Nuprl Lemma : b2i_bounds
∀[b:𝔹]. ((0 ≤ b2i(b)) ∧ (b2i(b) ≤ 1))
Proof
Definitions occuring in Statement :
b2i: b2i(b),
bool: 𝔹,
uall: ∀[x:A]. B[x],
le: A ≤ B,
and: P ∧ Q,
natural_number: $n
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
and: P ∧ Q,
le: A ≤ B,
not: ¬A,
implies: P ⇒ Q,
false: False,
prop: ℙ,
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
b2i: b2i(b),
ifthenelse: if b then t else f fi ,
cand: A c∧ B,
less_than': less_than'(a;b),
bfalse: ff
Lemmas referenced :
less_than'_wf,
b2i_wf,
bool_wf,
false_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
sqequalHypSubstitution,
productElimination,
thin,
independent_pairEquality,
lambdaEquality,
dependent_functionElimination,
hypothesisEquality,
voidElimination,
lemma_by_obid,
isectElimination,
hypothesis,
natural_numberEquality,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
unionElimination,
equalityElimination,
independent_pairFormation,
lambdaFormation,
because_Cache
Latex:
\mforall{}[b:\mBbbB{}]. ((0 \mleq{} b2i(b)) \mwedge{} (b2i(b) \mleq{} 1))
Date html generated:
2016_05_13-PM-03_55_59
Last ObjectModification:
2015_12_26-AM-10_52_51
Theory : bool_1
Home
Index