Nuprl Lemma : member-partial-permutations-list
∀n:ℕ+. ∀i:ℤ. ∀f:ℕn →⟶ ℕn. (f ∈ partial-permutations-list(n;i)) supposing (f (n - 1)) = i ∈ ℤ
Proof
Definitions occuring in Statement :
partial-permutations-list: partial-permutations-list(n;i),
injection: A →⟶ B,
l_member: (x ∈ l),
int_seg: {i..j-},
nat_plus: ℕ+,
uimplies: b supposing a,
all: ∀x:A. B[x],
apply: f a,
subtract: n - m,
natural_number: $n,
int: ℤ,
equal: s = t ∈ T
Definitions unfolded in proof :
rev_uimplies: rev_uimplies(P;Q),
uiff: uiff(P;Q),
cand: A c∧ B,
rev_implies: P ⇐ Q,
iff: P ⇐⇒ Q,
so_apply: x[s],
so_lambda: λ2x.t[x],
subtype_rel: A ⊆r B,
prop: ℙ,
top: Top,
false: False,
exists: ∃x:A. B[x],
satisfiable_int_formula: satisfiable_int_formula(fmla),
implies: P ⇒ Q,
not: ¬A,
or: P ∨ Q,
decidable: Dec(P),
and: P ∧ Q,
lelt: i ≤ j < k,
nat_plus: ℕ+,
int_seg: {i..j-},
injection: A →⟶ B,
uall: ∀[x:A]. B[x],
partial-permutations-list: partial-permutations-list(n;i),
member: t ∈ T,
uimplies: b supposing a,
all: ∀x:A. B[x]
Lemmas referenced :
nat_plus_wf,
int_subtype_base,
equal-wf-T-base,
assert_of_eq_int,
member-permutations-list,
l_member_wf,
all_wf,
no_repeats_wf,
list_wf,
nat_plus_subtype_nat,
permutations-list_wf,
int_seg_wf,
injection_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,
member_filter
Rules used in proof :
productElimination,
productEquality,
setEquality,
sqequalRule,
voidEquality,
voidElimination,
isect_memberEquality,
intEquality,
int_eqEquality,
dependent_pairFormation,
independent_functionElimination,
approximateComputation,
independent_isectElimination,
unionElimination,
hypothesisEquality,
independent_pairFormation,
natural_numberEquality,
dependent_set_memberEquality,
setElimination,
applyEquality,
lambdaEquality,
dependent_functionElimination,
because_Cache,
isectElimination,
sqequalHypSubstitution,
extract_by_obid,
rename,
thin,
hypothesis,
axiomEquality,
introduction,
cut,
isect_memberFormation,
lambdaFormation,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution
Latex:
\mforall{}n:\mBbbN{}\msupplus{}. \mforall{}i:\mBbbZ{}. \mforall{}f:\mBbbN{}n \mrightarrow{}{}\mrightarrow{} \mBbbN{}n. (f \mmember{} partial-permutations-list(n;i)) supposing (f (n - 1)) = i
Date html generated:
2018_05_21-PM-08_23_56
Last ObjectModification:
2017_12_15-PM-00_03_30
Theory : general
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