Nuprl Lemma : list-permutations
∀n:ℕ. (∃P:ℕn →⟶ ℕn List [(no_repeats(ℕn →⟶ ℕn;P) ∧ (∀f:ℕn →⟶ ℕn. (f ∈ P)))])
Proof
Definitions occuring in Statement :
injection: A →⟶ B,
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,
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,
subtype_rel: A ⊆r B,
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,
nat_plus_subtype_nat,
fact_wf,
int_seg_wf,
injection_wf,
equipollent-iff-list,
equipollent-factorial
Rules used in proof :
lambdaEquality,
productEquality,
independent_pairFormation,
dependent_set_memberEquality,
independent_functionElimination,
productElimination,
sqequalRule,
applyEquality,
because_Cache,
rename,
setElimination,
natural_numberEquality,
isectElimination,
hypothesisEquality,
thin,
dependent_functionElimination,
sqequalHypSubstitution,
hypothesis,
lambdaFormation,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution,
extract_by_obid,
introduction,
cut
Latex:
\mforall{}n:\mBbbN{}. (\mexists{}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_04
Last ObjectModification:
2017_12_11-AM-10_31_44
Theory : general
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