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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