### Nuprl Lemma : l-ordered-nil

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

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]` function: `x:A ⟶ B[x]` universe: `Type`
Definitions unfolded in proof :  l-ordered: `l-ordered(T;x,y.R[x; y];L)` uall: `∀[x:A]. B[x]` all: `∀x:A. B[x]` implies: `P `` Q` l_before: `x before y ∈ l` member: `t ∈ T` iff: `P `⇐⇒` Q` and: `P ∧ Q` false: `False` prop: `ℙ`
Lemmas referenced :  cons_sublist_nil cons_wf nil_wf l_before_wf
Rules used in proof :  sqequalSubstitution sqequalRule sqequalReflexivity sqequalTransitivity computationStep isect_memberFormation lambdaFormation sqequalHypSubstitution cut lemma_by_obid isectElimination thin because_Cache dependent_functionElimination hypothesisEquality hypothesis productElimination independent_functionElimination voidElimination functionEquality cumulativity universeEquality

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

Date html generated: 2016_05_15-PM-04_36_13
Last ObjectModification: 2015_12_27-PM-02_45_27

Theory : general

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