Nuprl Lemma : permutation-sign_wf
∀[n:ℕ]. ∀[f:ℕn ⟶ ℕn]. (permutation-sign(n;f) ∈ {s:ℤ| |s| = 1 ∈ ℤ} )
Proof
Definitions occuring in Statement :
permutation-sign: permutation-sign(n;f),
absval: |i|,
int_seg: {i..j-},
nat: ℕ,
uall: ∀[x:A]. B[x],
member: t ∈ T,
set: {x:A| B[x]} ,
function: x:A ⟶ B[x],
natural_number: $n,
int: ℤ,
equal: s = t ∈ T
Definitions unfolded in proof :
lelt: i ≤ j < k,
int_seg: {i..j-},
or: P ∨ Q,
decidable: Dec(P),
rev_implies: P ⇐ Q,
iff: P ⇐⇒ Q,
guard: {T},
subtype_rel: A ⊆r B,
true: True,
less_than': less_than'(a;b),
le: A ≤ B,
squash: ↓T,
so_apply: x[s],
so_lambda: λ2x.t[x],
permutation-sign: permutation-sign(n;f),
prop: ℙ,
and: P ∧ Q,
top: Top,
all: ∀x:A. B[x],
exists: ∃x:A. B[x],
satisfiable_int_formula: satisfiable_int_formula(fmla),
not: ¬A,
uimplies: b supposing a,
ge: i ≥ j ,
false: False,
implies: P ⇒ Q,
nat: ℕ,
member: t ∈ T,
uall: ∀[x:A]. B[x],
assert: ↑b,
bnot: ¬bb,
sq_type: SQType(T),
bfalse: ff,
absval: |i|,
ifthenelse: if b then t else f fi ,
uiff: uiff(P;Q),
btrue: tt,
it: ⋅,
unit: Unit,
bool: 𝔹,
sign: sign(x)
Lemmas referenced :
nat_wf,
decidable__lt,
int_seg_properties,
sign_wf,
int_seg_subtype_nat,
int-prod_wf_absval_1,
int_term_value_subtract_lemma,
int_formula_prop_not_lemma,
itermSubtract_wf,
intformnot_wf,
subtract_wf,
decidable__le,
int_subtype_base,
equal-wf-base,
iff_weakening_equal,
le_wf,
false_wf,
absval_pos,
true_wf,
squash_wf,
equal_wf,
int_prod0_lemma,
int_seg_wf,
less_than_wf,
ge_wf,
int_formula_prop_wf,
int_formula_prop_less_lemma,
int_term_value_var_lemma,
int_term_value_constant_lemma,
int_formula_prop_le_lemma,
int_formula_prop_and_lemma,
intformless_wf,
itermVar_wf,
itermConstant_wf,
intformle_wf,
intformand_wf,
full-omega-unsat,
nat_properties,
assert-bnot,
bool_subtype_base,
subtype_base_sq,
bool_cases_sqequal,
eqff_to_assert,
assert_of_le_int,
eqtt_to_assert,
bool_wf,
lelt_wf,
le_int_wf
Rules used in proof :
unionElimination,
closedConclusion,
baseApply,
productElimination,
baseClosed,
imageMemberEquality,
because_Cache,
universeEquality,
imageElimination,
applyEquality,
dependent_set_memberEquality,
functionEquality,
equalitySymmetry,
equalityTransitivity,
axiomEquality,
independent_pairFormation,
voidEquality,
voidElimination,
isect_memberEquality,
dependent_functionElimination,
intEquality,
int_eqEquality,
lambdaEquality,
dependent_pairFormation,
independent_functionElimination,
approximateComputation,
independent_isectElimination,
natural_numberEquality,
lambdaFormation,
intWeakElimination,
sqequalRule,
rename,
setElimination,
hypothesis,
hypothesisEquality,
thin,
isectElimination,
sqequalHypSubstitution,
extract_by_obid,
cut,
introduction,
isect_memberFormation,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution,
cumulativity,
instantiate,
promote_hyp,
equalityElimination,
functionExtensionality
Latex:
\mforall{}[n:\mBbbN{}]. \mforall{}[f:\mBbbN{}n {}\mrightarrow{} \mBbbN{}n]. (permutation-sign(n;f) \mmember{} \{s:\mBbbZ{}| |s| = 1\} )
Date html generated:
2018_05_21-PM-00_57_49
Last ObjectModification:
2017_12_10-PM-00_52_30
Theory : num_thy_1
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