Nuprl Lemma : llex-le_wf
∀[A:Type]. ∀[<:A ⟶ A ⟶ ℙ]. (llex-le(A;a,b.<[a;b]) ∈ (A List) ⟶ (A List) ⟶ ℙ)
Proof
Definitions occuring in Statement :
llex-le: llex-le(A;a,b.<[a; b]),
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,
llex-le: llex-le(A;a,b.<[a; b]),
infix_ap: x f y,
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
prop: ℙ
Lemmas referenced :
or_wf,
llex_wf,
equal_wf,
list_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
lambdaEquality,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
applyEquality,
cumulativity,
hypothesisEquality,
functionExtensionality,
hypothesis,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
functionEquality,
universeEquality,
isect_memberEquality,
because_Cache
Latex:
\mforall{}[A:Type]. \mforall{}[<:A {}\mrightarrow{} A {}\mrightarrow{} \mBbbP{}]. (llex-le(A;a,b.<[a;b]) \mmember{} (A List) {}\mrightarrow{} (A List) {}\mrightarrow{} \mBbbP{})
Date html generated:
2017_02_20-AM-10_55_33
Last ObjectModification:
2017_02_02-PM-09_25_13
Theory : general
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