Nuprl Lemma : monoid_hom_p_wf
∀[a,b:GrpSig]. ∀[f:|a| ⟶ |b|].  (IsMonHom{a,b}(f) ∈ ℙ)
Proof
Definitions occuring in Statement : 
monoid_hom_p: IsMonHom{M1,M2}(f)
, 
grp_car: |g|
, 
grp_sig: GrpSig
, 
uall: ∀[x:A]. B[x]
, 
prop: ℙ
, 
member: t ∈ T
, 
function: x:A ⟶ B[x]
Definitions unfolded in proof : 
monoid_hom_p: IsMonHom{M1,M2}(f)
, 
uall: ∀[x:A]. B[x]
, 
member: t ∈ T
Lemmas referenced : 
and_wf, 
fun_thru_2op_wf, 
grp_car_wf, 
grp_op_wf, 
equal_wf, 
grp_id_wf, 
grp_sig_wf
Rules used in proof : 
sqequalSubstitution, 
sqequalRule, 
sqequalReflexivity, 
sqequalTransitivity, 
computationStep, 
isect_memberFormation, 
introduction, 
cut, 
lemma_by_obid, 
sqequalHypSubstitution, 
isectElimination, 
thin, 
hypothesisEquality, 
hypothesis, 
applyEquality, 
axiomEquality, 
equalityTransitivity, 
equalitySymmetry, 
functionEquality, 
isect_memberEquality, 
because_Cache
Latex:
\mforall{}[a,b:GrpSig].  \mforall{}[f:|a|  {}\mrightarrow{}  |b|].    (IsMonHom\{a,b\}(f)  \mmember{}  \mBbbP{})
Date html generated:
2016_05_15-PM-00_09_46
Last ObjectModification:
2015_12_26-PM-11_45_13
Theory : groups_1
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