Nuprl Lemma : algebra_times_one
∀[A:Rng]. ∀[m:algebra{i:l}(A)]. ∀[x:m.car]. (((x m.times m.one) = x ∈ m.car) ∧ ((m.one m.times x) = x ∈ m.car))
Proof
Definitions occuring in Statement :
algebra: algebra{i:l}(A),
alg_one: a.one,
alg_times: a.times,
alg_car: a.car,
uall: ∀[x:A]. B[x],
infix_ap: x f y,
and: P ∧ Q,
equal: s = t ∈ T,
rng: Rng
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
and: P ∧ Q,
cand: A c∧ B,
all: ∀x:A. B[x],
rng: Rng,
algebra: algebra{i:l}(A),
module: A-Module,
guard: {T},
monoid_p: IsMonoid(T;op;id),
ident: Ident(T;op;id)
Lemmas referenced :
algebra_properties,
alg_car_wf,
rng_car_wf,
algebra_wf,
rng_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
lemma_by_obid,
sqequalHypSubstitution,
dependent_functionElimination,
thin,
hypothesisEquality,
hypothesis,
productElimination,
independent_pairFormation,
sqequalRule,
independent_pairEquality,
axiomEquality,
isectElimination,
setElimination,
rename,
isect_memberEquality,
because_Cache
Latex:
\mforall{}[A:Rng]. \mforall{}[m:algebra\{i:l\}(A)]. \mforall{}[x:m.car]. (((x m.times m.one) = x) \mwedge{} ((m.one m.times x) = x))
Date html generated:
2016_05_16-AM-07_27_32
Last ObjectModification:
2015_12_28-PM-05_07_40
Theory : algebras_1
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