Nuprl Lemma : outl_wf
∀[A,B:Type]. ∀[x:A + B]. outl(x) ∈ A supposing ↑isl(x)
Proof
Definitions occuring in Statement :
outl: outl(x),
assert: ↑b,
isl: isl(x),
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
member: t ∈ T,
union: left + right,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
outl: outl(x),
isl: isl(x),
assert: ↑b,
ifthenelse: if b then t else f fi ,
bfalse: ff,
false: False,
prop: ℙ
Lemmas referenced :
assert_wf,
isl_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
unionElimination,
thin,
sqequalRule,
sqequalHypSubstitution,
hypothesisEquality,
voidElimination,
hypothesis,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
lemma_by_obid,
isectElimination,
isect_memberEquality,
because_Cache,
unionEquality,
universeEquality
Latex:
\mforall{}[A,B:Type]. \mforall{}[x:A + B]. outl(x) \mmember{} A supposing \muparrow{}isl(x)
Date html generated:
2016_05_13-PM-03_20_22
Last ObjectModification:
2015_12_26-AM-09_10_51
Theory : union
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