Nuprl Lemma : sq_stable__module_hom_p
∀A:RngSig. ∀M,N:algebra_sig{i:l}(|A|). ∀f:M.car ⟶ N.car. SqStable(module_hom_p(A; M; N; f))
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),
sq_stable: SqStable(P),
all: ∀x:A. B[x],
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),
fun_thru_1op: fun_thru_1op(A;B;opa;opb;f),
fun_thru_2op: FunThru2op(A;B;opa;opb;f),
all: ∀x:A. B[x],
uall: ∀[x:A]. B[x],
member: t ∈ T,
so_lambda: λ2x.t[x],
infix_ap: x f y,
so_apply: x[s],
prop: ℙ,
implies: P ⇒ Q,
sq_stable: SqStable(P)
Lemmas referenced :
sq_stable__and,
uall_wf,
alg_car_wf,
rng_car_wf,
equal_wf,
alg_plus_wf,
all_wf,
alg_act_wf,
infix_ap_wf,
sq_stable__uall,
sq_stable__equal,
squash_wf,
sq_stable__all,
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,
isect_memberEquality,
because_Cache,
independent_functionElimination,
isect_memberFormation,
introduction,
axiomEquality,
functionEquality
Latex:
\mforall{}A:RngSig. \mforall{}M,N:algebra\_sig\{i:l\}(|A|). \mforall{}f:M.car {}\mrightarrow{} N.car. SqStable(module\_hom\_p(A; M; N; f))
Date html generated:
2016_05_16-AM-07_27_07
Last ObjectModification:
2015_12_28-PM-05_08_02
Theory : algebras_1
Home
Index