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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