Nuprl Lemma : same_order_wf
∀[T:Type]. ∀[L:T List]. ∀[x1,x2,y1,y2:T]. (same_order(x1;y1;x2;y2;L;T) ∈ ℙ)
Proof
Definitions occuring in Statement :
same_order: same_order(x1;y1;x2;y2;L;T),
list: T List,
uall: ∀[x:A]. B[x],
prop: ℙ,
member: t ∈ T,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
same_order: same_order(x1;y1;x2;y2;L;T),
implies: P ⇒ Q,
prop: ℙ
Lemmas referenced :
strong_before_wf,
l_member_wf,
list_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation_alt,
introduction,
cut,
sqequalRule,
functionEquality,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
inhabitedIsType,
isect_memberEquality,
because_Cache,
universeIsType,
universeEquality
Latex:
\mforall{}[T:Type]. \mforall{}[L:T List]. \mforall{}[x1,x2,y1,y2:T]. (same\_order(x1;y1;x2;y2;L;T) \mmember{} \mBbbP{})
Date html generated:
2019_10_15-AM-10_53_15
Last ObjectModification:
2018_09_27-AM-09_37_34
Theory : list!
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