Nuprl Lemma : list_subtype_fset
∀[A,B:Type]. (A List) ⊆r fset(B) supposing A ⊆r B
Proof
Definitions occuring in Statement :
fset: fset(T),
list: T List,
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,
fset: fset(T),
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
all: ∀x:A. B[x],
implies: P ⇒ Q
Lemmas referenced :
list_wf,
subtype_rel_wf,
set-equal_wf,
set-equal-equiv,
subtype_rel_list,
set-equal-reflex,
quotient-member-eq
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
lambdaEquality,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
sqequalRule,
axiomEquality,
isect_memberEquality,
because_Cache,
equalityTransitivity,
equalitySymmetry,
universeEquality,
applyEquality,
independent_isectElimination,
dependent_functionElimination,
independent_functionElimination
Latex:
\mforall{}[A,B:Type]. (A List) \msubseteq{}r fset(B) supposing A \msubseteq{}r B
Date html generated:
2016_05_14-PM-03_38_01
Last ObjectModification:
2015_12_26-PM-06_42_21
Theory : finite!sets
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