Nuprl Lemma : omral_times_assoc_a
∀[g:OCMon]. ∀[a:CDRng]. ∀[ps,qs,rs:|omral(g;a)|]. ((ps ** (qs ** rs)) = ((ps ** qs) ** rs) ∈ |omral(g;a)|)
Proof
Definitions occuring in Statement :
omral_times: ps ** qs,
omralist: omral(g;r),
uall: ∀[x:A]. B[x],
equal: s = t ∈ T,
cdrng: CDRng,
ocmon: OCMon,
set_car: |p|
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
assoc: Assoc(T;op),
infix_ap: x f y,
all: ∀x:A. B[x]
Lemmas referenced :
omral_times_assoc
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
lemma_by_obid,
sqequalHypSubstitution,
sqequalRule,
hypothesis,
dependent_functionElimination,
thin,
hypothesisEquality,
isectElimination,
because_Cache,
isect_memberEquality,
axiomEquality
Latex:
\mforall{}[g:OCMon]. \mforall{}[a:CDRng]. \mforall{}[ps,qs,rs:|omral(g;a)|]. ((ps ** (qs ** rs)) = ((ps ** qs) ** rs))
Date html generated:
2016_05_16-AM-08_26_15
Last ObjectModification:
2015_12_28-PM-06_38_30
Theory : polynom_3
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