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Proof step 52 from proof validfieldinits-def-01 (previous step)

sk0 .fs = mkfs(class, ty, fieldvar), ∀ str, st. validfieldinits(str, fis0, st) ↔ validfieldinits(fis0, st) ∧ ¬ junkrefs(str, fis0 .vals, st) ∧ (∀ sk. sk ∈ fis0 → type∃(str, sk .fs .type)) ⊦ is_fskey(sk0) ∧ validval(str, val, ty, st) ∧ type∃(str, ty) ∧ validfieldinits(str, fis0, st) ↔ validfieldinits((sk0 × val) ' + fis0, st) ∧ ¬ junkrefs(str, val ' + fis0 .vals, st) ∧ (∀ sk. sk ∈ (sk0 × val) ' + fis0 → type∃(str, sk .fs .type))

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 4:
⊦ validfieldinits((sk × val) ' + fis, st) ↔ 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) ∧ validfieldinits(fis, st)
Proof step 51:
sk0 .fs = mkfs(class, ty, fieldvar), ∀ str, st. validfieldinits(str, fis0, st) ↔ validfieldinits(fis0, st) ∧ ¬ junkrefs(str, fis0 .vals, st) ∧ (∀ sk. sk ∈ fis0 → type∃(str, sk .fs .type)) ⊦ is_fskey(sk0) ∧ validval(str, val, ty, st) ∧ type∃(str, ty) ∧ validfieldinits(str, fis0, st) ↔ is_fskey(sk0) ∧ oktype(val, sk0 .fs .type, st) ∧ ( is_referencevalue(val) → val .refval = jvmref ∨ val .refval -- _type ∈ st ∧ is_typevalue(st[val .refval -- _type]) ∧ st[val .refval -- _type] .type ≤ sk0 .fs .type) ∧ validfieldinits(fis0, st) ∧ ¬ junkrefs(str, val ' + fis0 .vals, st) ∧ (∀ sk. sk ∈ (sk0 × val) ' + fis0 → type∃(str, sk .fs .type))

Rule argument

[speclemmaarg: , validfieldinits((sk × val) ' + fis, st) ↔ 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) ∧ validfieldinits(fis, st) ,[st, fis, val, sk] → [st, fis0, val, sk0] ,F ,addfuns , ,validfieldinits-rec ]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (st, fis0, val, sk0)]]