Nuprl Lemma : oobright-rval_wf
∀[A,B:Type]. ∀[x:one_or_both(A;B)]. oobright-rval(x) ∈ B supposing ↑oobright?(x)
Proof
Definitions occuring in Statement :
oobright-rval: oobright-rval(x),
oobright?: oobright?(x),
one_or_both: one_or_both(A;B),
assert: ↑b,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
member: t ∈ T,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
oobright-rval: oobright-rval(x),
one_or_both: one_or_both(A;B),
oobboth: oobboth(bval),
oobright?: oobright?(x),
all: ∀x:A. B[x],
so_lambda: λ2x.t[x],
top: Top,
so_apply: x[s],
assert: ↑b,
ifthenelse: if b then t else f fi ,
bfalse: ff,
implies: P ⇒ Q,
false: False,
prop: ℙ,
oobleft: oobleft(lval),
oobright: oobright(rval),
btrue: tt
Lemmas referenced :
one_or_both_ind_oobboth_lemma,
false_wf,
one_or_both_oobleft_lemma,
one_or_both_ind_oobright_lemma,
true_wf,
assert_wf,
oobright?_wf,
one_or_both_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
thin,
sqequalHypSubstitution,
unionElimination,
productElimination,
lemma_by_obid,
dependent_functionElimination,
isect_memberEquality,
voidElimination,
voidEquality,
hypothesis,
lambdaFormation,
hypothesisEquality,
independent_functionElimination,
equalityTransitivity,
equalitySymmetry,
axiomEquality,
isectElimination,
because_Cache,
universeEquality
Latex:
\mforall{}[A,B:Type]. \mforall{}[x:one\_or\_both(A;B)]. oobright-rval(x) \mmember{} B supposing \muparrow{}oobright?(x)
Date html generated:
2016_05_15-PM-05_35_15
Last ObjectModification:
2015_12_27-PM-02_07_28
Theory : general
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