Nuprl Lemma : is-mfun_wf
∀[X,Y:Type]. ∀[d:metric(X)]. ∀[d':metric(Y)]. ∀[f:X ⟶ Y]. (f:FUN(X;Y) ∈ ℙ)
Proof
Definitions occuring in Statement :
is-mfun: f:FUN(X;Y),
metric: metric(X),
uall: ∀[x:A]. B[x],
prop: ℙ,
member: t ∈ T,
function: x:A ⟶ B[x],
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
is-mfun: f:FUN(X;Y),
prop: ℙ,
all: ∀x:A. B[x],
implies: P ⇒ Q,
so_apply: x[s]
Lemmas referenced :
meq_wf,
metric_wf,
istype-universe
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation_alt,
introduction,
cut,
sqequalRule,
functionEquality,
hypothesisEquality,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesis,
applyEquality,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
functionIsType,
universeIsType,
isect_memberEquality_alt,
isectIsTypeImplies,
inhabitedIsType,
instantiate,
universeEquality
Latex:
\mforall{}[X,Y:Type]. \mforall{}[d:metric(X)]. \mforall{}[d':metric(Y)]. \mforall{}[f:X {}\mrightarrow{} Y]. (f:FUN(X;Y) \mmember{} \mBbbP{})
Date html generated:
2019_10_29-AM-11_15_38
Last ObjectModification:
2019_10_02-AM-09_55_56
Theory : reals
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