Nuprl Lemma : dcdr-to-bool-equivalence
∀[P:ℙ]. ∀d:Dec(P). (↑[d]b ⇐⇒ P)
Proof
Definitions occuring in Statement :
dcdr-to-bool: [d]b,
assert: ↑b,
decidable: Dec(P),
uall: ∀[x:A]. B[x],
prop: ℙ,
all: ∀x:A. B[x],
iff: P ⇐⇒ Q
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
iff: P ⇐⇒ Q,
and: P ∧ Q,
implies: P ⇒ Q,
member: t ∈ T,
prop: ℙ,
rev_implies: P ⇐ Q,
decidable: Dec(P),
or: P ∨ Q,
dcdr-to-bool: [d]b,
assert: ↑b,
ifthenelse: if b then t else f fi ,
false: False,
true: True,
not: ¬A
Lemmas referenced :
assert_wf,
dcdr-to-bool_wf,
assert_witness,
decidable_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
lambdaFormation,
independent_pairFormation,
cut,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
introduction,
independent_functionElimination,
universeEquality,
unionElimination,
sqequalRule,
voidElimination,
natural_numberEquality
Latex:
\mforall{}[P:\mBbbP{}]. \mforall{}d:Dec(P). (\muparrow{}[d]\msubb{} \mLeftarrow{}{}\mRightarrow{} P)
Date html generated:
2016_05_13-PM-03_58_26
Last ObjectModification:
2015_12_26-AM-10_50_56
Theory : bool_1
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