Nuprl Lemma : omral_plus_wf
∀g:OCMon. ∀r:CDRng. ∀ps,qs:(|g| × |r|) List. (ps ++ qs ∈ (|g| × |r|) List)
Proof
Definitions occuring in Statement :
omral_plus: ps ++ qs,
list: T List,
all: ∀x:A. B[x],
member: t ∈ T,
product: x:A × B[x],
cdrng: CDRng,
rng_car: |r|,
ocmon: OCMon,
grp_car: |g|
Definitions unfolded in proof :
omral_plus: ps ++ qs,
all: ∀x:A. B[x],
member: t ∈ T,
uall: ∀[x:A]. B[x],
ocmon: OCMon,
abmonoid: AbMon,
mon: Mon,
cdrng: CDRng,
crng: CRng,
rng: Rng,
and: P ∧ Q,
omon: OMon,
so_lambda: λ2x y.t[x; y],
infix_ap: x f y,
so_apply: x[s1;s2],
prop: ℙ,
oset_of_ocmon: g↓oset,
dset_of_mon: g↓set,
set_car: |p|,
pi1: fst(t),
add_grp_of_rng: r↓+gp,
grp_car: |g|
Lemmas referenced :
list_wf,
grp_car_wf,
rng_car_wf,
cdrng_wf,
ocmon_wf,
cdrng_is_abdmonoid,
oal_merge_wf,
oset_of_ocmon_wf,
ulinorder_wf,
assert_wf,
grp_le_wf,
equal_wf,
bool_wf,
grp_eq_wf,
band_wf
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
lambdaFormation,
cut,
sqequalHypSubstitution,
hypothesis,
introduction,
extract_by_obid,
isectElimination,
thin,
productEquality,
setElimination,
rename,
hypothesisEquality,
productElimination,
equalityTransitivity,
equalitySymmetry,
dependent_functionElimination,
dependent_set_memberEquality,
lambdaEquality,
applyEquality,
because_Cache,
functionEquality
Latex:
\mforall{}g:OCMon. \mforall{}r:CDRng. \mforall{}ps,qs:(|g| \mtimes{} |r|) List. (ps ++ qs \mmember{} (|g| \mtimes{} |r|) List)
Date html generated:
2018_05_22-AM-07_46_36
Last ObjectModification:
2018_05_19-AM-08_26_50
Theory : polynom_3
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