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Proof step 8 from proof validfieldinits-rec (previous step)

sk .fs = mkfs(class, ty, fieldvar), ∀ sk0, val0. sk0 × val0 = sk × val ∨ sk0 × val0 ∈ fis → is_fskey(sk0) ∧ okval(val0, sk0 .fs .type) ∧ ( 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) ∧ ( sk0 × val0 ∈ fis → ¬ is_indexkey(sk0) ∧ okval(val0, sk0 .fs .type) ∧ ( is_referencevalue(val0) → val0 .refval = jvmref ∨ val0 .refval -- _type ∈ st ∧ is_typevalue(st[val0 .refval -- _type]) ∧ st[val0 .refval -- _type] .type ≤ sk0 .fs .type))

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 7:
sk0 .fs = mkfs(class0, ty0, fieldvar0), sk .fs = mkfs(class, ty, fieldvar), ∀ sk0, val0. sk0 × val0 = sk × val ∨ sk0 × val0 ∈ fis → is_fskey(sk0) ∧ okval(val0, sk0 .fs .type) ∧ ( 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) ∧ ( sk0 × val0 ∈ fis → ¬ is_indexkey(sk0) ∧ okval(val0, ty0) ∧ ( is_referencevalue(val0) → val0 .refval = jvmref ∨ val0 .refval -- _type ∈ st ∧ is_typevalue(st[val0 .refval -- _type]) ∧ st[val0 .refval -- _type] .type ≤ ty0))

Rule argument

[speclemmaarg: , class = fs .class ∧ ty = fs .type ∧ fieldvar = fs .field ↔ fs = mkfs(class, ty, fieldvar) ,[fs, class, ty, fieldvar] → [sk0 .fs, class0, ty0, fieldvar0] ,T ,fieldspec , ,elim ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPELIM : ⊦ class = fs .class ∧ ty = fs .type ∧ fieldvar = fs .field ↔ fs = mkfs(class, ty, fieldvar)])], [EXTRATERMS : (sk0 .fs, class0, ty0, fieldvar0)]]