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Proof step 21 from proof validfieldinits-rec (previous step)

sk .fs = mkfs(class, ty, fieldvar) ⊦ validfieldinits((sk × val) ' + fis, st) ↔ ¬ is_indexkey(sk) ∧ 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(fis, st)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 1:
⊦ 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 20:
sk .fs = mkfs(class, ty, fieldvar) ⊦ validfieldinits((sk × val) ' + fis, st) ↔ ¬ is_indexkey(sk) ∧ 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) ∧ (∀ 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))

Rule argument

[crewrite-arg: validfieldinits-all, F, [st, fis] → [st, fis]]

Additional information

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