Nuprl Lemma : no_repeats-partial-permutations-list
∀[n:ℕ+]. ∀[i:ℤ]. no_repeats(ℕn →⟶ ℕn;partial-permutations-list(n;i))
Proof
Definitions occuring in Statement :
partial-permutations-list: partial-permutations-list(n;i),
injection: A →⟶ B,
no_repeats: no_repeats(T;l),
int_seg: {i..j-},
nat_plus: ℕ+,
uall: ∀[x:A]. B[x],
natural_number: $n,
int: ℤ
Definitions unfolded in proof :
top: Top,
false: False,
exists: ∃x:A. B[x],
satisfiable_int_formula: satisfiable_int_formula(fmla),
not: ¬A,
uimplies: b supposing a,
or: P ∨ Q,
decidable: Dec(P),
lelt: i ≤ j < k,
int_seg: {i..j-},
injection: A →⟶ B,
implies: P ⇒ Q,
all: ∀x:A. B[x],
so_apply: x[s],
prop: ℙ,
and: P ∧ Q,
so_lambda: λ2x.t[x],
nat_plus: ℕ+,
subtype_rel: A ⊆r B,
partial-permutations-list: partial-permutations-list(n;i),
member: t ∈ T,
uall: ∀[x:A]. B[x]
Lemmas referenced :
nat_plus_wf,
partial-permutations-list_wf,
no_repeats_witness,
equal_wf,
lelt_wf,
decidable__lt,
int_formula_prop_wf,
int_formula_prop_less_lemma,
int_term_value_var_lemma,
int_term_value_subtract_lemma,
int_term_value_constant_lemma,
int_formula_prop_le_lemma,
int_formula_prop_not_lemma,
int_formula_prop_and_lemma,
intformless_wf,
itermVar_wf,
itermSubtract_wf,
itermConstant_wf,
intformle_wf,
intformnot_wf,
intformand_wf,
full-omega-unsat,
decidable__le,
nat_plus_properties,
subtract_wf,
eq_int_wf,
no_repeats_filter,
l_member_wf,
all_wf,
no_repeats_wf,
int_seg_wf,
injection_wf,
list_wf,
set_wf,
nat_plus_subtype_nat,
permutations-list_wf
Rules used in proof :
equalitySymmetry,
equalityTransitivity,
voidEquality,
voidElimination,
isect_memberEquality,
intEquality,
int_eqEquality,
dependent_pairFormation,
independent_functionElimination,
approximateComputation,
independent_isectElimination,
unionElimination,
dependent_functionElimination,
independent_pairFormation,
dependent_set_memberEquality,
productElimination,
lambdaFormation,
productEquality,
lambdaEquality,
because_Cache,
rename,
setElimination,
natural_numberEquality,
sqequalRule,
hypothesis,
applyEquality,
hypothesisEquality,
thin,
isectElimination,
sqequalHypSubstitution,
extract_by_obid,
cut,
introduction,
isect_memberFormation,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution
Latex:
\mforall{}[n:\mBbbN{}\msupplus{}]. \mforall{}[i:\mBbbZ{}]. no\_repeats(\mBbbN{}n \mrightarrow{}{}\mrightarrow{} \mBbbN{}n;partial-permutations-list(n;i))
Date html generated:
2018_05_21-PM-08_23_44
Last ObjectModification:
2017_12_15-AM-11_41_53
Theory : general
Home
Index