Nuprl Lemma : omral_action_times_r2
∀g:OCMon. ∀r:CDRng. ∀v:|r|. ∀ps,qs:|omral(g;r)|. ((v ⋅⋅ (ps ** qs)) = (ps ** (v ⋅⋅ qs)) ∈ |omral(g;r)|)
Proof
Definitions occuring in Statement :
omral_action: v ⋅⋅ ps,
omral_times: ps ** qs,
omralist: omral(g;r),
all: ∀x:A. B[x],
equal: s = t ∈ T,
cdrng: CDRng,
rng_car: |r|,
ocmon: OCMon,
set_car: |p|
Definitions unfolded in proof :
all: ∀x:A. B[x],
member: t ∈ T,
squash: ↓T,
uall: ∀[x:A]. B[x],
prop: ℙ,
subtype_rel: A ⊆r B,
dset: DSet,
cdrng: CDRng,
crng: CRng,
rng: Rng,
true: True,
uimplies: b supposing a,
guard: {T},
iff: P ⇐⇒ Q,
and: P ∧ Q,
rev_implies: P ⇐ Q,
implies: P ⇒ Q
Lemmas referenced :
equal_wf,
squash_wf,
true_wf,
omral_action_wf,
set_car_wf,
omralist_wf,
dset_wf,
rng_car_wf,
cdrng_wf,
ocmon_wf,
omral_times_comm_a,
iff_weakening_equal,
omral_times_wf2,
omral_action_times_r1
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
cut,
applyEquality,
thin,
lambdaEquality,
sqequalHypSubstitution,
imageElimination,
introduction,
extract_by_obid,
isectElimination,
hypothesisEquality,
equalityTransitivity,
hypothesis,
equalitySymmetry,
universeEquality,
because_Cache,
dependent_functionElimination,
setElimination,
rename,
sqequalRule,
natural_numberEquality,
imageMemberEquality,
baseClosed,
independent_isectElimination,
productElimination,
independent_functionElimination
Latex:
\mforall{}g:OCMon. \mforall{}r:CDRng. \mforall{}v:|r|. \mforall{}ps,qs:|omral(g;r)|. ((v \mcdot{}\mcdot{} (ps ** qs)) = (ps ** (v \mcdot{}\mcdot{} qs)))
Date html generated:
2017_10_01-AM-10_07_02
Last ObjectModification:
2017_03_03-PM-01_14_40
Theory : polynom_3
Home
Index