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Proof step 44 from proof validfieldinits-def-01 (previous step)

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)), validfieldinits(str, fis0, st) ↔ validfieldinits(fis0, st) ∧ ¬ junkrefs(str, fis0 .vals, st) ∧ (∀ sk. sk ∈ fis0 → type∃(str, sk .fs .type)), ∀ 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)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 43:
validfieldinits(str, fis0, st) ↔ (∀ sk. sk ∈ fis0 → type∃(str, sk .fs .type)), okval(val, ty), validfieldinits(fis0, st), is_referencevalue(val) → val .refval = jvmref ∨ val .refval -- _type ∈ st ∧ is_typevalue(st[val .refval -- _type]) ∧ st[val .refval -- _type] .type ≤ ty, ¬ is_referencevalue(val) ∨ ¬ junkref(str, val .refval, st), ∀ str, st. validfieldinits(str, fis0, st) ↔ validfieldinits(fis0, st) ∧ ¬ junkrefs(str, fis0 .vals, st) ∧ (∀ sk. sk ∈ fis0 → type∃(str, sk .fs .type)), ∀ sk. sk = mkfs(class, ty, fieldvar) ' ∨ sk ∈ fis0 → type∃(str, sk .fs .type) ⊦ junkrefs(str, fis0 .vals, st), validval(str, val, ty, st) ∧ type∃(str, ty) ∧ validfieldinits(str, fis0, st)

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ (fis + fis0) + fis1 = fis + fis0 + fis1], [CSIMPSEQ : ⊦ sk ∈ (sk0 × val) ' ↔ sk = sk0], [CSIMPSEQ : ⊦ sk ∈ fis + fis0 ↔ sk ∈ fis ∨ sk ∈ fis0])]]