Nuprl Lemma : sq_stable__is-msfun
∀[X,Y:Type]. ∀d:metric(X). ∀[d':metric(Y)]. ∀[f:X ⟶ Y]. SqStable(is-msfun(X;d;Y;d';f))
Proof
Definitions occuring in Statement :
is-msfun: is-msfun(X;d;Y;d';f),
metric: metric(X),
sq_stable: SqStable(P),
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
function: x:A ⟶ B[x],
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
is-msfun: is-msfun(X;d;Y;d';f),
member: t ∈ T,
so_lambda: λ2x.t[x],
prop: ℙ,
implies: P ⇒ Q,
so_apply: x[s]
Lemmas referenced :
sq_stable__all,
msep_wf,
sq_stable__msep,
metric_wf,
istype-universe
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation_alt,
lambdaFormation_alt,
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
sqequalRule,
lambdaEquality_alt,
functionEquality,
applyEquality,
hypothesis,
universeIsType,
independent_functionElimination,
because_Cache,
inhabitedIsType,
dependent_functionElimination,
functionIsType,
instantiate,
universeEquality
Latex:
\mforall{}[X,Y:Type]. \mforall{}d:metric(X). \mforall{}[d':metric(Y)]. \mforall{}[f:X {}\mrightarrow{} Y]. SqStable(is-msfun(X;d;Y;d';f))
Date html generated:
2019_10_30-AM-06_25_50
Last ObjectModification:
2019_10_02-AM-10_01_15
Theory : reals
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