Nuprl Lemma : dec2bool_wf
∀[d:Decision]. (dec2bool(d) ∈ 𝔹)
Proof
Definitions occuring in Statement :
dec2bool: dec2bool(d),
decision: Decision,
bool: 𝔹,
uall: ∀[x:A]. B[x],
member: t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
dec2bool: dec2bool(d),
decision: Decision,
all: ∀x:A. B[x],
implies: P ⇒ Q,
prop: ℙ
Lemmas referenced :
top_wf,
btrue_wf,
bfalse_wf,
equal_wf,
decision_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
sqequalHypSubstitution,
hypothesisEquality,
equalityTransitivity,
hypothesis,
equalitySymmetry,
thin,
unionEquality,
extract_by_obid,
lambdaFormation,
unionElimination,
isectElimination,
dependent_functionElimination,
independent_functionElimination,
axiomEquality
Latex:
\mforall{}[d:Decision]. (dec2bool(d) \mmember{} \mBbbB{})
Date html generated:
2019_10_15-AM-10_46_49
Last ObjectModification:
2018_08_21-PM-01_57_35
Theory : basic
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