Nuprl Lemma : b2i_wf
∀[b:𝔹]. (b2i(b) ∈ ℤ)
Proof
Definitions occuring in Statement :
b2i: b2i(b),
bool: 𝔹,
uall: ∀[x:A]. B[x],
member: t ∈ T,
int: ℤ
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
b2i: b2i(b),
all: ∀x:A. B[x],
implies: P ⇒ Q,
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
uiff: uiff(P;Q),
and: P ∧ Q,
uimplies: b supposing a,
ifthenelse: if b then t else f fi ,
bfalse: ff,
prop: ℙ
Lemmas referenced :
bool_wf,
eqtt_to_assert,
uiff_transitivity,
equal-wf-T-base,
assert_wf,
bnot_wf,
not_wf,
eqff_to_assert,
assert_of_bnot,
equal_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
Error :isect_memberFormation_alt,
introduction,
cut,
sqequalRule,
hypothesisEquality,
thin,
extract_by_obid,
hypothesis,
lambdaFormation,
sqequalHypSubstitution,
unionElimination,
equalityElimination,
isectElimination,
because_Cache,
productElimination,
independent_isectElimination,
natural_numberEquality,
baseClosed,
independent_functionElimination,
equalityTransitivity,
equalitySymmetry,
dependent_functionElimination,
axiomEquality,
Error :universeIsType
Latex:
\mforall{}[b:\mBbbB{}]. (b2i(b) \mmember{} \mBbbZ{})
Date html generated:
2019_06_20-AM-11_31_10
Last ObjectModification:
2018_09_26-AM-11_29_28
Theory : bool_1
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