Nuprl Lemma : subtype_rel_list
∀[A,B:Type]. (A List) ⊆r (B List) supposing A ⊆r B
Proof
Definitions occuring in Statement :
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,
list: T List,
so_lambda: λ2x.t[x],
nat: ℕ,
so_apply: x[s],
all: ∀x:A. B[x],
implies: P ⇒ Q,
prop: ℙ,
subtype_rel: A ⊆r B
Lemmas referenced :
subtype_rel_sets,
colist_wf,
has-value_wf-partial,
nat_wf,
set-value-type,
le_wf,
int-value-type,
colength_wf,
subtype_rel_set,
subtype_rel_colist,
subtype_rel_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
sqequalRule,
lambdaEquality,
independent_isectElimination,
intEquality,
natural_numberEquality,
cumulativity,
because_Cache,
lambdaFormation,
axiomEquality,
isect_memberEquality,
equalityTransitivity,
equalitySymmetry,
universeEquality
Latex:
\mforall{}[A,B:Type]. (A List) \msubseteq{}r (B List) supposing A \msubseteq{}r B
Date html generated:
2016_05_14-AM-06_25_45
Last ObjectModification:
2015_12_26-PM-00_42_25
Theory : list_0
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