Nuprl Lemma : l_contains_nil
∀[T:Type]. ∀L:T List. [] ⊆ L
Proof
Definitions occuring in Statement :
l_contains: A ⊆ B,
nil: [],
list: T List,
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
universe: Type
Definitions unfolded in proof :
l_contains: A ⊆ B,
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
so_lambda: λ2x.t[x],
member: t ∈ T,
top: Top,
so_apply: x[s]
Lemmas referenced :
l_all_nil,
list_wf
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
isect_memberFormation,
lambdaFormation,
cut,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
isect_memberEquality,
voidElimination,
voidEquality,
hypothesis,
hypothesisEquality,
universeEquality
Latex:
\mforall{}[T:Type]. \mforall{}L:T List. [] \msubseteq{} L
Date html generated:
2016_05_14-AM-07_54_29
Last ObjectModification:
2015_12_26-PM-04_48_47
Theory : list_1
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