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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