Nuprl Lemma : l-ordered-no_repeats
∀[T:Type]. ∀[as:T List]. ∀[R:T ⟶ T ⟶ ℙ].
(no_repeats(T;as)) supposing (l-ordered(T;x,y.R[x;y];as) and (∀x:T. (¬R[x;x])))
Proof
Definitions occuring in Statement :
l-ordered: l-ordered(T;x,y.R[x; y];L),
no_repeats: no_repeats(T;l),
list: T List,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
prop: ℙ,
so_apply: x[s1;s2],
all: ∀x:A. B[x],
not: ¬A,
function: x:A ⟶ B[x],
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
uiff: uiff(P;Q),
and: P ∧ Q,
not: ¬A,
implies: P ⇒ Q,
false: False,
all: ∀x:A. B[x],
prop: ℙ,
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
so_lambda: λ2x.t[x],
so_apply: x[s],
guard: {T},
l-ordered: l-ordered(T;x,y.R[x; y];L)
Lemmas referenced :
no_repeats_iff,
equal_wf,
l_before_wf,
no_repeats_witness,
l-ordered_wf,
all_wf,
not_wf,
list_wf,
and_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
productElimination,
independent_isectElimination,
lambdaFormation,
hypothesis,
dependent_functionElimination,
cumulativity,
independent_functionElimination,
voidElimination,
sqequalRule,
lambdaEquality,
because_Cache,
isect_memberEquality,
equalityTransitivity,
equalitySymmetry,
applyEquality,
functionExtensionality,
functionEquality,
universeEquality,
hyp_replacement,
dependent_set_memberEquality,
independent_pairFormation,
applyLambdaEquality,
setElimination,
rename
Latex:
\mforall{}[T:Type]. \mforall{}[as:T List]. \mforall{}[R:T {}\mrightarrow{} T {}\mrightarrow{} \mBbbP{}].
(no\_repeats(T;as)) supposing (l-ordered(T;x,y.R[x;y];as) and (\mforall{}x:T. (\mneg{}R[x;x])))
Date html generated:
2018_05_21-PM-07_39_36
Last ObjectModification:
2017_07_26-PM-05_13_53
Theory : general
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