Nuprl Lemma : omral_alg_wf
∀g:OCMon. ∀r:CDRng. (omral_alg(g;r) ∈ algebra_sig{i:l}(|r|))
Proof
Definitions occuring in Statement :
omral_alg: omral_alg(g;r),
algebra_sig: algebra_sig{i:l}(A),
all: ∀x:A. B[x],
member: t ∈ T,
cdrng: CDRng,
rng_car: |r|,
ocmon: OCMon
Definitions unfolded in proof :
omral_alg: omral_alg(g;r),
algebra_sig: algebra_sig{i:l}(A),
all: ∀x:A. B[x],
member: t ∈ T,
uall: ∀[x:A]. B[x],
subtype_rel: A ⊆r B,
cdrng: CDRng,
crng: CRng,
rng: Rng
Lemmas referenced :
set_car_wf,
omralist_wf,
set_eq_wf,
btrue_wf,
omral_plus_wf2,
omral_zero_wf,
omral_minus_wf,
omral_times_wf2,
omral_one_wf,
it_wf,
omral_action_wf,
rng_car_wf,
unit_wf2,
bool_wf,
cdrng_wf,
ocmon_wf
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
lambdaFormation,
cut,
dependent_pairEquality,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
dependent_functionElimination,
hypothesisEquality,
hypothesis,
applyEquality,
because_Cache,
lambdaEquality,
inrEquality,
setElimination,
rename,
functionEquality,
productEquality,
unionEquality,
cumulativity
Latex:
\mforall{}g:OCMon. \mforall{}r:CDRng. (omral\_alg(g;r) \mmember{} algebra\_sig\{i:l\}(|r|))
Date html generated:
2016_05_16-AM-08_27_19
Last ObjectModification:
2015_12_28-PM-06_38_17
Theory : polynom_3
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