Nuprl Lemma : calgebra_properties
∀A:Rng. ∀m:CAlg(A). Comm(m.car;m.times)
Proof
Definitions occuring in Statement :
calgebra: CAlg(A),
alg_times: a.times,
alg_car: a.car,
comm: Comm(T;op),
all: ∀x:A. B[x],
rng: Rng
Definitions unfolded in proof :
all: ∀x:A. B[x],
calgebra: CAlg(A),
uall: ∀[x:A]. B[x],
member: t ∈ T,
rng: Rng,
algebra: algebra{i:l}(A),
module: A-Module,
sq_stable: SqStable(P),
implies: P ⇒ Q,
squash: ↓T
Lemmas referenced :
rng_wf,
calgebra_wf,
alg_times_wf,
rng_car_wf,
alg_car_wf,
sq_stable__comm
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
sqequalHypSubstitution,
setElimination,
thin,
rename,
cut,
lemma_by_obid,
isectElimination,
dependent_functionElimination,
hypothesisEquality,
hypothesis,
independent_functionElimination,
introduction,
sqequalRule,
imageMemberEquality,
baseClosed,
imageElimination
Latex:
\mforall{}A:Rng. \mforall{}m:CAlg(A). Comm(m.car;m.times)
Date html generated:
2016_05_16-AM-07_27_45
Last ObjectModification:
2016_01_16-PM-09_59_54
Theory : algebras_1
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