Nuprl Lemma : p-minus-int
∀[p:ℕ+]. ∀[k:ℤ]. (-(k(p)) = -k(p) ∈ p-adics(p))
Proof
Definitions occuring in Statement :
p-int: k(p),
p-minus: -(x),
p-adics: p-adics(p),
nat_plus: ℕ+,
uall: ∀[x:A]. B[x],
minus: -n,
int: ℤ,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
all: ∀x:A. B[x],
uiff: uiff(P;Q),
and: P ∧ Q,
rev_uimplies: rev_uimplies(P;Q),
uimplies: b supposing a,
p-int: k(p),
p-minus: -(x),
p-reduce: i mod(p^n),
subtype_rel: A ⊆r B,
nat_plus: ℕ+,
int_seg: {i..j-},
implies: P ⇒ Q,
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q
Lemmas referenced :
p-adics-equal,
p-minus_wf,
p-int_wf,
nat_plus_wf,
exp_wf2,
nat_plus_subtype_nat,
modulus_wf_int_mod,
exp_wf_nat_plus,
int-subtype-int_mod,
int_seg_wf,
eqmod_functionality_wrt_eqmod,
eqmod_transitivity,
mod-eqmod,
minus_functionality_wrt_eqmod,
eqmod_weakening
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
extract_by_obid,
sqequalHypSubstitution,
dependent_functionElimination,
thin,
hypothesisEquality,
isectElimination,
hypothesis,
minusEquality,
productElimination,
independent_isectElimination,
lambdaFormation,
sqequalRule,
intEquality,
isect_memberEquality,
axiomEquality,
because_Cache,
applyEquality,
setElimination,
rename,
lambdaEquality,
natural_numberEquality,
independent_functionElimination
Latex:
\mforall{}[p:\mBbbN{}\msupplus{}]. \mforall{}[k:\mBbbZ{}]. (-(k(p)) = -k(p))
Date html generated:
2018_05_21-PM-03_19_01
Last ObjectModification:
2018_05_19-AM-08_10_00
Theory : rings_1
Home
Index