Nuprl Lemma : alg_p_wf
∀r:RngSig. ∀a:algebra_sig{i:l}(|r|).  (AlgP(r;a) ∈ ℙ)
Proof
Definitions occuring in Statement : 
alg_p: AlgP(r;a)
, 
algebra_sig: algebra_sig{i:l}(A)
, 
prop: ℙ
, 
all: ∀x:A. B[x]
, 
member: t ∈ T
, 
rng_car: |r|
, 
rng_sig: RngSig
Definitions unfolded in proof : 
alg_p: AlgP(r;a)
, 
all: ∀x:A. B[x]
, 
member: t ∈ T
, 
prop: ℙ
, 
and: P ∧ Q
, 
uall: ∀[x:A]. B[x]
, 
so_lambda: λ2x.t[x]
, 
so_apply: x[s]
Lemmas referenced : 
rng_p_wf, 
rng_of_alg_wf, 
rng_car_wf, 
action_p_wf, 
rng_times_wf, 
rng_one_wf, 
alg_car_wf, 
alg_act_wf, 
bilinear_p_wf, 
rng_plus_wf, 
alg_plus_wf, 
all_wf, 
dist_1op_2op_lr_wf, 
alg_times_wf, 
algebra_sig_wf, 
rng_sig_wf
Rules used in proof : 
sqequalSubstitution, 
sqequalRule, 
sqequalReflexivity, 
sqequalTransitivity, 
computationStep, 
lambdaFormation, 
cut, 
productEquality, 
lemma_by_obid, 
sqequalHypSubstitution, 
dependent_functionElimination, 
thin, 
isectElimination, 
hypothesisEquality, 
hypothesis, 
because_Cache, 
lambdaEquality, 
applyEquality
Latex:
\mforall{}r:RngSig.  \mforall{}a:algebra\_sig\{i:l\}(|r|).    (AlgP(r;a)  \mmember{}  \mBbbP{})
Date html generated:
2016_05_16-AM-08_13_59
Last ObjectModification:
2015_12_28-PM-06_09_36
Theory : polynom_1
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