Nuprl Lemma : nameset-equipollent
∀L:Cname List. nameset(L) ~ ℕ||remove-repeats(CnameDeq;L)||
Proof
Definitions occuring in Statement :
nameset: nameset(L),
cname_deq: CnameDeq,
coordinate_name: Cname,
equipollent: A ~ B,
remove-repeats: remove-repeats(eq;L),
length: ||as||,
list: T List,
int_seg: {i..j-},
all: ∀x:A. B[x],
natural_number: $n
Definitions unfolded in proof :
all: ∀x:A. B[x],
uall: ∀[x:A]. B[x],
member: t ∈ T,
implies: P ⇒ Q,
uimplies: b supposing a,
prop: ℙ,
iff: P ⇐⇒ Q,
and: P ∧ Q,
rev_implies: P ⇐ Q,
nameset: nameset(L),
ext-eq: A ≡ B,
subtype_rel: A ⊆r B
Lemmas referenced :
equipollent-length,
coordinate_name_wf,
remove-repeats_wf,
cname_deq_wf,
decidable__equal-coordinate_name,
remove-repeats-no_repeats,
list_wf,
nameset_wf,
int_seg_wf,
length_wf,
l_member_wf,
equipollent_weakening_ext-eq,
equipollent_functionality_wrt_equipollent2,
equipollent_inversion,
member-remove-repeats
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
cut,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesis,
dependent_functionElimination,
hypothesisEquality,
independent_functionElimination,
because_Cache,
independent_isectElimination,
natural_numberEquality,
setEquality,
productElimination,
independent_pairFormation,
lambdaEquality,
setElimination,
rename,
dependent_set_memberEquality
Latex:
\mforall{}L:Cname List. nameset(L) \msim{} \mBbbN{}||remove-repeats(CnameDeq;L)||
Date html generated:
2016_05_20-AM-09_28_08
Last ObjectModification:
2015_12_28-PM-04_48_28
Theory : cubical!sets
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