Nuprl Lemma : sq_stable__is-mfun
∀[X,Y:Type]. ∀[d:metric(X)]. ∀[d':metric(Y)]. ∀[f:X ⟶ Y]. SqStable(f:FUN(X;Y))
Proof
Definitions occuring in Statement :
is-mfun: f:FUN(X;Y),
metric: metric(X),
sq_stable: SqStable(P),
uall: ∀[x:A]. B[x],
function: x:A ⟶ B[x],
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
implies: P ⇒ Q,
sq_stable: SqStable(P),
is-mfun: f:FUN(X;Y),
all: ∀x:A. B[x],
meq: x ≡ y,
metric: metric(X),
so_apply: x[s]
Lemmas referenced :
sq_stable__from_stable,
is-mfun_wf,
stable__is-mfun,
req_witness,
int-to-real_wf,
metric_wf,
istype-universe
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation_alt,
introduction,
cut,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
independent_functionElimination,
sqequalRule,
lambdaEquality_alt,
dependent_functionElimination,
applyEquality,
setElimination,
rename,
natural_numberEquality,
functionIsTypeImplies,
inhabitedIsType,
functionIsType,
universeIsType,
isect_memberEquality_alt,
because_Cache,
isectIsTypeImplies,
instantiate,
universeEquality
Latex:
\mforall{}[X,Y:Type]. \mforall{}[d:metric(X)]. \mforall{}[d':metric(Y)]. \mforall{}[f:X {}\mrightarrow{} Y]. SqStable(f:FUN(X;Y))
Date html generated:
2019_10_29-AM-11_16_18
Last ObjectModification:
2019_10_02-AM-09_56_31
Theory : reals
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