Nuprl Lemma : n-to-bool-list
∀n:ℕ. ∃L:(ℕn ⟶ 𝔹) List. (no_repeats(ℕn ⟶ 𝔹;L) ∧ (∀f:ℕn ⟶ 𝔹. (f ∈ L)))
Proof
Definitions occuring in Statement :
no_repeats: no_repeats(T;l),
l_member: (x ∈ l),
list: T List,
int_seg: {i..j-},
nat: ℕ,
bool: 𝔹,
all: ∀x:A. B[x],
exists: ∃x:A. B[x],
and: P ∧ Q,
function: x:A ⟶ B[x],
natural_number: $n
Definitions unfolded in proof :
all: ∀x:A. B[x],
uall: ∀[x:A]. B[x],
member: t ∈ T,
nat: ℕ,
iff: P ⇐⇒ Q,
and: P ∧ Q,
rev_implies: P ⇐ Q,
implies: P ⇒ Q,
so_lambda: λ2x.t[x],
so_apply: x[s]
Lemmas referenced :
finite-iff-listable,
int_seg_wf,
bool_wf,
finite-function,
nsub_finite,
finite-bool,
istype-nat
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation_alt,
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
functionEquality,
natural_numberEquality,
setElimination,
rename,
hypothesisEquality,
hypothesis,
productElimination,
independent_pairFormation,
independent_functionElimination,
dependent_functionElimination,
because_Cache,
sqequalRule,
lambdaEquality_alt,
universeIsType
Latex:
\mforall{}n:\mBbbN{}. \mexists{}L:(\mBbbN{}n {}\mrightarrow{} \mBbbB{}) List. (no\_repeats(\mBbbN{}n {}\mrightarrow{} \mBbbB{};L) \mwedge{} (\mforall{}f:\mBbbN{}n {}\mrightarrow{} \mBbbB{}. (f \mmember{} L)))
Date html generated:
2019_10_15-AM-10_25_11
Last ObjectModification:
2019_09_27-PM-02_11_08
Theory : equipollence!!cardinality!
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