Nuprl Lemma : assert-dectt
∀[p:ℙ]. ∀d:Dec(p). (↑dectt(d) ⇐⇒ p)
Proof
Definitions occuring in Statement :
dectt: dectt(d),
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],
dectt: dectt(d),
decidable: Dec(P),
or: P ∨ Q,
isl: isl(x),
assert: ↑b,
ifthenelse: if b then t else f fi ,
btrue: tt,
iff: P ⇐⇒ Q,
and: P ∧ Q,
implies: P ⇒ Q,
member: t ∈ T,
prop: ℙ,
rev_implies: P ⇐ Q,
true: True,
bfalse: ff,
false: False,
not: ¬A
Lemmas referenced :
true_wf,
false_wf,
decidable_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
lambdaFormation,
sqequalHypSubstitution,
unionElimination,
thin,
sqequalRule,
independent_pairFormation,
hypothesis,
cut,
lemma_by_obid,
natural_numberEquality,
hypothesisEquality,
voidElimination,
independent_functionElimination,
isectElimination,
universeEquality
Latex:
\mforall{}[p:\mBbbP{}]. \mforall{}d:Dec(p). (\muparrow{}dectt(d) \mLeftarrow{}{}\mRightarrow{} p)
Date html generated:
2016_05_15-PM-03_58_15
Last ObjectModification:
2015_12_27-PM-03_07_29
Theory : general
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