Nuprl Lemma : mon_properties
∀[g:Mon]. IsMonoid(|g|;*;e)
Proof
Definitions occuring in Statement :
mon: Mon,
grp_id: e,
grp_op: *,
grp_car: |g|,
monoid_p: IsMonoid(T;op;id),
uall: ∀[x:A]. B[x]
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
monoid_p: IsMonoid(T;op;id),
and: P ∧ Q,
assoc: Assoc(T;op),
mon: Mon,
ident: Ident(T;op;id),
prop: ℙ,
implies: P ⇒ Q,
sq_stable: SqStable(P),
squash: ↓T
Lemmas referenced :
squash_wf,
sq_stable__ident,
sq_stable__assoc,
grp_id_wf,
ident_wf,
grp_op_wf,
assoc_wf,
sq_stable__and,
mon_wf,
grp_car_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
sqequalHypSubstitution,
productElimination,
thin,
independent_pairEquality,
isect_memberEquality,
isectElimination,
hypothesisEquality,
axiomEquality,
hypothesis,
lemma_by_obid,
setElimination,
rename,
independent_functionElimination,
lambdaFormation,
because_Cache,
lambdaEquality,
dependent_functionElimination,
imageMemberEquality,
baseClosed,
imageElimination
Latex:
\mforall{}[g:Mon]. IsMonoid(|g|;*;e)
Date html generated:
2016_05_15-PM-00_07_00
Last ObjectModification:
2016_01_15-PM-11_06_27
Theory : groups_1
Home
Index