Nuprl Lemma : bool-to-dcdr_wf
∀[A:Type]. ∀[f:A ⟶ 𝔹]. ∀[x:A]. ({f}b x ∈ Dec(f x = tt))
Proof
Definitions occuring in Statement :
bool-to-dcdr: {f}b,
btrue: tt,
bool: 𝔹,
decidable: Dec(P),
uall: ∀[x:A]. B[x],
member: t ∈ T,
apply: f a,
function: x:A ⟶ B[x],
universe: Type,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
bool-to-dcdr: {f}b,
subtype_rel: A ⊆r B,
all: ∀x:A. B[x],
prop: ℙ
Lemmas referenced :
bool_wf,
bool-to-dcdr-aux,
decidable_wf,
equal-wf-T-base
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalHypSubstitution,
hypothesis,
sqequalRule,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
hypothesisEquality,
isect_memberEquality,
isectElimination,
thin,
because_Cache,
functionEquality,
extract_by_obid,
universeEquality,
applyEquality,
instantiate,
lambdaEquality,
isectEquality,
cumulativity,
baseClosed,
functionExtensionality
Latex:
\mforall{}[A:Type]. \mforall{}[f:A {}\mrightarrow{} \mBbbB{}]. \mforall{}[x:A]. (\{f\}\msubb{} x \mmember{} Dec(f x = tt))
Date html generated:
2018_05_21-PM-06_29_18
Last ObjectModification:
2018_05_19-PM-04_40_13
Theory : general
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