Nuprl Lemma : omral_times_ident_r
∀g:OCMon. ∀r:CDRng. ∀ps:|omral(g;r)|. ((ps ** 11) = ps ∈ |omral(g;r)|)
Proof
Definitions occuring in Statement :
omral_one: 11,
omral_times: ps ** qs,
omralist: omral(g;r),
all: ∀x:A. B[x],
equal: s = t ∈ T,
cdrng: CDRng,
ocmon: OCMon,
set_car: |p|
Definitions unfolded in proof :
all: ∀x:A. B[x],
member: t ∈ T,
uall: ∀[x:A]. B[x],
subtype_rel: A ⊆r B,
dset: DSet,
comm: Comm(T;op),
infix_ap: x f y,
squash: ↓T,
prop: ℙ,
true: True,
uimplies: b supposing a,
guard: {T},
iff: P ⇐⇒ Q,
and: P ∧ Q,
rev_implies: P ⇐ Q,
implies: P ⇒ Q
Lemmas referenced :
omral_times_comm,
set_car_wf,
omralist_wf,
dset_wf,
cdrng_wf,
ocmon_wf,
equal_wf,
squash_wf,
true_wf,
omral_one_wf,
iff_weakening_equal,
omral_times_ident_l
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
dependent_functionElimination,
thin,
hypothesisEquality,
hypothesis,
isectElimination,
applyEquality,
lambdaEquality,
setElimination,
rename,
sqequalRule,
imageElimination,
equalityTransitivity,
equalitySymmetry,
universeEquality,
because_Cache,
natural_numberEquality,
imageMemberEquality,
baseClosed,
independent_isectElimination,
productElimination,
independent_functionElimination
Latex:
\mforall{}g:OCMon. \mforall{}r:CDRng. \mforall{}ps:|omral(g;r)|. ((ps ** 11) = ps)
Date html generated:
2017_10_01-AM-10_06_51
Last ObjectModification:
2017_03_03-PM-01_14_29
Theory : polynom_3
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