Nuprl Lemma : dec2bool_decidable
∀[P:ℙ]. ∀p:Dec(P). {↑dec2bool(p) ⇐⇒ P}
Proof
Definitions occuring in Statement :
dec2bool: dec2bool(d),
assert: ↑b,
decidable: Dec(P),
uall: ∀[x:A]. B[x],
prop: ℙ,
guard: {T},
all: ∀x:A. B[x],
iff: P ⇐⇒ Q
Definitions unfolded in proof :
guard: {T},
dec2bool: dec2bool(d),
decidable: Dec(P),
or: P ∨ Q,
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
iff: P ⇐⇒ Q,
and: P ∧ Q,
implies: P ⇒ Q,
assert: ↑b,
ifthenelse: if b then t else f fi ,
btrue: tt,
bfalse: ff,
false: False,
member: t ∈ T,
prop: ℙ,
rev_implies: P ⇐ Q,
true: True,
not: ¬A
Lemmas referenced :
assert_wf,
not_wf,
btrue_wf,
bfalse_wf,
equal_wf,
assert_witness
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
isect_memberFormation,
lambdaFormation,
independent_pairFormation,
unionElimination,
thin,
sqequalHypSubstitution,
hypothesis,
voidElimination,
cut,
introduction,
extract_by_obid,
isectElimination,
hypothesisEquality,
equalityTransitivity,
equalitySymmetry,
unionEquality,
cumulativity,
dependent_functionElimination,
independent_functionElimination,
natural_numberEquality,
universeEquality
Latex:
\mforall{}[P:\mBbbP{}]. \mforall{}p:Dec(P). \{\muparrow{}dec2bool(p) \mLeftarrow{}{}\mRightarrow{} P\}
Date html generated:
2019_10_15-AM-10_46_57
Last ObjectModification:
2018_08_21-PM-01_57_38
Theory : basic
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