Nuprl Lemma : dcdr-to-bool_wf
∀[P:ℙ]. ∀[d:Dec(P)]. ([d]b ∈ 𝔹)
Proof
Definitions occuring in Statement :
dcdr-to-bool: [d]b,
bool: 𝔹,
decidable: Dec(P),
uall: ∀[x:A]. B[x],
prop: ℙ,
member: t ∈ T
Definitions unfolded in proof :
dcdr-to-bool: [d]b,
bool: 𝔹,
decidable: Dec(P),
uall: ∀[x:A]. B[x],
member: t ∈ T,
or: P ∨ Q,
prop: ℙ,
all: ∀x:A. B[x],
implies: P ⇒ Q
Lemmas referenced :
not_wf,
it_wf,
unit_wf2,
equal_wf,
or_wf
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
isect_memberFormation,
introduction,
cut,
sqequalHypSubstitution,
hypothesisEquality,
equalityTransitivity,
hypothesis,
equalitySymmetry,
thin,
unionEquality,
cumulativity,
extract_by_obid,
isectElimination,
lambdaFormation,
unionElimination,
inlEquality,
inrEquality,
dependent_functionElimination,
independent_functionElimination,
axiomEquality,
isect_memberEquality,
because_Cache,
universeEquality
Latex:
\mforall{}[P:\mBbbP{}]. \mforall{}[d:Dec(P)]. ([d]\msubb{} \mmember{} \mBbbB{})
Date html generated:
2019_06_20-AM-11_32_14
Last ObjectModification:
2018_08_21-PM-01_52_55
Theory : bool_1
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