Nuprl Lemma : permutations-list_wf
∀[n:ℕ]. (permutations-list(n) ∈ {P:ℕn →⟶ ℕn List| no_repeats(ℕn →⟶ ℕn;P) ∧ (∀f:ℕn →⟶ ℕn. (f ∈ P))} )
Proof
Definitions occuring in Statement :
permutations-list: permutations-list(n),
injection: A →⟶ 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]} ,
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,
permutations-list: permutations-list(n),
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,
injection_wf,
list_wf,
sq_exists_wf,
nat_wf,
all_wf,
list-permutations
Rules used in proof :
equalitySymmetry,
equalityTransitivity,
axiomEquality,
productEquality,
because_Cache,
rename,
setElimination,
natural_numberEquality,
isectElimination,
hypothesisEquality,
sqequalHypSubstitution,
lambdaEquality,
hypothesis,
extract_by_obid,
instantiate,
thin,
applyEquality,
cut,
introduction,
isect_memberFormation,
computationStep,
sqequalTransitivity,
sqequalReflexivity,
sqequalRule,
sqequalSubstitution
Latex:
\mforall{}[n:\mBbbN{}]
(permutations-list(n) \mmember{} \{P:\mBbbN{}n \mrightarrow{}{}\mrightarrow{} \mBbbN{}n List| no\_repeats(\mBbbN{}n \mrightarrow{}{}\mrightarrow{} \mBbbN{}n;P) \mwedge{} (\mforall{}f:\mBbbN{}n \mrightarrow{}{}\mrightarrow{} \mBbbN{}n. (f \mmember{} P))\} )
Date html generated:
2018_05_21-PM-08_21_27
Last ObjectModification:
2017_12_11-AM-10_34_19
Theory : general
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