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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