Nuprl Lemma : Des_wf
∀[A:Type]. ∀[<:A ⟶ A ⟶ ℙ]. (Des(A;a,b.<[a;b]) ∈ ℙ)
Proof
Definitions occuring in Statement :
Des: Des(A;a,b.<[a; b]),
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,
Des: Des(A;a,b.<[a; b]),
so_lambda: λ2x.t[x],
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
prop: ℙ,
so_apply: x[s]
Lemmas referenced :
set_wf,
list_wf,
descending_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
lambdaEquality,
applyEquality,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
functionEquality,
cumulativity,
universeEquality,
isect_memberEquality,
because_Cache
Latex:
\mforall{}[A:Type]. \mforall{}[<:A {}\mrightarrow{} A {}\mrightarrow{} \mBbbP{}]. (Des(A;a,b.<[a;b]) \mmember{} \mBbbP{})
Date html generated:
2016_05_15-PM-04_17_05
Last ObjectModification:
2015_12_27-PM-02_57_13
Theory : general
Home
Index