Nuprl Lemma : exp-minusone-2n-add
∀[n,k:ℕ]. ((-1)^((2 * n) + k) = (-1)^k ∈ ℤ)
Proof
Definitions occuring in Statement :
exp: i^n,
nat: ℕ,
uall: ∀[x:A]. B[x],
multiply: n * m,
add: n + m,
minus: -n,
natural_number: $n,
int: ℤ,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
squash: ↓T,
nat: ℕ,
ge: i ≥ j ,
all: ∀x:A. B[x],
decidable: Dec(P),
or: P ∨ Q,
uimplies: b supposing a,
not: ¬A,
implies: P ⇒ Q,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
false: False,
top: Top,
and: P ∧ Q,
prop: ℙ,
true: True,
subtype_rel: A ⊆r B,
guard: {T},
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q
Lemmas referenced :
equal_wf,
exp_wf2,
exp-minusone,
nat_properties,
decidable__le,
full-omega-unsat,
intformand_wf,
intformnot_wf,
intformle_wf,
itermConstant_wf,
itermAdd_wf,
itermMultiply_wf,
itermVar_wf,
istype-int,
int_formula_prop_and_lemma,
istype-void,
int_formula_prop_not_lemma,
int_formula_prop_le_lemma,
int_term_value_constant_lemma,
int_term_value_add_lemma,
int_term_value_mul_lemma,
int_term_value_var_lemma,
int_formula_prop_wf,
istype-le,
iff_weakening_equal,
add-commutes,
ifthenelse_wf,
eq_int_wf,
mod2-add2n
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
Error :isect_memberFormation_alt,
introduction,
cut,
equalitySymmetry,
applyEquality,
thin,
Error :lambdaEquality_alt,
sqequalHypSubstitution,
imageElimination,
extract_by_obid,
isectElimination,
because_Cache,
hypothesis,
intEquality,
hypothesisEquality,
minusEquality,
natural_numberEquality,
Error :dependent_set_memberEquality_alt,
addEquality,
multiplyEquality,
setElimination,
rename,
dependent_functionElimination,
unionElimination,
independent_isectElimination,
approximateComputation,
independent_functionElimination,
Error :dependent_pairFormation_alt,
int_eqEquality,
Error :isect_memberEquality_alt,
voidElimination,
sqequalRule,
independent_pairFormation,
Error :universeIsType,
imageMemberEquality,
baseClosed,
equalityTransitivity,
productElimination,
Error :inhabitedIsType,
axiomEquality,
Error :isectIsTypeImplies
Latex:
\mforall{}[n,k:\mBbbN{}]. ((-1)\^{}((2 * n) + k) = (-1)\^{}k)
Date html generated:
2019_06_20-PM-02_31_03
Last ObjectModification:
2019_01_22-PM-00_42_47
Theory : num_thy_1
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