### Nuprl Lemma : xxorder_eq_order

`∀[T:Type]. ∀[R:T ⟶ T ⟶ ℙ].  (order(T;R) = Order(T;x,y.R x y) ∈ ℙ)`

Proof

Definitions occuring in Statement :  xxorder: `order(T;R)` order: `Order(T;x,y.R[x; y])` uall: `∀[x:A]. B[x]` prop: `ℙ` apply: `f a` function: `x:A ⟶ B[x]` universe: `Type` equal: `s = t ∈ T`
Definitions unfolded in proof :  uall: `∀[x:A]. B[x]` member: `t ∈ T` order: `Order(T;x,y.R[x; y])` xxorder: `order(T;R)` xxanti_sym: `anti_sym(T;R)` xxtrans: `trans(T;E)` xxrefl: `refl(T;E)` so_lambda: `λ2x y.t[x; y]` so_apply: `x[s1;s2]` prop: `ℙ`
Lemmas referenced :  and_wf refl_wf trans_wf anti_sym_wf
Rules used in proof :  sqequalSubstitution sqequalTransitivity computationStep sqequalReflexivity isect_memberFormation introduction cut lemma_by_obid sqequalHypSubstitution isectElimination thin hypothesisEquality sqequalRule lambdaEquality applyEquality hypothesis functionEquality cumulativity universeEquality isect_memberEquality axiomEquality because_Cache

Latex:
\mforall{}[T:Type].  \mforall{}[R:T  {}\mrightarrow{}  T  {}\mrightarrow{}  \mBbbP{}].    (order(T;R)  =  Order(T;x,y.R  x  y))

Date html generated: 2016_05_15-PM-00_01_23
Last ObjectModification: 2015_12_26-PM-11_26_15

Theory : gen_algebra_1

Home Index