Nuprl Lemma : oobboth-bval_wf
∀[A,B:Type]. ∀[x:one_or_both(A;B)]. oobboth-bval(x) ∈ A × B supposing ↑oobboth?(x)
Proof
Definitions occuring in Statement :
oobboth-bval: oobboth-bval(x),
oobboth?: oobboth?(x),
one_or_both: one_or_both(A;B),
assert: ↑b,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
member: t ∈ T,
product: x:A × B[x],
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
oobboth-bval: oobboth-bval(x),
one_or_both: one_or_both(A;B),
oobboth: oobboth(bval),
oobboth?: oobboth?(x),
all: ∀x:A. B[x],
so_lambda: λ2x.t[x],
so_apply: x[s],
assert: ↑b,
ifthenelse: if b then t else f fi ,
btrue: tt,
implies: P ⇒ Q,
oobleft: oobleft(lval),
bfalse: ff,
false: False,
oobright: oobright(rval)
Lemmas referenced :
one_or_both_ind_oobboth_lemma,
istype-true,
one_or_both_oobleft_lemma,
istype-void,
one_or_both_ind_oobright_lemma,
istype-assert,
oobboth?_wf,
one_or_both_wf,
istype-universe
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation_alt,
introduction,
cut,
sqequalRule,
thin,
sqequalHypSubstitution,
unionElimination,
productElimination,
extract_by_obid,
dependent_functionElimination,
Error :memTop,
hypothesis,
lambdaFormation_alt,
independent_pairEquality,
hypothesisEquality,
voidElimination,
independent_functionElimination,
equalityTransitivity,
equalitySymmetry,
axiomEquality,
isectElimination,
isect_memberEquality_alt,
isectIsTypeImplies,
inhabitedIsType,
universeIsType,
instantiate,
universeEquality
Latex:
\mforall{}[A,B:Type]. \mforall{}[x:one\_or\_both(A;B)]. oobboth-bval(x) \mmember{} A \mtimes{} B supposing \muparrow{}oobboth?(x)
Date html generated:
2020_05_20-AM-08_11_19
Last ObjectModification:
2020_01_28-PM-04_27_42
Theory : general
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