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Proof step 11 from proof validfieldinits-rec (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 10:
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) ⊦ ¬ is_indexkey(sk) ∧ validval(str, val, ty, st) ∧ type∃(str, ty) ∧ (sk0 × val0 ∈ fis → ¬ is_indexkey(sk0) ∧ type∃(str, sk0 .fs .type) ∧ validval(str, val0, sk0 .fs .type, st))

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ()]]