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Proof step 10 from proof validfieldinits-rec (previous step)

sk0 .fs = mkfs(class0, ty0, fieldvar0), okval(val, ty), ∀ 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), sk0 = mkfs(class, ty, fieldvar) ' ∧ val0 = val ∨ sk0 × val0 ∈ fis, 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_fskey(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) ⊦ ¬ 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)

User applied rule case distinction

And closed the goal!

Rule argument

[CASEDARG : pos: right 1, ()]

Additional information

[[CONCRETESIMPRULES : ([CSIMPFORWARD : ⊦ r -- sk ∈ st → r ∈ st], [CSIMPSEQ : ⊦ is_indexkey(sk) → ¬ is_fskey(sk)], [CSIMPSEQ : ⊦ fs ' .fs = fs], [CSIMPSEQ : ⊦ mkfs(class, ty, fieldvar) = mkfs(class0, ty0, fieldvar0) ↔ class = class0 ∧ ty = ty0 ∧ fieldvar = fieldvar0], [CSIMPSEQ : ⊦ ¬ is_indexkey(fs ')])]]