Nuprl Lemma : itop_unroll_empty
∀[g:IMonoid]. ∀[i,j:ℤ]. ∀[E:{i..j-} ⟶ |g|]. (Π(*,e) i ≤ k < j. E[k] = e ∈ |g|) supposing j ≤ i
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-},
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
so_apply: x[s],
le: A ≤ B,
function: x:A ⟶ B[x],
int: ℤ,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
int_seg: {i..j-},
lelt: i ≤ j < k,
and: P ∧ Q,
not: ¬A,
implies: P ⇒ Q,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
false: False,
all: ∀x:A. B[x],
top: Top,
prop: ℙ,
itop: Π(op,id) lb ≤ i < ub. E[i],
ycomb: Y,
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
subtype_rel: A ⊆r B,
uiff: uiff(P;Q),
ifthenelse: if b then t else f fi ,
bfalse: ff,
guard: {T},
imon: IMonoid
Lemmas referenced :
int_seg_wf,
int_seg_properties,
full-omega-unsat,
intformand_wf,
intformless_wf,
itermVar_wf,
intformle_wf,
istype-int,
int_formula_prop_and_lemma,
istype-void,
int_formula_prop_less_lemma,
int_term_value_var_lemma,
int_formula_prop_le_lemma,
int_formula_prop_wf,
istype-le,
imon_wf,
lt_int_wf,
uiff_transitivity,
equal-wf-base,
bool_wf,
int_subtype_base,
assert_wf,
less_than_wf,
eqtt_to_assert,
assert_of_lt_int,
le_int_wf,
le_wf,
bnot_wf,
eqff_to_assert,
assert_functionality_wrt_uiff,
bnot_of_lt_int,
assert_of_le_int,
grp_id_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation_alt,
introduction,
cut,
hypothesis,
functionIsType,
universeIsType,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
setElimination,
rename,
productElimination,
natural_numberEquality,
independent_isectElimination,
approximateComputation,
independent_functionElimination,
dependent_pairFormation_alt,
lambdaEquality_alt,
int_eqEquality,
dependent_functionElimination,
isect_memberEquality_alt,
voidElimination,
sqequalRule,
independent_pairFormation,
axiomEquality,
isectIsTypeImplies,
inhabitedIsType,
lambdaFormation_alt,
unionElimination,
equalityElimination,
baseApply,
closedConclusion,
baseClosed,
applyEquality,
because_Cache,
equalityIstype,
equalityTransitivity,
equalitySymmetry
Latex:
\mforall{}[g:IMonoid]. \mforall{}[i,j:\mBbbZ{}]. \mforall{}[E:\{i..j\msupminus{}\} {}\mrightarrow{} |g|]. (\mPi{}(*,e) i \mleq{} k < j. E[k] = e) supposing j \mleq{} i
Date html generated:
2019_10_15-AM-10_32_54
Last ObjectModification:
2019_08_13-PM-05_08_21
Theory : groups_1
Home
Index