Nuprl Lemma : interleaved_family_wf
∀[T,I:Type]. ∀[L:I ⟶ (T List)]. ∀[L2:T List]. (interleaved_family(T;I;L;L2) ∈ ℙ)
Proof
Definitions occuring in Statement :
interleaved_family: interleaved_family(T;I;L;L2),
list: T List,
uall: ∀[x:A]. B[x],
prop: ℙ,
member: t ∈ T,
function: x:A ⟶ B[x],
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
interleaved_family: interleaved_family(T;I;L;L2),
so_lambda: λ2x.t[x],
so_apply: x[s]
Lemmas referenced :
exists_wf,
int_seg_wf,
length_wf,
interleaved_family_occurence_wf,
list_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation_alt,
introduction,
cut,
sqequalRule,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
functionEquality,
hypothesisEquality,
natural_numberEquality,
applyEquality,
hypothesis,
lambdaEquality,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
universeIsType,
isect_memberEquality,
because_Cache,
functionIsType,
inhabitedIsType,
universeEquality
Latex:
\mforall{}[T,I:Type]. \mforall{}[L:I {}\mrightarrow{} (T List)]. \mforall{}[L2:T List]. (interleaved\_family(T;I;L;L2) \mmember{} \mBbbP{})
Date html generated:
2019_10_15-AM-10_57_55
Last ObjectModification:
2018_09_27-AM-09_50_15
Theory : list!
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