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Proof step 3 from proof validfieldinits-one (previous step)

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

User applied rule case distinction

And obtained the following new goals

Proof step 2:
∀ sk0, val0. sk0 × val0 = sk × val → is_fskey(sk0) ∧ type∃(str, sk0 .fs .type) ∧ validval(str, val0, sk0 .fs .type, st), sk .fs = mkfs(class, ty, fieldvar) ⊦ ¬ is_indexkey(sk) ∧ type∃(str, ty) ∧ validval(str, val, ty, st)

Rule argument

[CASEDARG : pos: right 1, ()]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ sk × val = sk0 × val0 ↔ sk = sk0 ∧ val = val0], [CSIMPSEQ : ⊦ ¬ is_indexkey(sk) ↔ is_fskey(sk)], [CSIMPSEQ : ⊦ ¬ is_fskey(sk) ↔ is_indexkey(sk)], [CSIMPSEQ : ⊦ is_indexkey(sk) → ¬ is_fskey(sk)], [CSIMPSEQ : ⊦ mkfs(class, ty, fieldvar) .type = ty])]]