Nuprl Lemma : stable__is-mfun
∀[X,Y:Type]. ∀[d:metric(X)]. ∀[d':metric(Y)]. ∀[f:X ⟶ Y]. Stable{f:FUN(X;Y)}
Proof
Definitions occuring in Statement :
is-mfun: f:FUN(X;Y),
metric: metric(X),
stable: Stable{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,
is-mfun: f:FUN(X;Y),
meq: x ≡ y,
so_lambda: λ2x.t[x],
prop: ℙ,
all: ∀x:A. B[x],
implies: P ⇒ Q,
metric: metric(X),
so_apply: x[s],
stable: Stable{P},
uimplies: b supposing a
Lemmas referenced :
stable__all,
req_wf,
int-to-real_wf,
stable_req,
req_witness,
metric_wf,
istype-universe
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation_alt,
introduction,
cut,
sqequalRule,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
lambdaEquality_alt,
functionEquality,
applyEquality,
setElimination,
rename,
hypothesis,
natural_numberEquality,
universeIsType,
independent_functionElimination,
lambdaFormation_alt,
because_Cache,
inhabitedIsType,
isect_memberEquality_alt,
dependent_functionElimination,
functionIsTypeImplies,
isectIsTypeImplies,
functionIsType,
instantiate,
universeEquality
Latex:
\mforall{}[X,Y:Type]. \mforall{}[d:metric(X)]. \mforall{}[d':metric(Y)]. \mforall{}[f:X {}\mrightarrow{} Y]. Stable\{f:FUN(X;Y)\}
Date html generated:
2019_10_29-AM-11_15_58
Last ObjectModification:
2019_10_02-AM-09_56_14
Theory : reals
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