Nuprl Lemma : algebra_wf
∀A:RngSig. (algebra{i:l}(A) ∈ 𝕌')
Proof
Definitions occuring in Statement : 
algebra: algebra{i:l}(A)
, 
all: ∀x:A. B[x]
, 
member: t ∈ T
, 
universe: Type
, 
rng_sig: RngSig
Definitions unfolded in proof : 
algebra: algebra{i:l}(A)
, 
all: ∀x:A. B[x]
, 
member: t ∈ T
, 
and: P ∧ Q
, 
uall: ∀[x:A]. B[x]
, 
module: A-Module
, 
subtype_rel: A ⊆r B
, 
prop: ℙ
, 
so_lambda: λ2x.t[x]
, 
so_apply: x[s]
Lemmas referenced : 
module_wf, 
monoid_p_wf, 
alg_car_wf, 
rng_car_wf, 
alg_times_wf, 
alg_one_wf, 
bilinear_wf, 
alg_plus_wf, 
all_wf, 
dist_1op_2op_lr_wf, 
alg_act_wf, 
rng_sig_wf
Rules used in proof : 
sqequalSubstitution, 
sqequalRule, 
sqequalReflexivity, 
sqequalTransitivity, 
computationStep, 
lambdaFormation, 
cut, 
setEquality, 
lemma_by_obid, 
sqequalHypSubstitution, 
dependent_functionElimination, 
thin, 
hypothesisEquality, 
hypothesis, 
productEquality, 
isectElimination, 
because_Cache, 
setElimination, 
rename, 
applyEquality, 
lambdaEquality, 
cumulativity, 
universeEquality
Latex:
\mforall{}A:RngSig.  (algebra\{i:l\}(A)  \mmember{}  \mBbbU{}')
Date html generated:
2016_05_16-AM-07_27_22
Last ObjectModification:
2015_12_28-PM-05_07_52
Theory : algebras_1
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