Nuprl Lemma : decdr-to-bool_wf
∀[T:Type]. ∀[A,B:T ⟶ ℙ]. ∀[d:x:T ⟶ (A[x] + B[x])]. (bool(d) ∈ T ⟶ 𝔹)
Proof
Definitions occuring in Statement :
decdr-to-bool: bool(d),
bool: 𝔹,
uall: ∀[x:A]. B[x],
prop: ℙ,
so_apply: x[s],
member: t ∈ T,
function: x:A ⟶ B[x],
union: left + right,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
so_apply: x[s],
subtype_rel: A ⊆r B,
prop: ℙ,
decdr-to-bool: bool(d),
it: ⋅,
bfalse: ff,
btrue: tt,
ifthenelse: if b then t else f fi ,
all: ∀x:A. B[x],
implies: P ⇒ Q
Lemmas referenced :
subtype_rel_self,
btrue_wf,
bfalse_wf,
equal_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
cut,
sqequalHypSubstitution,
hypothesis,
functionEquality,
hypothesisEquality,
unionEquality,
applyEquality,
thin,
sqequalRule,
instantiate,
introduction,
extract_by_obid,
isectElimination,
because_Cache,
cumulativity,
universeEquality,
lambdaEquality,
lambdaFormation,
equalityTransitivity,
equalitySymmetry,
unionElimination,
dependent_functionElimination,
independent_functionElimination
Latex:
\mforall{}[T:Type]. \mforall{}[A,B:T {}\mrightarrow{} \mBbbP{}]. \mforall{}[d:x:T {}\mrightarrow{} (A[x] + B[x])]. (bool(d) \mmember{} T {}\mrightarrow{} \mBbbB{})
Date html generated:
2019_10_30-AM-07_36_05
Last ObjectModification:
2018_08_21-PM-02_01_15
Theory : reals
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