Nuprl Lemma : mon_reduce_functionality_wrt_permr
∀g:IAbMonoid. ∀xs,ys:|g| List. ((xs ≡(|g|) ys) ⇒ ((Π xs) = (Π ys) ∈ |g|))
Proof
Definitions occuring in Statement :
mon_reduce: mon_reduce,
permr: as ≡(T) bs,
list: T List,
all: ∀x:A. B[x],
implies: P ⇒ Q,
equal: s = t ∈ T,
iabmonoid: IAbMonoid,
grp_car: |g|
Definitions unfolded in proof :
all: ∀x:A. B[x],
implies: P ⇒ Q,
member: t ∈ T,
uall: ∀[x:A]. B[x],
iabmonoid: IAbMonoid,
imon: IMonoid,
prop: ℙ,
permr: as ≡(T) bs,
cand: A c∧ B,
exists: ∃x:A. B[x],
true: True,
squash: ↓T,
subtype_rel: A ⊆r B,
uimplies: b supposing a,
guard: {T},
iff: P ⇐⇒ Q,
and: P ∧ Q,
rev_implies: P ⇐ Q,
so_lambda: λ2x.t[x],
int_seg: {i..j-},
lelt: i ≤ j < k,
decidable: Dec(P),
or: P ∨ Q,
not: ¬A,
satisfiable_int_formula: satisfiable_int_formula(fmla),
false: False,
top: Top,
so_apply: x[s],
sym_grp: Sym(n),
perm: Perm(T),
ge: i ≥ j ,
nat: ℕ,
less_than: a < b
Lemmas referenced :
permr_wf,
grp_car_wf,
list_wf,
iabmonoid_wf,
equal_wf,
squash_wf,
true_wf,
istype-universe,
mon_reduce_eq_itop,
subtype_rel_self,
iff_weakening_equal,
mon_itop_wf,
select_wf,
int_seg_properties,
decidable__le,
full-omega-unsat,
intformand_wf,
intformnot_wf,
intformle_wf,
itermConstant_wf,
itermVar_wf,
istype-int,
int_formula_prop_and_lemma,
istype-void,
int_formula_prop_not_lemma,
int_formula_prop_le_lemma,
int_term_value_constant_lemma,
int_term_value_var_lemma,
int_formula_prop_wf,
decidable__lt,
intformless_wf,
int_formula_prop_less_lemma,
int_seg_wf,
length_wf,
intformeq_wf,
int_formula_prop_eq_lemma,
le_wf,
less_than_wf,
imon_wf,
length_wf_nat,
perm_f_wf,
non_neg_length,
nat_properties,
mon_itop_perm_invar
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation_alt,
cut,
hypothesis,
universeIsType,
introduction,
extract_by_obid,
sqequalHypSubstitution,
dependent_functionElimination,
thin,
isectElimination,
setElimination,
rename,
because_Cache,
hypothesisEquality,
inhabitedIsType,
productElimination,
natural_numberEquality,
applyEquality,
lambdaEquality_alt,
imageElimination,
equalityTransitivity,
equalitySymmetry,
universeEquality,
sqequalRule,
imageMemberEquality,
baseClosed,
instantiate,
independent_isectElimination,
independent_functionElimination,
unionElimination,
approximateComputation,
dependent_pairFormation_alt,
int_eqEquality,
isect_memberEquality_alt,
voidElimination,
independent_pairFormation,
dependent_set_memberEquality_alt,
productIsType,
functionIsType,
applyLambdaEquality
Latex:
\mforall{}g:IAbMonoid. \mforall{}xs,ys:|g| List. ((xs \mequiv{}(|g|) ys) {}\mRightarrow{} ((\mPi{} xs) = (\mPi{} ys)))
Date html generated:
2019_10_16-PM-01_02_26
Last ObjectModification:
2018_10_08-AM-11_42_17
Theory : list_2
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