Nuprl Lemma : mon_nat_op_one
∀[g:IMonoid]. ∀[e:|g|]. ((1 ⋅ e) = e ∈ |g|)
Proof
Definitions occuring in Statement :
mon_nat_op: n ⋅ e,
imon: IMonoid,
grp_car: |g|,
uall: ∀[x:A]. B[x],
natural_number: $n,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
imon: IMonoid,
squash: ↓T,
prop: ℙ,
nat_plus: ℕ+,
less_than: a < b,
less_than': less_than'(a;b),
true: True,
and: P ∧ Q,
subtype_rel: A ⊆r B,
uimplies: b supposing a,
guard: {T},
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
implies: P ⇒ Q,
subtract: n - m,
top: Top,
infix_ap: x f y
Lemmas referenced :
grp_car_wf,
imon_wf,
equal_wf,
squash_wf,
true_wf,
mon_nat_op_unroll,
less_than_wf,
iff_weakening_equal,
add-commutes,
grp_op_wf,
mon_nat_op_zero,
mon_ident
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
hypothesis,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
setElimination,
rename,
hypothesisEquality,
sqequalRule,
isect_memberEquality,
axiomEquality,
because_Cache,
applyEquality,
lambdaEquality,
imageElimination,
equalityTransitivity,
equalitySymmetry,
universeEquality,
dependent_set_memberEquality,
natural_numberEquality,
independent_pairFormation,
imageMemberEquality,
baseClosed,
independent_isectElimination,
productElimination,
independent_functionElimination,
voidElimination,
voidEquality
Latex:
\mforall{}[g:IMonoid]. \mforall{}[e:|g|]. ((1 \mcdot{} e) = e)
Date html generated:
2017_10_01-AM-08_16_27
Last ObjectModification:
2017_02_28-PM-02_01_00
Theory : groups_1
Home
Index