Nuprl Lemma : apply?_wf
∀[A,T:Type]. ∀[f:A ⟶ (T + Top)]. ∀[x:A]. ∀[d:T]. (f(x)?d ∈ T)
Proof
Definitions occuring in Statement :
apply?: f(x)?d,
uall: ∀[x:A]. B[x],
top: Top,
member: t ∈ T,
function: x:A ⟶ B[x],
union: left + right,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
apply?: f(x)?d,
all: ∀x:A. B[x],
implies: P ⇒ Q,
isl: isl(x),
outl: outl(x),
ifthenelse: if b then t else f fi ,
btrue: tt,
bfalse: ff,
prop: ℙ
Lemmas referenced :
top_wf,
equal_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
applyEquality,
functionExtensionality,
hypothesisEquality,
cumulativity,
thin,
unionEquality,
extract_by_obid,
hypothesis,
lambdaFormation,
unionElimination,
sqequalRule,
sqequalHypSubstitution,
isectElimination,
equalityTransitivity,
equalitySymmetry,
dependent_functionElimination,
independent_functionElimination,
axiomEquality,
isect_memberEquality,
because_Cache,
functionEquality,
universeEquality
Latex:
\mforall{}[A,T:Type]. \mforall{}[f:A {}\mrightarrow{} (T + Top)]. \mforall{}[x:A]. \mforall{}[d:T]. (f(x)?d \mmember{} T)
Date html generated:
2017_10_01-AM-09_13_12
Last ObjectModification:
2017_07_26-PM-04_48_41
Theory : general
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