Nuprl Lemma : mdivides_refl
∀g:IAbMonoid. ∀a:|g|. (a | a)
Proof
Definitions occuring in Statement :
mdivides: b | a,
all: ∀x:A. B[x],
iabmonoid: IAbMonoid,
grp_car: |g|
Definitions unfolded in proof :
all: ∀x:A. B[x],
member: t ∈ T,
uall: ∀[x:A]. B[x],
iabmonoid: IAbMonoid,
imon: IMonoid,
mdivides: b | a,
exists: ∃x:A. B[x],
prop: ℙ,
infix_ap: x f y,
squash: ↓T,
and: P ∧ Q,
true: True,
subtype_rel: A ⊆r B,
uimplies: b supposing a,
guard: {T},
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
implies: P ⇒ Q
Lemmas referenced :
grp_car_wf,
iabmonoid_wf,
grp_id_wf,
equal_wf,
grp_op_wf,
squash_wf,
true_wf,
mon_ident,
iff_weakening_equal
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
setElimination,
rename,
hypothesisEquality,
hypothesis,
dependent_pairFormation,
because_Cache,
applyEquality,
lambdaEquality,
imageElimination,
equalityTransitivity,
equalitySymmetry,
universeEquality,
productElimination,
natural_numberEquality,
sqequalRule,
imageMemberEquality,
baseClosed,
independent_isectElimination,
independent_functionElimination
Latex:
\mforall{}g:IAbMonoid. \mforall{}a:|g|. (a | a)
Date html generated:
2017_10_01-AM-09_57_47
Last ObjectModification:
2017_03_03-PM-00_58_39
Theory : factor_1
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