Nuprl Lemma : module_hom_p_wf
∀a:RngSig. ∀m,n:algebra_sig{i:l}(|a|). ∀f:m.car ⟶ n.car. (module_hom_p(a; m; n; f) ∈ ℙ)
Proof
Definitions occuring in Statement :
module_hom_p: module_hom_p(a; m; n; f),
alg_car: a.car,
algebra_sig: algebra_sig{i:l}(A),
prop: ℙ,
all: ∀x:A. B[x],
member: t ∈ T,
function: x:A ⟶ B[x],
rng_car: |r|,
rng_sig: RngSig
Definitions unfolded in proof :
module_hom_p: module_hom_p(a; m; n; f),
all: ∀x:A. B[x],
member: t ∈ T,
uall: ∀[x:A]. B[x],
so_lambda: λ2x.t[x],
so_apply: x[s]
Lemmas referenced :
and_wf,
fun_thru_2op_wf,
alg_car_wf,
rng_car_wf,
alg_plus_wf,
all_wf,
fun_thru_1op_wf,
alg_act_wf,
algebra_sig_wf,
rng_sig_wf
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
lambdaFormation,
cut,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
dependent_functionElimination,
hypothesisEquality,
hypothesis,
lambdaEquality,
applyEquality,
functionEquality
Latex:
\mforall{}a:RngSig. \mforall{}m,n:algebra\_sig\{i:l\}(|a|). \mforall{}f:m.car {}\mrightarrow{} n.car. (module\_hom\_p(a; m; n; f) \mmember{} \mBbbP{})
Date html generated:
2016_05_16-AM-07_27_05
Last ObjectModification:
2015_12_28-PM-05_07_41
Theory : algebras_1
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