Nuprl Lemma : no_repeats-functions-list
∀[n,b:ℕ]. no_repeats(ℕn ⟶ ℕb;functions-list(n;b))
Proof
Definitions occuring in Statement :
functions-list: functions-list(n;b),
no_repeats: no_repeats(T;l),
int_seg: {i..j-},
nat: ℕ,
uall: ∀[x:A]. B[x],
function: x:A ⟶ B[x],
natural_number: $n
Definitions unfolded in proof :
subtype_rel: A ⊆r B,
squash: ↓T,
sq_stable: SqStable(P),
implies: P ⇒ Q,
all: ∀x:A. B[x],
so_apply: x[s],
prop: ℙ,
and: P ∧ Q,
so_lambda: λ2x.t[x],
nat: ℕ,
member: t ∈ T,
uall: ∀[x:A]. B[x]
Lemmas referenced :
nat_wf,
no_repeats_witness,
equal_wf,
sq_stable__no_repeats,
l_member_wf,
all_wf,
no_repeats_wf,
int_seg_wf,
list_wf,
set_wf,
functions-list_wf
Rules used in proof :
isect_memberEquality,
setEquality,
dependent_functionElimination,
equalitySymmetry,
equalityTransitivity,
imageElimination,
baseClosed,
imageMemberEquality,
productElimination,
independent_functionElimination,
lambdaFormation,
applyEquality,
functionExtensionality,
productEquality,
lambdaEquality,
sqequalRule,
because_Cache,
rename,
setElimination,
natural_numberEquality,
functionEquality,
hypothesis,
hypothesisEquality,
thin,
isectElimination,
sqequalHypSubstitution,
extract_by_obid,
cut,
introduction,
isect_memberFormation,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution
Latex:
\mforall{}[n,b:\mBbbN{}]. no\_repeats(\mBbbN{}n {}\mrightarrow{} \mBbbN{}b;functions-list(n;b))
Date html generated:
2018_05_21-PM-08_24_56
Last ObjectModification:
2017_12_14-PM-10_41_35
Theory : general
Home
Index