Nuprl Lemma : bool-to-dcdr-aux
∀[A:Type]. ∀f:A ⟶ 𝔹. ∀x:A. Dec(f x = tt)
Proof
Definitions occuring in Statement :
btrue: tt,
bool: 𝔹,
decidable: Dec(P),
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
apply: f a,
function: x:A ⟶ B[x],
universe: Type,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
member: t ∈ T
Lemmas referenced :
decidable__equal_bool,
btrue_wf,
bool_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
lambdaFormation,
cut,
lemma_by_obid,
sqequalHypSubstitution,
dependent_functionElimination,
thin,
applyEquality,
hypothesisEquality,
hypothesis,
functionEquality,
universeEquality
Latex:
\mforall{}[A:Type]. \mforall{}f:A {}\mrightarrow{} \mBbbB{}. \mforall{}x:A. Dec(f x = tt)
Date html generated:
2016_05_15-PM-03_27_45
Last ObjectModification:
2015_12_27-PM-01_08_46
Theory : general
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