Nuprl Lemma : type-monotone_wf
∀[F:Type ⟶ Type]. (Monotone(T.F[T]) ∈ ℙ')
Proof
Definitions occuring in Statement :
type-monotone: Monotone(T.F[T]),
uall: ∀[x:A]. B[x],
prop: ℙ,
so_apply: x[s],
member: t ∈ T,
function: x:A ⟶ B[x],
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
type-monotone: Monotone(T.F[T]),
so_lambda: λ2x.t[x],
prop: ℙ,
uimplies: b supposing a,
so_apply: x[s]
Lemmas referenced :
uall_wf,
subtype_rel_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
thin,
instantiate,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
universeEquality,
lambdaEquality,
cumulativity,
isectEquality,
hypothesisEquality,
hypothesis,
applyEquality,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
functionEquality
Latex:
\mforall{}[F:Type {}\mrightarrow{} Type]. (Monotone(T.F[T]) \mmember{} \mBbbP{}')
Date html generated:
2016_05_13-PM-04_09_37
Last ObjectModification:
2015_12_26-AM-11_22_40
Theory : subtype_1
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