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Proof step 5 from proof validfieldinits-one (previous step)

sk .fs = mkfs(class, ty, fieldvar) ⊦ validfieldinits((sk × val) ', 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)

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 4:
sk .fs = mkfs(class, ty, fieldvar) ⊦ (∀ sk0, val0. sk0 × val0 ∈ (sk × val) ' → is_fskey(sk0) ∧ oktype(val0, sk0 .fs .type, st) ∧ ( is_referencevalue(val0) → val0 .refval = jvmref ∨ val0 .refval -- _type ∈ st ∧ is_typevalue(st[val0 .refval -- _type]) ∧ st[val0 .refval -- _type] .type ≤ sk0 .fs .type)) ↔ ¬ 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)

Rule argument

[crewrite-arg: validfieldinits-all, F, [st, fis] → [st, (sk × val) ']]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (st, (sk × val) ')]]