Nuprl Lemma : opt_wf
∀[T:Type]. ∀[x:T]. ∀[b:𝔹]. ((b?x) ∈ T?)
Proof
Definitions occuring in Statement :
opt: (b?x),
bool: 𝔹,
uall: ∀[x:A]. B[x],
unit: Unit,
member: t ∈ T,
union: left + right,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
opt: (b?x),
all: ∀x:A. B[x],
implies: P ⇒ Q,
exposed-bfalse: exposed-bfalse,
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 :
eqtt_to_assert,
unit_wf2,
uiff_transitivity,
equal-wf-T-base,
bool_wf,
assert_wf,
bnot_wf,
not_wf,
eqff_to_assert,
assert_of_bnot,
it_wf,
equal_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation_alt,
introduction,
cut,
sqequalRule,
hypothesisEquality,
thin,
because_Cache,
lambdaFormation,
sqequalHypSubstitution,
unionElimination,
equalityElimination,
extract_by_obid,
isectElimination,
hypothesis,
productElimination,
independent_isectElimination,
inlEquality,
baseClosed,
independent_functionElimination,
inrEquality,
equalityTransitivity,
equalitySymmetry,
dependent_functionElimination,
axiomEquality,
universeIsType,
isect_memberEquality,
universeEquality
Latex:
\mforall{}[T:Type]. \mforall{}[x:T]. \mforall{}[b:\mBbbB{}]. ((b?x) \mmember{} T?)
Date html generated:
2019_10_15-AM-10_46_43
Last ObjectModification:
2018_09_27-AM-09_37_27
Theory : basic
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