Nuprl Lemma : strong-continuous-function
∀[F:Type ⟶ Type]. ∀[A:Type]. Continuous+(T.A ⟶ F[T]) supposing Continuous+(T.F[T])
Proof
Definitions occuring in Statement :
strong-type-continuous: Continuous+(T.F[T]),
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
so_apply: x[s],
function: x:A ⟶ B[x],
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
strong-type-continuous: Continuous+(T.F[T]),
ext-eq: A ≡ B,
and: P ∧ Q,
subtype_rel: A ⊆r B,
prop: ℙ,
so_lambda: λ2x.t[x],
so_apply: x[s],
nat: ℕ,
le: A ≤ B,
less_than': less_than'(a;b),
false: False,
not: ¬A,
implies: P ⇒ Q,
uiff: uiff(P;Q),
all: ∀x:A. B[x]
Lemmas referenced :
nat_wf,
strong-type-continuous_wf,
false_wf,
le_wf,
subtype_rel_isect,
subtype_rel_dep_function
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
independent_pairFormation,
sqequalRule,
sqequalHypSubstitution,
productElimination,
thin,
independent_pairEquality,
axiomEquality,
hypothesis,
functionEquality,
cumulativity,
lemma_by_obid,
universeEquality,
isect_memberEquality,
isectElimination,
hypothesisEquality,
lambdaEquality,
applyEquality,
because_Cache,
equalityTransitivity,
equalitySymmetry,
dependent_set_memberEquality,
natural_numberEquality,
lambdaFormation,
isectEquality,
functionExtensionality,
independent_isectElimination
Latex:
\mforall{}[F:Type {}\mrightarrow{} Type]. \mforall{}[A:Type]. Continuous+(T.A {}\mrightarrow{} F[T]) supposing Continuous+(T.F[T])
Date html generated:
2016_05_13-PM-04_09_47
Last ObjectModification:
2015_12_26-AM-11_22_45
Theory : subtype_1
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