Nuprl Lemma : subtype_rel_image
∀[A,B:Type]. ∀[f:Base]. Image(A,f) ⊆r Image(B,f) supposing A ⊆r B
Proof
Definitions occuring in Statement :
uimplies: b supposing a,
subtype_rel: A ⊆r B,
uall: ∀[x:A]. B[x],
image-type: Image(T,f),
base: Base,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
subtype_rel: A ⊆r B
Lemmas referenced :
image-type_wf,
subtype_rel_wf,
base_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
lambdaEquality,
imageElimination,
sqequalHypSubstitution,
hypothesis,
lemma_by_obid,
isectElimination,
thin,
hypothesisEquality,
sqequalRule,
axiomEquality,
isect_memberEquality,
because_Cache,
equalityTransitivity,
equalitySymmetry,
universeEquality,
imageMemberEquality,
applyEquality
Latex:
\mforall{}[A,B:Type]. \mforall{}[f:Base]. Image(A,f) \msubseteq{}r Image(B,f) supposing A \msubseteq{}r B
Date html generated:
2016_05_13-PM-03_18_40
Last ObjectModification:
2015_12_26-AM-09_08_25
Theory : subtype_0
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