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Proof step 18 from proof validfieldinits-rec (previous step)

sk .fs = mkfs(class, ty, fieldvar) ⊦ (∀ sk0, val0. sk0 × val0 ∈ (sk × val) ' + fis → is_fskey(sk0) ∧ oktype(val0, sk0 .fs .type, st) ∧ ( 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. 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 simplifier applied rule simplifier

And obtained the following new goals

Proof step 17:
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. 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))

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ oktype(val, ty, st) ↔ okval(val, ty)], [CSIMPSEQ : ⊦ (fis + fis0) + fis1 = fis + fis0 + fis1], [CSIMPSEQ : ⊦ ¬ fv ∈ fv0 ' + fis ↔ fv ≠ fv0 ∧ ¬ fv ∈ fis])]]