Nuprl Lemma : subtype_rel_fset
∀[A,B:Type].  fset(A) ⊆r fset(B) supposing A ⊆r B
Proof
Definitions occuring in Statement : 
fset: fset(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
, 
subtype_rel: A ⊆r B
Lemmas referenced : 
fset-subtype, 
subtype_rel_wf
Rules used in proof : 
sqequalSubstitution, 
sqequalTransitivity, 
computationStep, 
sqequalReflexivity, 
isect_memberFormation, 
introduction, 
cut, 
lemma_by_obid, 
sqequalHypSubstitution, 
isectElimination, 
thin, 
hypothesisEquality, 
independent_isectElimination, 
hypothesis, 
sqequalRule, 
axiomEquality, 
isect_memberEquality, 
because_Cache, 
equalityTransitivity, 
equalitySymmetry, 
universeEquality
Latex:
\mforall{}[A,B:Type].    fset(A)  \msubseteq{}r  fset(B)  supposing  A  \msubseteq{}r  B
Date html generated:
2016_05_14-PM-03_37_59
Last ObjectModification:
2015_12_26-PM-06_42_20
Theory : finite!sets
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