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Proof step 14 from proof validfieldinits-rec (previous step)

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, sk0 .fs .type) ∧ validval(str, val0, sk0 .fs .type, st)

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 13:
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)

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)]]