Nuprl Lemma : no_repeats-settype
∀[T:Type]. ∀[P:T ⟶ ℙ]. ∀[L:{x:T| P[x]} List]. uiff(no_repeats(T;L);no_repeats({x:T| P[x]} ;L))
Proof
Definitions occuring in Statement :
no_repeats: no_repeats(T;l),
list: T List,
uiff: uiff(P;Q),
uall: ∀[x:A]. B[x],
prop: ℙ,
so_apply: x[s],
set: {x:A| B[x]} ,
function: x:A ⟶ B[x],
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uiff: uiff(P;Q),
and: P ∧ Q,
uimplies: b supposing a,
so_apply: x[s],
subtype_rel: A ⊆r B,
prop: ℙ,
implies: P ⇒ Q,
so_lambda: λ2x.t[x]
Lemmas referenced :
no_repeats-subtype,
no_repeats_witness,
no_repeats_wf,
subtype_rel_list,
no_repeats-strong-subtype,
strong-subtype-set3,
strong-subtype-self,
list_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
independent_pairFormation,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
setEquality,
applyEquality,
hypothesis,
lambdaEquality,
sqequalRule,
universeEquality,
independent_isectElimination,
setElimination,
rename,
because_Cache,
independent_functionElimination,
productElimination,
independent_pairEquality,
isect_memberEquality,
equalityTransitivity,
equalitySymmetry,
functionEquality,
cumulativity
Latex:
\mforall{}[T:Type]. \mforall{}[P:T {}\mrightarrow{} \mBbbP{}]. \mforall{}[L:\{x:T| P[x]\} List]. uiff(no\_repeats(T;L);no\_repeats(\{x:T| P[x]\} ;L))
Date html generated:
2016_05_14-PM-01_27_06
Last ObjectModification:
2015_12_26-PM-04_50_39
Theory : list_1
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