Nuprl Lemma : mon_when_of_id
∀[g:IMonoid]. ∀[b:𝔹].  ((when b. e) = e ∈ |g|)
Proof
Definitions occuring in Statement : 
mon_when: when b. p
, 
imon: IMonoid
, 
grp_id: e
, 
grp_car: |g|
, 
bool: 𝔹
, 
uall: ∀[x:A]. B[x]
, 
equal: s = t ∈ T
Definitions unfolded in proof : 
uall: ∀[x:A]. B[x]
, 
member: t ∈ T
, 
mon_when: when b. p
, 
bool: 𝔹
, 
unit: Unit
, 
it: ⋅
, 
btrue: tt
, 
ifthenelse: if b then t else f fi 
, 
imon: IMonoid
, 
bfalse: ff
Lemmas referenced : 
grp_id_wf, 
bool_wf, 
imon_wf
Rules used in proof : 
sqequalSubstitution, 
sqequalTransitivity, 
computationStep, 
sqequalReflexivity, 
isect_memberFormation, 
introduction, 
cut, 
sqequalHypSubstitution, 
unionElimination, 
thin, 
equalityElimination, 
sqequalRule, 
lemma_by_obid, 
isectElimination, 
setElimination, 
rename, 
hypothesisEquality, 
hypothesis, 
because_Cache, 
isect_memberEquality, 
axiomEquality
Latex:
\mforall{}[g:IMonoid].  \mforall{}[b:\mBbbB{}].    ((when  b.  e)  =  e)
Date html generated:
2016_05_15-PM-00_18_41
Last ObjectModification:
2015_12_26-PM-11_38_14
Theory : groups_1
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