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Proof step 13 from proof validfieldinits-rec (previous step)

sk0 .fs = mkfs(class0, ty0, fieldvar0), validval(str, val, ty, st), type∃(str, ty), sk0 = mkfs(class, ty, fieldvar) ' ∧ val0 = val ∨ sk0 × val0 ∈ fis, ∀ sk1, val1. sk1 × val1 ∈ fis → is_fskey(sk1) ∧ type∃(str, sk1 .fs .type) ∧ validval(str, val1, sk1 .fs .type, st) ⊦ ¬ is_indexkey(sk0) ∧ type∃(str, ty0) ∧ validval(str, val0, ty0, st)

User applied rule case distinction

And obtained the following new goals

Proof step 12:
sk0 × val0 ∈ fis, sk0 .fs = mkfs(class0, ty0, fieldvar0), validval(str, val, ty, st), type∃(str, ty), ∀ sk1, val1. sk1 × val1 ∈ fis → is_fskey(sk1) ∧ type∃(str, sk1 .fs .type) ∧ validval(str, val1, sk1 .fs .type, st) ⊦ ¬ is_indexkey(sk0) ∧ type∃(str, ty0) ∧ validval(str, val0, ty0, st)

Rule argument

[CASEDARG : pos: left 4, ()]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ fs ' .fs = fs], [CSIMPSEQ : ⊦ mkfs(class, ty, fieldvar) = mkfs(class0, ty0, fieldvar0) ↔ class = class0 ∧ ty = ty0 ∧ fieldvar = fieldvar0], [CSIMPSEQ : ⊦ ¬ is_indexkey(fs ')])]]