Nuprl Lemma : exists_det_fun_a
∀[T:Type]. ∀[A:T ⟶ ℙ]. ((∀x:T. SqStable(A x)) ⇒ (detach_fun(T;A) ⇐⇒ {∀x:T. Dec(A x)}))
Proof
Definitions occuring in Statement :
detach_fun: detach_fun(T;A),
sq_stable: SqStable(P),
decidable: Dec(P),
uall: ∀[x:A]. B[x],
prop: ℙ,
guard: {T},
all: ∀x:A. B[x],
iff: P ⇐⇒ Q,
implies: P ⇒ Q,
apply: f a,
function: x:A ⟶ B[x],
universe: Type
Definitions unfolded in proof :
guard: {T}
Lemmas referenced :
exists_det_fun
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
cut,
lemma_by_obid,
hypothesis
Latex:
\mforall{}[T:Type]. \mforall{}[A:T {}\mrightarrow{} \mBbbP{}]. ((\mforall{}x:T. SqStable(A x)) {}\mRightarrow{} (detach\_fun(T;A) \mLeftarrow{}{}\mRightarrow{} \{\mforall{}x:T. Dec(A x)\}))
Date html generated:
2016_05_15-PM-00_00_28
Last ObjectModification:
2015_12_26-PM-11_26_41
Theory : gen_algebra_1
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