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Proof step 16 from proof validfieldinits-rec (previous step)

¬ 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. 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)), 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)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 15:
sk .fs = mkfs(class, ty, fieldvar), okval(val, ty), is_fskey(sk), is_referencevalue(val) → val .refval = jvmref ∨ val .refval -- _type ∈ st ∧ is_typevalue(st[val .refval -- _type]) ∧ st[val .refval -- _type] .type ≤ ty, sk0 = sk ∧ 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)

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ ¬ is_fskey(sk) ↔ is_indexkey(sk)], [CSIMPSEQ : ⊦ sk × val = sk0 × val0 ↔ sk = sk0 ∧ val = val0], [CSIMPSEQ : ⊦ ¬ is_indexkey(sk) ↔ is_fskey(sk)])]]