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Proof step 18 from proof validfieldinits-rec (previous step)

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. sk0 × val0 ∈ fis → ¬ is_indexkey(sk0) ∧ type∃(str, sk0 .fs .type) ∧ validval(str, val0, sk0 .fs .type, st))

User applied rule case distinction

And obtained the following new goals

Proof step 11:
∀ 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))
Proof step 17:
¬ 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)

Rule argument

[CASEDARG : pos: right 1, ()]

Additional information

[[CONCRETESIMPRULES : ()]]