Nuprl Lemma : l_all2_wf
∀[T:Type]. ∀[L:T List]. ∀[P:T ⟶ T ⟶ ℙ]. ((∀x<y∈L.P[x;y]) ∈ ℙ)
Proof
Definitions occuring in Statement :
l_all2: (∀x<y∈L.P[x; y]),
list: T List,
uall: ∀[x:A]. B[x],
prop: ℙ,
so_apply: x[s1;s2],
member: t ∈ T,
function: x:A ⟶ B[x],
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
l_all2: (∀x<y∈L.P[x; y]),
so_lambda: λ2x.t[x],
implies: P ⇒ Q,
prop: ℙ,
so_apply: x[s1;s2],
so_apply: x[s]
Lemmas referenced :
all_wf,
l_before_wf,
list_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation_alt,
introduction,
cut,
sqequalRule,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
lambdaEquality,
functionEquality,
hypothesis,
applyEquality,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
functionIsType,
universeIsType,
inhabitedIsType,
universeEquality,
isect_memberEquality,
cumulativity,
because_Cache
Latex:
\mforall{}[T:Type]. \mforall{}[L:T List]. \mforall{}[P:T {}\mrightarrow{} T {}\mrightarrow{} \mBbbP{}]. ((\mforall{}x<y\mmember{}L.P[x;y]) \mmember{} \mBbbP{})
Date html generated:
2019_10_15-AM-10_54_35
Last ObjectModification:
2018_09_27-AM-09_37_32
Theory : list!
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