Nuprl Lemma : subtype_rel_colist
∀[A,B:Type]. colist(A) ⊆r colist(B) supposing A ⊆r B
Proof
Definitions occuring in Statement :
colist: colist(T),
uimplies: b supposing a,
subtype_rel: A ⊆r B,
uall: ∀[x:A]. B[x],
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
colist: colist(T),
so_lambda: λ2x.t[x],
so_apply: x[s],
all: ∀x:A. B[x],
and: P ∧ Q,
subtype_rel: A ⊆r B,
type-monotone: Monotone(T.F[T])
Lemmas referenced :
corec-subtype-corec,
b-union_wf,
unit_wf2,
subtype_rel_b-union,
subtype_rel_self,
subtype_rel_product,
subtype_rel_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
sqequalRule,
lambdaEquality,
hypothesis,
productEquality,
hypothesisEquality,
universeEquality,
independent_isectElimination,
lambdaFormation,
because_Cache,
independent_pairFormation,
axiomEquality,
isect_memberEquality,
equalityTransitivity,
equalitySymmetry
Latex:
\mforall{}[A,B:Type]. colist(A) \msubseteq{}r colist(B) supposing A \msubseteq{}r B
Date html generated:
2016_05_14-AM-06_25_20
Last ObjectModification:
2015_12_26-PM-00_42_38
Theory : list_0
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