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Proof step 4 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)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 3:
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)

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ fv ∈ fv0 ' ↔ fv = fv0])]]