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 ⊆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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