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Proof step 13 from proof validfieldinits-rec (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, sk0 = mkfs(class, ty, fieldvar) ' ∧ val0 = val ∨ sk0 × val0 ∈ fis, ∀ sk1, val1. sk1 × val1 ∈ fis → is_fskey(sk1) ∧ okval(val1, sk1 .fs .type) ∧ ( is_referencevalue(val1) → val1 .refval = jvmref ∨ val1 .refval -- _type ∈ st ∧ is_typevalue(st[val1 .refval -- _type]) ∧ st[val1 .refval -- _type] .type ≤ sk1 .fs .type) ⊦ ¬ 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 12:
sk0 .fs = mkfs(class0, ty0, fieldvar0), 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 = mkfs(class, ty, fieldvar) ' ∧ val0 = val ∨ sk0 × val0 ∈ fis, ∀ sk1, val1. sk1 × val1 ∈ fis → is_fskey(sk1) ∧ okval(val1, sk1 .fs .type) ∧ ( is_referencevalue(val1) → val1 .refval = jvmref ∨ val1 .refval -- _type ∈ st ∧ is_typevalue(st[val1 .refval -- _type]) ∧ st[val1 .refval -- _type] .type ≤ sk1 .fs .type) ⊦ ¬ 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)]]