Nuprl Lemma : comp_id_mon_wf
∀[T:Type]. ((<o,Id> monoid on T) ∈ IMonoid)
Proof
Definitions occuring in Statement :
comp_id_mon: (<o,Id> monoid on T),
imon: IMonoid,
uall: ∀[x:A]. B[x],
member: t ∈ T,
universe: Type
Definitions unfolded in proof :
comp_id_mon: (<o,Id> monoid on T),
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
assoc: Assoc(T;op),
infix_ap: x f y,
ident: Ident(T;op;id),
and: P ∧ Q,
tidentity: Id{T}
Lemmas referenced :
mk_imon,
btrue_wf,
compose_wf,
identity_wf,
comp_assoc,
comp_id_r,
comp_id_l
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
isect_memberFormation,
introduction,
cut,
sqequalHypSubstitution,
hypothesis,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
universeEquality,
lemma_by_obid,
isectElimination,
thin,
functionEquality,
hypothesisEquality,
lambdaEquality,
because_Cache,
independent_isectElimination,
isect_memberEquality,
independent_pairFormation,
productElimination,
independent_pairEquality
Latex:
\mforall{}[T:Type]. ((<o,Id> monoid on T) \mmember{} IMonoid)
Date html generated:
2016_05_15-PM-00_17_15
Last ObjectModification:
2015_12_26-PM-11_39_00
Theory : groups_1
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