Nuprl Lemma : l_contains_weakening
∀[T:Type]. ∀A,B:T List. A ⊆ B supposing A = B ∈ (T List)
Proof
Definitions occuring in Statement :
l_contains: A ⊆ B,
list: T List,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
universe: Type,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
uimplies: b supposing a,
member: t ∈ T,
l_contains: A ⊆ B,
l_all: (∀x∈L.P[x]),
prop: ℙ
Lemmas referenced :
select_member,
int_seg_wf,
length_wf,
l_contains_wf,
equal_wf,
list_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
lambdaFormation,
cut,
introduction,
axiomEquality,
hypothesis,
thin,
rename,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
hypothesisEquality,
dependent_functionElimination,
natural_numberEquality,
cumulativity,
hyp_replacement,
equalitySymmetry,
Error :applyLambdaEquality,
sqequalRule,
universeEquality
Latex:
\mforall{}[T:Type]. \mforall{}A,B:T List. A \msubseteq{} B supposing A = B
Date html generated:
2016_10_21-AM-10_05_18
Last ObjectModification:
2016_07_12-AM-05_25_14
Theory : list_1
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