Nuprl Lemma : ulinorder_wf
∀[T:Type]. ∀[R:T ⟶ T ⟶ ℙ]. (UniformLinorder(T;x,y.R[x;y]) ∈ ℙ)
Proof
Definitions occuring in Statement :
ulinorder: UniformLinorder(T;x,y.R[x; y]),
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,
ulinorder: UniformLinorder(T;x,y.R[x; y]),
prop: ℙ,
and: P ∧ Q,
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
so_lambda: λ2x.t[x],
uimplies: b supposing a,
subtype_rel: A ⊆r B,
so_apply: x[s]
Lemmas referenced :
uorder_wf,
connex_wf,
uall_wf,
isect_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
productEquality,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
cumulativity,
hypothesisEquality,
lambdaEquality,
applyEquality,
functionExtensionality,
because_Cache,
hypothesis,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
functionEquality,
universeEquality,
isect_memberEquality
Latex:
\mforall{}[T:Type]. \mforall{}[R:T {}\mrightarrow{} T {}\mrightarrow{} \mBbbP{}]. (UniformLinorder(T;x,y.R[x;y]) \mmember{} \mBbbP{})
Date html generated:
2016_10_21-AM-09_42_27
Last ObjectModification:
2016_08_01-PM-09_48_37
Theory : rel_1
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