Nuprl Lemma : nat_op_zero
∀[g:IMonoid]. ∀[e:|g|]. (0 x(*;e) e = e ∈ |g|)
Proof
Definitions occuring in Statement :
nat_op: n x(op;id) e,
imon: IMonoid,
grp_id: e,
grp_op: *,
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,
nat_op: n x(op;id) e,
squash: ↓T,
prop: ℙ,
uimplies: b supposing a,
so_lambda: λ2x.t[x],
so_apply: x[s],
true: True,
subtype_rel: A ⊆r B,
guard: {T},
iff: P ⇐⇒ Q,
and: P ∧ Q,
rev_implies: P ⇐ Q,
implies: P ⇒ Q
Lemmas referenced :
grp_car_wf,
imon_wf,
equal_wf,
squash_wf,
true_wf,
itop_unroll_base,
int_seg_wf,
grp_id_wf,
iff_weakening_equal
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,
natural_numberEquality,
independent_isectElimination,
imageMemberEquality,
baseClosed,
productElimination,
independent_functionElimination
Latex:
\mforall{}[g:IMonoid]. \mforall{}[e:|g|]. (0 x(*;e) e = e)
Date html generated:
2017_10_01-AM-08_15_59
Last ObjectModification:
2017_02_28-PM-02_00_52
Theory : groups_1
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