Nuprl Lemma : omral_action_inj
∀g:OCMon. ∀r:CDRng. ∀k:|g|. ∀v,v':|r|. ((v ⋅⋅ inj(k,v')) = inj(k,v * v') ∈ |omral(g;r)|)
Proof
Definitions occuring in Statement :
omral_action: v ⋅⋅ ps,
omral_inj: inj(k,v),
omralist: omral(g;r),
infix_ap: x f y,
all: ∀x:A. B[x],
equal: s = t ∈ T,
cdrng: CDRng,
rng_times: *,
rng_car: |r|,
ocmon: OCMon,
grp_car: |g|,
set_car: |p|
Definitions unfolded in proof :
all: ∀x:A. B[x],
member: t ∈ T,
infix_ap: x f y,
uall: ∀[x:A]. B[x],
cdrng: CDRng,
crng: CRng,
rng: Rng,
implies: P ⇒ Q,
squash: ↓T,
prop: ℙ,
true: True,
subtype_rel: A ⊆r B,
uimplies: b supposing a,
guard: {T},
iff: P ⇐⇒ Q,
and: P ∧ Q,
rev_implies: P ⇐ Q,
ocmon: OCMon,
abmonoid: AbMon,
mon: Mon,
rng_when: rng_when
Lemmas referenced :
omral_lookups_same_a,
omral_action_wf,
omral_inj_wf,
rng_times_wf,
equal_wf,
squash_wf,
true_wf,
rng_car_wf,
lookup_omral_action,
lookup_omral_inj,
iff_weakening_equal,
grp_car_wf,
cdrng_wf,
ocmon_wf,
rng_times_when_l,
grp_eq_wf,
rng_when_wf,
infix_ap_wf,
bool_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
dependent_functionElimination,
thin,
hypothesisEquality,
hypothesis,
applyEquality,
isectElimination,
setElimination,
rename,
independent_functionElimination,
lambdaEquality,
imageElimination,
equalityTransitivity,
equalitySymmetry,
universeEquality,
because_Cache,
natural_numberEquality,
sqequalRule,
imageMemberEquality,
baseClosed,
independent_isectElimination,
productElimination
Latex:
\mforall{}g:OCMon. \mforall{}r:CDRng. \mforall{}k:|g|. \mforall{}v,v':|r|. ((v \mcdot{}\mcdot{} inj(k,v')) = inj(k,v * v'))
Date html generated:
2017_10_01-AM-10_07_08
Last ObjectModification:
2017_03_03-PM-01_14_53
Theory : polynom_3
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