Nuprl Lemma : omralist_wf
∀g:OCMon. ∀r:CDRng. (omral(g;r) ∈ DSet)
Proof
Definitions occuring in Statement :
omralist: omral(g;r),
all: ∀x:A. B[x],
member: t ∈ T,
cdrng: CDRng,
ocmon: OCMon,
dset: DSet
Definitions unfolded in proof :
all: ∀x:A. B[x],
uall: ∀[x:A]. B[x],
member: t ∈ T,
and: P ∧ Q,
omralist: omral(g;r),
ocmon: OCMon,
omon: OMon,
abmonoid: AbMon,
mon: Mon,
so_lambda: λ2x y.t[x; y],
infix_ap: x f y,
so_apply: x[s1;s2],
prop: ℙ
Lemmas referenced :
cdrng_is_abdmonoid,
oalist_wf,
oset_of_ocmon_wf,
ulinorder_wf,
grp_car_wf,
assert_wf,
grp_le_wf,
equal_wf,
bool_wf,
grp_eq_wf,
band_wf,
cdrng_wf,
ocmon_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
productElimination,
hypothesis,
sqequalRule,
dependent_functionElimination,
setElimination,
rename,
dependent_set_memberEquality,
productEquality,
lambdaEquality,
applyEquality,
because_Cache,
functionEquality
Latex:
\mforall{}g:OCMon. \mforall{}r:CDRng. (omral(g;r) \mmember{} DSet)
Date html generated:
2018_05_22-AM-07_46_34
Last ObjectModification:
2018_05_19-AM-08_26_36
Theory : polynom_3
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