Nuprl Lemma : itop_unroll_lo
∀[g:IMonoid]. ∀[i,j:ℤ].
∀[E:{i..j-} ⟶ |g|]. (Π(*,e) i ≤ k < j. E[k] = (E[i] * Π(*,e) i + 1 ≤ k < j. E[k]) ∈ |g|) supposing i < j
Proof
Definitions occuring in Statement :
itop: Π(op,id) lb ≤ i < ub. E[i],
imon: IMonoid,
grp_id: e,
grp_op: *,
grp_car: |g|,
int_seg: {i..j-},
less_than: a < b,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
infix_ap: x f y,
so_apply: x[s],
function: x:A ⟶ B[x],
add: n + m,
natural_number: $n,
int: ℤ,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
imon: IMonoid,
prop: ℙ,
all: ∀x:A. B[x],
so_lambda: λ2x.t[x],
int_upper: {i...},
so_apply: x[s],
int_seg: {i..j-},
lelt: i ≤ j < k,
and: P ∧ Q,
guard: {T},
decidable: Dec(P),
or: P ∨ Q,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
false: False,
implies: P ⇒ Q,
not: ¬A,
top: Top,
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
infix_ap: x f y,
squash: ↓T,
true: True,
subtype_rel: A ⊆r B
Lemmas referenced :
int_seg_wf,
grp_car_wf,
less_than_wf,
imon_wf,
int_lt_to_int_upper_uniform,
uall_wf,
equal_wf,
itop_wf,
grp_op_wf,
grp_id_wf,
infix_ap_wf,
int_upper_properties,
decidable__le,
satisfiable-full-omega-tt,
intformnot_wf,
intformle_wf,
itermVar_wf,
int_formula_prop_not_lemma,
int_formula_prop_le_lemma,
int_term_value_var_lemma,
int_formula_prop_wf,
decidable__lt,
intformand_wf,
intformless_wf,
itermAdd_wf,
itermConstant_wf,
int_formula_prop_and_lemma,
int_formula_prop_less_lemma,
int_term_value_add_lemma,
int_term_value_constant_lemma,
lelt_wf,
int_upper_wf,
int_upper_ind_uniform,
int_seg_properties,
squash_wf,
true_wf,
itop_unroll_hi,
iff_weakening_equal,
subtract_wf,
itermSubtract_wf,
int_term_value_subtract_lemma,
decidable__equal_int,
intformeq_wf,
int_formula_prop_eq_lemma,
mon_assoc,
itop_unroll_unit,
itop_unroll_base,
mon_ident
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
sqequalHypSubstitution,
isect_memberEquality,
isectElimination,
thin,
hypothesisEquality,
axiomEquality,
hypothesis,
functionEquality,
extract_by_obid,
setElimination,
rename,
equalityTransitivity,
equalitySymmetry,
intEquality,
because_Cache,
dependent_functionElimination,
lambdaEquality,
applyEquality,
functionExtensionality,
dependent_set_memberEquality,
independent_pairFormation,
addEquality,
natural_numberEquality,
unionElimination,
independent_isectElimination,
dependent_pairFormation,
int_eqEquality,
voidElimination,
voidEquality,
computeAll,
productElimination,
independent_functionElimination,
instantiate,
lambdaFormation,
imageElimination,
universeEquality,
imageMemberEquality,
baseClosed
Latex:
\mforall{}[g:IMonoid]. \mforall{}[i,j:\mBbbZ{}].
\mforall{}[E:\{i..j\msupminus{}\} {}\mrightarrow{} |g|]. (\mPi{}(*,e) i \mleq{} k < j. E[k] = (E[i] * \mPi{}(*,e) i + 1 \mleq{} k < j. E[k]))
supposing i < j
Date html generated:
2017_10_01-AM-08_15_47
Last ObjectModification:
2017_02_28-PM-02_00_44
Theory : groups_1
Home
Index