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
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