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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