Nuprl Lemma : alg_from_rng_wf
∀A:Type. ∀r:RngSig. ∀act:A ⟶ |r| ⟶ |r|. (alg_from_rng(A;r;act) ∈ algebra_sig{i:l}(A))
Proof
Definitions occuring in Statement :
alg_from_rng: alg_from_rng(A;r;act),
algebra_sig: algebra_sig{i:l}(A),
all: ∀x:A. B[x],
member: t ∈ T,
function: x:A ⟶ B[x],
universe: Type,
rng_car: |r|,
rng_sig: RngSig
Definitions unfolded in proof :
alg_from_rng: alg_from_rng(A;r;act),
algebra_sig: algebra_sig{i:l}(A),
all: ∀x:A. B[x],
member: t ∈ T,
uall: ∀[x:A]. B[x]
Lemmas referenced :
rng_car_wf,
rng_eq_wf,
rng_le_wf,
rng_plus_wf,
rng_zero_wf,
rng_minus_wf,
rng_times_wf,
rng_one_wf,
rng_div_wf,
unit_wf2,
bool_wf,
rng_sig_wf
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
lambdaFormation,
cut,
dependent_pairEquality,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
because_Cache,
functionEquality,
cumulativity,
productEquality,
unionEquality,
universeEquality
Latex:
\mforall{}A:Type. \mforall{}r:RngSig. \mforall{}act:A {}\mrightarrow{} |r| {}\mrightarrow{} |r|. (alg\_from\_rng(A;r;act) \mmember{} algebra\_sig\{i:l\}(A))
Date html generated:
2016_05_16-AM-08_14_44
Last ObjectModification:
2015_12_28-PM-06_09_15
Theory : polynom_1
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