Nuprl Lemma : stream-subtype
∀[A,B:Type]. stream(A) ⊆r stream(B) supposing A ⊆r B
Proof
Definitions occuring in Statement :
stream: stream(A),
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,
stream: stream(A),
so_lambda: λ2x.t[x],
so_apply: x[s],
all: ∀x:A. B[x],
implies: P ⇒ Q,
subtype_rel: A ⊆r B
Lemmas referenced :
corec-subtype-corec2,
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,
productEquality,
hypothesisEquality,
universeEquality,
independent_isectElimination,
lambdaFormation,
hypothesis,
because_Cache,
axiomEquality,
isect_memberEquality,
equalityTransitivity,
equalitySymmetry
Latex:
\mforall{}[A,B:Type]. stream(A) \msubseteq{}r stream(B) supposing A \msubseteq{}r B
Date html generated:
2016_05_14-AM-06_22_05
Last ObjectModification:
2015_12_26-AM-11_59_46
Theory : co-recursion
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