### Nuprl Lemma : l-ordered-nil-true

`∀[T:Type]. ∀[R:T ⟶ T ⟶ ℙ].  (l-ordered(T;x,y.R[x;y];[]) `⇐⇒` True)`

Proof

Definitions occuring in Statement :  l-ordered: `l-ordered(T;x,y.R[x; y];L)` nil: `[]` uall: `∀[x:A]. B[x]` prop: `ℙ` so_apply: `x[s1;s2]` iff: `P `⇐⇒` Q` true: `True` function: `x:A ⟶ B[x]` universe: `Type`
Definitions unfolded in proof :  uall: `∀[x:A]. B[x]` iff: `P `⇐⇒` Q` and: `P ∧ Q` implies: `P `` Q` true: `True` member: `t ∈ T` prop: `ℙ` so_lambda: `λ2x y.t[x; y]` so_apply: `x[s1;s2]` rev_implies: `P `` Q`
Lemmas referenced :  l-ordered_wf nil_wf l-ordered-nil true_wf
Rules used in proof :  sqequalSubstitution sqequalTransitivity computationStep sqequalReflexivity isect_memberFormation independent_pairFormation lambdaFormation natural_numberEquality cut lemma_by_obid sqequalHypSubstitution isectElimination thin hypothesisEquality hypothesis sqequalRule lambdaEquality applyEquality functionEquality cumulativity universeEquality

Latex:
\mforall{}[T:Type].  \mforall{}[R:T  {}\mrightarrow{}  T  {}\mrightarrow{}  \mBbbP{}].    (l-ordered(T;x,y.R[x;y];[])  \mLeftarrow{}{}\mRightarrow{}  True)

Date html generated: 2016_05_15-PM-04_36_20
Last ObjectModification: 2015_12_27-PM-02_45_19

Theory : general

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