Nuprl Lemma : l_subset_pos_length
∀[T:Type]. ∀[A,B:T List]. (0 < ||B||) supposing (0 < ||A|| and l_subset(T;A;B))
Proof
Definitions occuring in Statement :
l_subset: l_subset(T;as;bs),
length: ||as||,
list: T List,
less_than: a < b,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
natural_number: $n,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
prop: ℙ,
all: ∀x:A. B[x],
iff: P ⇐⇒ Q,
and: P ∧ Q,
implies: P ⇒ Q
Lemmas referenced :
l_contains_pos_length,
member-less_than,
length_wf,
less_than_wf,
l_subset_wf,
list_wf,
l_subset-l_contains
Rules used in proof :
cut,
lemma_by_obid,
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
hypothesis,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
introduction,
independent_isectElimination,
sqequalRule,
isect_memberEquality,
natural_numberEquality,
equalityTransitivity,
equalitySymmetry,
because_Cache,
universeEquality,
dependent_functionElimination,
productElimination,
independent_functionElimination
Latex:
\mforall{}[T:Type]. \mforall{}[A,B:T List]. (0 < ||B||) supposing (0 < ||A|| and l\_subset(T;A;B))
Date html generated:
2016_05_14-AM-07_53_40
Last ObjectModification:
2015_12_26-PM-04_47_41
Theory : list_1
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