Nuprl Lemma : mon_when_wf
∀[g:IMonoid]. ∀[b:𝔹]. ∀[p:|g|]. (when b. p ∈ |g|)
Proof
Definitions occuring in Statement :
mon_when: when b. p,
imon: IMonoid,
grp_car: |g|,
bool: 𝔹,
uall: ∀[x:A]. B[x],
member: t ∈ T
Definitions unfolded in proof :
mon_when: when b. p,
uall: ∀[x:A]. B[x],
member: t ∈ T,
imon: IMonoid
Lemmas referenced :
ifthenelse_wf,
grp_car_wf,
grp_id_wf,
bool_wf,
imon_wf
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
isect_memberFormation,
introduction,
cut,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
setElimination,
rename,
hypothesis,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
isect_memberEquality,
because_Cache
Latex:
\mforall{}[g:IMonoid]. \mforall{}[b:\mBbbB{}]. \mforall{}[p:|g|]. (when b. p \mmember{} |g|)
Date html generated:
2016_05_15-PM-00_18_27
Last ObjectModification:
2015_12_26-PM-11_38_25
Theory : groups_1
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