Nuprl Lemma : functions-list_wf
∀[n,b:ℕ]. (functions-list(n;b) ∈ {P:(ℕn ⟶ ℕb) List| no_repeats(ℕn ⟶ ℕb;P) ∧ (∀f:ℕn ⟶ ℕb. (f ∈ P))} )
Proof
Definitions occuring in Statement :
functions-list: functions-list(n;b),
no_repeats: no_repeats(T;l),
l_member: (x ∈ l),
list: T List,
int_seg: {i..j-},
nat: ℕ,
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
and: P ∧ Q,
member: t ∈ T,
set: {x:A| B[x]} ,
function: x:A ⟶ B[x],
natural_number: $n
Definitions unfolded in proof :
so_apply: x[s],
and: P ∧ Q,
prop: ℙ,
nat: ℕ,
so_lambda: λ2x.t[x],
all: ∀x:A. B[x],
subtype_rel: A ⊆r B,
functions-list: functions-list(n;b),
member: t ∈ T,
uall: ∀[x:A]. B[x],
sq_exists: ∃x:A [B[x]]
Lemmas referenced :
l_member_wf,
no_repeats_wf,
int_seg_wf,
list_wf,
sq_exists_wf,
nat_wf,
all_wf,
list-functions
Rules used in proof :
isect_memberEquality,
equalitySymmetry,
equalityTransitivity,
axiomEquality,
functionExtensionality,
productEquality,
rename,
setElimination,
natural_numberEquality,
functionEquality,
because_Cache,
isectElimination,
hypothesisEquality,
sqequalHypSubstitution,
lambdaEquality,
hypothesis,
extract_by_obid,
instantiate,
thin,
applyEquality,
cut,
introduction,
isect_memberFormation,
computationStep,
sqequalTransitivity,
sqequalReflexivity,
sqequalRule,
sqequalSubstitution
Latex:
\mforall{}[n,b:\mBbbN{}].
(functions-list(n;b) \mmember{} \{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_31
Last ObjectModification:
2017_12_14-PM-06_39_19
Theory : general
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