Nuprl Lemma : mon_when_is_hom
∀[g:IMonoid]. ∀[b:𝔹].  IsMonHom{g,g}(λp:|g|. when b. p)
Proof
Definitions occuring in Statement : 
mon_when: when b. p
, 
monoid_hom_p: IsMonHom{M1,M2}(f)
, 
imon: IMonoid
, 
grp_car: |g|
, 
tlambda: λx:T. b[x]
, 
bool: 𝔹
, 
uall: ∀[x:A]. B[x]
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)
, 
tlambda: λx:T. b[x]
, 
imon: IMonoid
Lemmas referenced : 
mon_when_thru_op, 
grp_car_wf, 
mon_when_of_id, 
bool_wf, 
imon_wf
Rules used in proof : 
sqequalSubstitution, 
sqequalTransitivity, 
computationStep, 
sqequalReflexivity, 
isect_memberFormation, 
introduction, 
cut, 
independent_pairFormation, 
sqequalRule, 
lemma_by_obid, 
sqequalHypSubstitution, 
isectElimination, 
thin, 
hypothesisEquality, 
hypothesis, 
setElimination, 
rename, 
isect_memberEquality, 
axiomEquality, 
because_Cache, 
productElimination, 
independent_pairEquality
Latex:
\mforall{}[g:IMonoid].  \mforall{}[b:\mBbbB{}].    IsMonHom\{g,g\}(\mlambda{}p:|g|.  when  b.  p)
Date html generated:
2016_05_15-PM-00_18_57
Last ObjectModification:
2015_12_26-PM-11_37_38
Theory : groups_1
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