Nuprl Lemma : mon_for_of_id
∀g:IAbMonoid. ∀A:Type. ∀as:A List. ((For{g} x ∈ as. e) = e ∈ |g|)
Proof
Definitions occuring in Statement :
mon_for: For{g} x ∈ as. f[x],
list: T List,
all: ∀x:A. B[x],
universe: Type,
equal: s = t ∈ T,
iabmonoid: IAbMonoid,
grp_id: e,
grp_car: |g|
Definitions unfolded in proof :
all: ∀x:A. B[x],
uall: ∀[x:A]. B[x],
member: t ∈ T,
so_lambda: λ2x.t[x],
iabmonoid: IAbMonoid,
imon: IMonoid,
so_apply: x[s],
implies: P ⇒ Q,
top: Top,
squash: ↓T,
prop: ℙ,
true: True,
subtype_rel: A ⊆r B,
uimplies: b supposing a,
guard: {T},
iff: P ⇐⇒ Q,
and: P ∧ Q,
rev_implies: P ⇐ Q,
infix_ap: x f y
Lemmas referenced :
list_induction,
equal_wf,
grp_car_wf,
mon_for_wf,
grp_id_wf,
list_wf,
mon_for_nil_lemma,
mon_for_cons_lemma,
squash_wf,
true_wf,
abmonoid_comm,
iff_weakening_equal,
grp_op_wf,
mon_ident,
iabmonoid_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
cut,
thin,
introduction,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
hypothesisEquality,
sqequalRule,
lambdaEquality,
setElimination,
rename,
hypothesis,
dependent_functionElimination,
cumulativity,
because_Cache,
independent_functionElimination,
isect_memberEquality,
voidElimination,
voidEquality,
applyEquality,
imageElimination,
equalityTransitivity,
equalitySymmetry,
equalityUniverse,
levelHypothesis,
natural_numberEquality,
imageMemberEquality,
baseClosed,
universeEquality,
independent_isectElimination,
productElimination
Latex:
\mforall{}g:IAbMonoid. \mforall{}A:Type. \mforall{}as:A List. ((For\{g\} x \mmember{} as. e) = e)
Date html generated:
2017_10_01-AM-09_55_27
Last ObjectModification:
2017_03_03-PM-00_50_25
Theory : list_2
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