Nuprl Lemma : monoid_hom_op
∀[g,h:GrpSig]. ∀[f:MonHom(g,h)]. ∀[u,v:|g|]. ((f (u * v)) = ((f u) * (f v)) ∈ |h|)
Proof
Definitions occuring in Statement :
monoid_hom: MonHom(M1,M2),
grp_op: *,
grp_car: |g|,
grp_sig: GrpSig,
uall: ∀[x:A]. B[x],
infix_ap: x f y,
apply: f a,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
monoid_hom_p: IsMonHom{M1,M2}(f),
and: P ∧ Q,
fun_thru_2op: FunThru2op(A;B;opa;opb;f)
Lemmas referenced :
grp_car_wf,
monoid_hom_wf,
grp_sig_wf,
monoid_hom_properties
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
hypothesis,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
sqequalRule,
isect_memberEquality,
axiomEquality,
because_Cache,
productElimination
Latex:
\mforall{}[g,h:GrpSig]. \mforall{}[f:MonHom(g,h)]. \mforall{}[u,v:|g|]. ((f (u * v)) = ((f u) * (f v)))
Date html generated:
2016_05_15-PM-00_10_03
Last ObjectModification:
2015_12_26-PM-11_44_50
Theory : groups_1
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