Nuprl Lemma : id-mfun
∀[X:Type]. ∀[d:metric(X)]. (λx.x ∈ FUN(X ⟶ X))
Proof
Definitions occuring in Statement :
mfun: FUN(X ⟶ Y),
metric: metric(X),
uall: ∀[x:A]. B[x],
member: t ∈ T,
lambda: λx.A[x],
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
mfun: FUN(X ⟶ Y),
is-mfun: f:FUN(X;Y),
all: ∀x:A. B[x],
implies: P ⇒ Q,
so_apply: x[s],
prop: ℙ
Lemmas referenced :
meq_wf,
is-mfun_wf,
metric_wf,
istype-universe
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation_alt,
introduction,
cut,
dependent_set_memberEquality_alt,
lambdaEquality_alt,
hypothesisEquality,
universeIsType,
lambdaFormation_alt,
sqequalRule,
sqequalHypSubstitution,
hypothesis,
extract_by_obid,
isectElimination,
thin,
inhabitedIsType,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
isect_memberEquality_alt,
isectIsTypeImplies,
instantiate,
universeEquality
Latex:
\mforall{}[X:Type]. \mforall{}[d:metric(X)]. (\mlambda{}x.x \mmember{} FUN(X {}\mrightarrow{} X))
Date html generated:
2019_10_30-AM-06_21_54
Last ObjectModification:
2019_10_02-AM-09_57_43
Theory : reals
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