A:Type, B,C:(AType), eq:EqDecider(A), f:fpf(A; a.B(a)), g:fpf(A; a.C(a)), x:A.
(fpf-dom(eq; x; f))  (fpf-ap(fpf-join(eq; f; g); eq; x) = fpf-ap(f; eq; x)  B(x)) 

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Definitions	x:A. B(x), x(s), P  Q, fpf-ap(f; eq; x), fpf-join(eq; f; g), t.2, fpf-cap(f; eq; x; z), if b then t else f fi , t  T, tt, x. t(x), ff, prop{i:l}, , Unit, P  Q, P  Q, A, False,
Lemmas	fpf-dom wf, bool wf, eqtt to assert, fpf-ap wf, iff transitivity, assert wf, bnot wf, not wf, eqff to assert, assert of bnot, fpf-trivial-subtype-top, fpf wf, deq wf