Nuprl Lemma : finite-fixed-length
∀T:Type. ∀n:ℕ. (finite(T) ⇒ finite({l:T List| ||l|| = n ∈ ℤ} ))
Proof
Definitions occuring in Statement :
finite: finite(T),
length: ||as||,
list: T List,
nat: ℕ,
all: ∀x:A. B[x],
implies: P ⇒ Q,
set: {x:A| B[x]} ,
int: ℤ,
universe: Type,
equal: s = t ∈ T
Definitions unfolded in proof :
all: ∀x:A. B[x],
implies: P ⇒ Q,
finite: finite(T),
exists: ∃x:A. B[x],
uall: ∀[x:A]. B[x],
member: t ∈ T,
prop: ℙ,
nat: ℕ
Lemmas referenced :
equipollent-list,
finite_wf,
nat_wf,
exp_wf4,
equipollent_wf,
list_wf,
equal_wf,
length_wf,
int_seg_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
sqequalHypSubstitution,
productElimination,
thin,
cut,
introduction,
extract_by_obid,
isectElimination,
hypothesisEquality,
dependent_functionElimination,
independent_functionElimination,
hypothesis,
cumulativity,
universeEquality,
dependent_pairFormation,
setEquality,
intEquality,
setElimination,
rename,
natural_numberEquality
Latex:
\mforall{}T:Type. \mforall{}n:\mBbbN{}. (finite(T) {}\mRightarrow{} finite(\{l:T List| ||l|| = n\} ))
Date html generated:
2017_04_17-AM-09_34_43
Last ObjectModification:
2017_02_27-PM-05_33_38
Theory : equipollence!!cardinality!
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