, st) ∧ (∀ sk. sk ∈ fis0 → type∃(str, sk .fs .type)) ⊦ validval(str, val, ty, st) ∧ type∃(str, ty) ∧ validfieldinits(str, fis0, st) ↔ okval(val, ty) ∧ ( is_referencevalue(val) → val .refval = jvmref ∨ val .refval -- _type ∈ st ∧ is_typevalue(st[val .refval -- _type]) ∧ st[val .refval -- _type] .type ≤ ty) ∧ validfieldinits(fis0, st) ∧ ¬ junkrefs(str, val ' + fis0 .vals, st) ∧ (∀ sk. sk ∈ (mkfs(class, ty, fieldvar) ' × val) ' + fis0 → type∃(str, sk .fs .type))

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 5:
⊦ junkrefs(str, val ' + vals, st) ↔ is_referencevalue(val) ∧ junkref(str, val .refval, st) ∨ junkrefs(str, vals, st)
Proof step 47:
∀ str, st. validfieldinits(str, fis0, st) ↔ validfieldinits(fis0, st) ∧ ¬ junkrefs(str, fis0 .vals, st) ∧ (∀ sk. sk ∈ fis0 → type∃(str, sk .fs .type)) ⊦ validval(str, val, ty, st) ∧ type∃(str, ty) ∧ validfieldinits(str, fis0, st) ↔ okval(val, ty) ∧ ( is_referencevalue(val) → val .refval = jvmref ∨ val .refval -- _type ∈ st ∧ is_typevalue(st[val .refval -- _type]) ∧ st[val .refval -- _type] .type ≤ ty) ∧ validfieldinits(fis0, st) ∧ ¬ (is_referencevalue(val) ∧ junkref(str, val .refval, st) ∨ junkrefs(str, fis0 .vals, st)) ∧ (∀ sk. sk ∈ (mkfs(class, ty, fieldvar) ' × val) ' + fis0 → type∃(str, sk .fs .type))

Rule argument

[crewrite-arg: junkreflist-rec , F , [st, vals, val, str] → [st, fis0 .vals, val, str] ]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (st, fis0 .vals, val, str)]]