Nuprl Lemma : image-metric_wf
∀[X,Y:Type]. ∀[f:X ⟶ Y]. ∀[d:metric(Y)]. (image-metric(d) ∈ metric(f[X]))
Proof
Definitions occuring in Statement :
image-metric: image-metric(d),
image-space: f[X],
metric: metric(X),
uall: ∀[x:A]. B[x],
member: t ∈ T,
function: x:A ⟶ B[x],
universe: Type
Definitions unfolded in proof :
prop: ℙ,
mdist: mdist(d;x;y),
pi1: fst(t),
all: ∀x:A. B[x],
cand: A c∧ B,
and: P ∧ Q,
top: Top,
image-space: f[X],
metric: metric(X),
image-metric: image-metric(d),
member: t ∈ T,
uall: ∀[x:A]. B[x]
Lemmas referenced :
istype-universe,
metric_wf,
int-to-real_wf,
req_wf,
radd_wf,
rleq_wf,
mdist-same,
mdist-triangle-inequality1,
image-space_wf,
istype-void,
pi1_wf_top
Rules used in proof :
universeEquality,
instantiate,
isectIsTypeImplies,
axiomEquality,
natural_numberEquality,
functionIsType,
productIsType,
because_Cache,
equalityElimination,
independent_pairFormation,
lambdaFormation_alt,
equalitySymmetry,
equalityTransitivity,
dependent_set_memberEquality_alt,
universeIsType,
inhabitedIsType,
voidElimination,
isect_memberEquality_alt,
independent_pairEquality,
productElimination,
isectElimination,
extract_by_obid,
hypothesis,
hypothesisEquality,
rename,
thin,
setElimination,
sqequalHypSubstitution,
applyEquality,
lambdaEquality_alt,
sqequalRule,
cut,
introduction,
isect_memberFormation_alt,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution
Latex:
\mforall{}[X,Y:Type]. \mforall{}[f:X {}\mrightarrow{} Y]. \mforall{}[d:metric(Y)]. (image-metric(d) \mmember{} metric(f[X]))
Date html generated:
2019_10_30-AM-06_35_27
Last ObjectModification:
2019_10_25-AM-11_11_40
Theory : reals
Home
Index