Nuprl Lemma : calgebra_times_comm
∀[A:Rng]. ∀[m:CAlg(A)]. ∀[x,y:m.car]. ((x m.times y) = (y m.times x) ∈ m.car)
Proof
Definitions occuring in Statement :
calgebra: CAlg(A),
alg_times: a.times,
alg_car: a.car,
uall: ∀[x:A]. B[x],
infix_ap: x f y,
equal: s = t ∈ T,
rng: Rng
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
all: ∀x:A. B[x],
comm: Comm(T;op),
rng: Rng,
calgebra: CAlg(A),
algebra: algebra{i:l}(A),
module: A-Module
Lemmas referenced :
calgebra_properties,
alg_car_wf,
rng_car_wf,
calgebra_wf,
rng_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
lemma_by_obid,
sqequalHypSubstitution,
dependent_functionElimination,
thin,
hypothesisEquality,
hypothesis,
sqequalRule,
isect_memberEquality,
isectElimination,
axiomEquality,
setElimination,
rename,
because_Cache
Latex:
\mforall{}[A:Rng]. \mforall{}[m:CAlg(A)]. \mforall{}[x,y:m.car]. ((x m.times y) = (y m.times x))
Date html generated:
2016_05_16-AM-07_27_47
Last ObjectModification:
2015_12_28-PM-05_07_29
Theory : algebras_1
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