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Proof step 50 from proof validfieldinits-def-01 (previous step)

sk0 .fs = mkfs(class, ty, fieldvar), is_fskey(sk0), ∀ 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 ∈ (sk0 × val) ' + fis0 → type∃(str, sk .fs .type))

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 49:
sk0 = fs ', fs = mkfs(class, ty, fieldvar), is_fskey(sk0), ∀ 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 ∈ (sk0 × val) ' + fis0 → type∃(str, sk .fs .type))

Rule argument

[speclemmaarg: ,is_fskey(sk) → (fs = sk .fs ↔ sk = fs ') ,[sk, fs] → [sk0, fs] ,T ,storekey , ,elim-03 ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPELIM : ⊦ is_fskey(sk) → (fs = sk .fs ↔ sk = fs ')])], [EXTRATERMS : (sk0, fs)]]