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Proof step 17 from proof validfieldinits-rec (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 16:
sk .fs = mkfs(class, ty, fieldvar), validval(str, val, ty, st), type∃(str, ty), is_fskey(sk), sk0 = sk ∧ 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)

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)])]]