Nuprl Lemma : sq_stable__alg_hom_p
∀a:RngSig. ∀m,n:algebra_sig{i:l}(|a|). ∀f:m.car ⟶ n.car. SqStable(alg_hom_p(a; m; n; f))
Proof
Definitions occuring in Statement :
alg_hom_p: alg_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 :
alg_hom_p: alg_hom_p(a; m; n; f),
all: ∀x:A. B[x],
uall: ∀[x:A]. B[x],
member: t ∈ T,
prop: ℙ,
implies: P ⇒ Q
Lemmas referenced :
sq_stable__and,
module_hom_p_wf,
and_wf,
fun_thru_2op_wf,
alg_car_wf,
rng_car_wf,
alg_times_wf,
equal_wf,
alg_one_wf,
sq_stable__module_hom_p,
sq_stable__fun_thru_2op,
sq_stable__equal,
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,
isect_memberEquality,
applyEquality,
independent_functionElimination,
because_Cache,
functionEquality
Latex:
\mforall{}a:RngSig. \mforall{}m,n:algebra\_sig\{i:l\}(|a|). \mforall{}f:m.car {}\mrightarrow{} n.car. SqStable(alg\_hom\_p(a; m; n; f))
Date html generated:
2016_05_16-AM-07_28_02
Last ObjectModification:
2015_12_28-PM-05_07_36
Theory : algebras_1
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