Nuprl Lemma : product_subtype_list
∀[T:Type]. ((T × (T List)) ⊆r (T List))
Proof
Definitions occuring in Statement :
list: T List,
subtype_rel: A ⊆r B,
uall: ∀[x:A]. B[x],
product: x:A × B[x],
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
subtype_rel: A ⊆r B,
uimplies: b supposing a,
guard: {T}
Lemmas referenced :
list-ext,
subtype_rel_transitivity,
list_wf,
b-union_wf,
unit_wf2,
subtype_rel_b-union-right,
ext-eq_inversion,
subtype_rel_weakening
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
sqequalRule,
axiomEquality,
hypothesis,
universeEquality,
productEquality,
independent_isectElimination,
because_Cache
Latex:
\mforall{}[T:Type]. ((T \mtimes{} (T List)) \msubseteq{}r (T List))
Date html generated:
2016_05_14-AM-06_25_48
Last ObjectModification:
2015_12_26-PM-00_42_21
Theory : list_0
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