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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