Nuprl Lemma : algebra_hom_wf
∀A:RngSig. ∀M,N:algebra_sig{i:l}(|A|). (algebra_hom(A; M; N) ∈ Type)
Proof
Definitions occuring in Statement :
algebra_hom: algebra_hom(A; M; N),
algebra_sig: algebra_sig{i:l}(A),
all: ∀x:A. B[x],
member: t ∈ T,
universe: Type,
rng_car: |r|,
rng_sig: RngSig
Definitions unfolded in proof :
algebra_hom: algebra_hom(A; M; N),
all: ∀x:A. B[x],
member: t ∈ T,
uall: ∀[x:A]. B[x],
module_hom: module_hom(A; M; N),
and: P ∧ Q,
prop: ℙ
Lemmas referenced :
module_hom_wf,
and_wf,
fun_thru_2op_wf,
alg_car_wf,
rng_car_wf,
alg_times_wf,
equal_wf,
alg_one_wf,
algebra_sig_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,
isectElimination,
setElimination,
rename,
applyEquality
Latex:
\mforall{}A:RngSig. \mforall{}M,N:algebra\_sig\{i:l\}(|A|). (algebra\_hom(A; M; N) \mmember{} Type)
Date html generated:
2016_05_16-AM-07_28_06
Last ObjectModification:
2015_12_28-PM-05_07_31
Theory : algebras_1
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