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

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