Nuprl Lemma : TR4b

[T:Type].

[P:T

].

[C:

]. ((

x:T. ((P x)

C))

(

x:T. (P x))

C)

Proof

Definitions occuring in Statement : uall:

[x:A]. B[x], prop:

, all:

x:A. B[x], exists:

x:A. B[x], implies: P

Q, apply: f a, function: x:A

B[x], universe: Type
Definitions : prop:

, member: t

T, uall:

[x:A]. B[x], so_lambda:

x.t[x], implies: P

Q, so_apply: x[s], exists:

x:A. B[x], all:

x:A. B[x]
Lemmas : exists_wf, all_wf
\mforall{}[T:Type]. \mforall{}[P:T {}\mrightarrow{} \mBbbP{}]. \mforall{}[C:\mBbbP{}]. ((\mexists{}x:T. ((P x) {}\mRightarrow{} C)) {}\mRightarrow{} (\mforall{}x:T. (P x)) {}\mRightarrow{} C) Date html generated: 2014_07_17-AM-09_55_40 Last ObjectModification: 2014_06_17-PM-02_29_57 Home Index