Nuprl Lemma : is-msfun_wf
∀[X,Y:Type]. ∀[d:metric(X)]. ∀[d':metric(Y)]. ∀[f:X ⟶ Y]. (is-msfun(X;d;Y;d';f) ∈ ℙ)
Proof
Definitions occuring in Statement :
is-msfun: is-msfun(X;d;Y;d';f),
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-msfun: is-msfun(X;d;Y;d';f),
prop: ℙ,
all: ∀x:A. B[x],
implies: P ⇒ Q,
so_apply: x[s]
Lemmas referenced :
msep_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,
applyEquality,
hypothesis,
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]. (is-msfun(X;d;Y;d';f) \mmember{} \mBbbP{})
Date html generated:
2019_10_30-AM-06_25_31
Last ObjectModification:
2019_10_02-AM-10_00_57
Theory : reals
Home
Index