Nuprl Lemma : assert_dec2bool
∀[d:Decision]. uiff(↑dec2bool(d);↑d)
Proof
Definitions occuring in Statement :
dec2bool: dec2bool(d),
decision: Decision,
assert: ↑b,
uiff: uiff(P;Q),
uall: ∀[x:A]. B[x]
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
assert: ↑b,
dec2bool: dec2bool(d),
ifthenelse: if b then t else f fi ,
bfalse: ff,
btrue: tt,
uiff: uiff(P;Q),
and: P ∧ Q,
uimplies: b supposing a,
member: t ∈ T,
decision: Decision,
true: True,
false: False,
all: ∀x:A. B[x],
implies: P ⇒ Q,
prop: ℙ
Lemmas referenced :
decision_wf,
true_wf,
false_wf,
equal_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
independent_pairFormation,
introduction,
cut,
sqequalHypSubstitution,
unionElimination,
thin,
sqequalRule,
natural_numberEquality,
voidElimination,
hypothesisEquality,
extract_by_obid,
hypothesis,
lambdaFormation,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
isectElimination,
dependent_functionElimination,
independent_functionElimination,
instantiate,
because_Cache
Latex:
\mforall{}[d:Decision]. uiff(\muparrow{}dec2bool(d);\muparrow{}d)
Date html generated:
2017_10_01-AM-08_28_34
Last ObjectModification:
2017_07_26-PM-04_23_34
Theory : basic
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