Nuprl Lemma : list-functions
∀n,b:ℕ. (∃P:(ℕn ⟶ ℕb) List [(no_repeats(ℕn ⟶ ℕb;P) ∧ (∀f:ℕn ⟶ ℕb. (f ∈ P)))])
Proof
Definitions occuring in Statement :
no_repeats: no_repeats(T;l),
l_member: (x ∈ l),
list: T List,
int_seg: {i..j-},
nat: ℕ,
all: ∀x:A. B[x],
sq_exists: ∃x:A [B[x]],
and: P ∧ Q,
function: x:A ⟶ B[x],
natural_number: $n
Definitions unfolded in proof :
so_apply: x[s],
so_lambda: λ2x.t[x],
prop: ℙ,
cand: A c∧ B,
sq_exists: ∃x:A [B[x]],
exists: ∃x:A. B[x],
implies: P ⇒ Q,
and: P ∧ Q,
iff: P ⇐⇒ Q,
nat: ℕ,
uall: ∀[x:A]. B[x],
member: t ∈ T,
all: ∀x:A. B[x]
Lemmas referenced :
nat_wf,
l_member_wf,
all_wf,
no_repeats_wf,
exp_wf4,
int_seg_wf,
equipollent-iff-list,
equipollent-exp
Rules used in proof :
applyEquality,
functionExtensionality,
lambdaEquality,
sqequalRule,
because_Cache,
productEquality,
independent_pairFormation,
dependent_set_memberEquality,
independent_functionElimination,
productElimination,
rename,
setElimination,
natural_numberEquality,
functionEquality,
isectElimination,
hypothesisEquality,
thin,
dependent_functionElimination,
sqequalHypSubstitution,
hypothesis,
lambdaFormation,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution,
extract_by_obid,
introduction,
cut
Latex:
\mforall{}n,b:\mBbbN{}. (\mexists{}P:(\mBbbN{}n {}\mrightarrow{} \mBbbN{}b) List [(no\_repeats(\mBbbN{}n {}\mrightarrow{} \mBbbN{}b;P) \mwedge{} (\mforall{}f:\mBbbN{}n {}\mrightarrow{} \mBbbN{}b. (f \mmember{} P)))])
Date html generated:
2018_05_21-PM-08_24_08
Last ObjectModification:
2017_12_14-PM-06_35_49
Theory : general
Home
Index