Nuprl Lemma : continuous-monotone-function
∀[F:Type ⟶ Type]. ∀[A:Type]. ContinuousMonotone(T.A ⟶ F[T]) supposing ContinuousMonotone(T.F[T])
Proof
Definitions occuring in Statement :
continuous-monotone: ContinuousMonotone(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,
so_lambda: λ2x y.t[x; y],
so_apply: x[s],
so_apply: x[s1;s2],
all: ∀x:A. B[x],
continuous-monotone: ContinuousMonotone(T.F[T]),
and: P ∧ Q,
type-monotone: Monotone(T.F[T]),
subtype_rel: A ⊆r B,
type-continuous: Continuous(T.F[T]),
prop: ℙ,
so_lambda: λ2x.t[x]
Lemmas referenced :
continuous-monotone-depfunction,
subtype_rel_wf,
nat_wf,
continuous-monotone_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
sqequalRule,
lambdaEquality,
applyEquality,
universeEquality,
independent_isectElimination,
lambdaFormation,
hypothesis,
because_Cache,
productElimination,
independent_pairEquality,
isect_memberEquality,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
functionEquality,
cumulativity
Latex:
\mforall{}[F:Type {}\mrightarrow{} Type]. \mforall{}[A:Type]. ContinuousMonotone(T.A {}\mrightarrow{} F[T]) supposing ContinuousMonotone(T.F[T])
Date html generated:
2016_05_13-PM-04_09_48
Last ObjectModification:
2015_12_26-AM-11_22_33
Theory : subtype_1
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