Nuprl Lemma : itop_wf
∀[A:Type]. ∀[op:A ⟶ A ⟶ A]. ∀[id:A]. ∀[p,q:ℤ]. ∀[E:{p..q-} ⟶ A]. (Π(op,id) p ≤ i < q. E[i] ∈ A)
Proof
Definitions occuring in Statement :
itop: Π(op,id) lb ≤ i < ub. E[i],
int_seg: {i..j-},
uall: ∀[x:A]. B[x],
so_apply: x[s],
member: t ∈ T,
function: x:A ⟶ B[x],
int: ℤ,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
all: ∀x:A. B[x],
int_upper: {i...},
nat: ℕ,
implies: P ⇒ Q,
false: False,
ge: i ≥ j ,
uimplies: b supposing a,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
not: ¬A,
top: Top,
and: P ∧ Q,
prop: ℙ,
guard: {T},
int_seg: {i..j-},
lelt: i ≤ j < k,
decidable: Dec(P),
or: P ∨ Q,
subtype_rel: A ⊆r B,
le: A ≤ B,
less_than': less_than'(a;b),
less_than: a < b,
itop: Π(op,id) lb ≤ i < ub. E[i],
ycomb: Y,
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
uiff: uiff(P;Q),
ifthenelse: if b then t else f fi ,
bfalse: ff,
infix_ap: x f y,
so_lambda: λ2x.t[x],
so_apply: x[s]
Lemmas referenced :
int_seg_wf,
int_upper_wf,
nat_properties,
satisfiable-full-omega-tt,
intformand_wf,
intformle_wf,
itermConstant_wf,
itermVar_wf,
intformless_wf,
int_formula_prop_and_lemma,
int_formula_prop_le_lemma,
int_term_value_constant_lemma,
int_term_value_var_lemma,
int_formula_prop_less_lemma,
int_formula_prop_wf,
ge_wf,
less_than_wf,
le_wf,
subtract_wf,
int_seg_properties,
decidable__le,
intformnot_wf,
itermSubtract_wf,
int_formula_prop_not_lemma,
int_term_value_subtract_lemma,
decidable__equal_int,
int_seg_subtype,
false_wf,
intformeq_wf,
int_formula_prop_eq_lemma,
int_upper_properties,
decidable__lt,
lelt_wf,
itermAdd_wf,
int_term_value_add_lemma,
nat_wf,
lt_int_wf,
bool_wf,
uiff_transitivity,
equal-wf-T-base,
assert_wf,
eqtt_to_assert,
assert_of_lt_int,
le_int_wf,
bnot_wf,
eqff_to_assert,
assert_functionality_wrt_uiff,
bnot_of_lt_int,
assert_of_le_int,
equal_wf,
equal-wf-base,
int_subtype_base,
infix_ap_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
sqequalHypSubstitution,
isect_memberEquality,
isectElimination,
thin,
hypothesisEquality,
axiomEquality,
equalityTransitivity,
hypothesis,
equalitySymmetry,
functionEquality,
extract_by_obid,
cumulativity,
intEquality,
because_Cache,
universeEquality,
lambdaFormation,
setElimination,
rename,
intWeakElimination,
natural_numberEquality,
independent_isectElimination,
dependent_pairFormation,
lambdaEquality,
int_eqEquality,
dependent_functionElimination,
voidElimination,
voidEquality,
independent_pairFormation,
computeAll,
independent_functionElimination,
productElimination,
unionElimination,
applyEquality,
applyLambdaEquality,
hypothesis_subsumption,
dependent_set_memberEquality,
addEquality,
equalityElimination,
baseClosed,
functionExtensionality,
baseApply,
closedConclusion
Latex:
\mforall{}[A:Type]. \mforall{}[op:A {}\mrightarrow{} A {}\mrightarrow{} A]. \mforall{}[id:A]. \mforall{}[p,q:\mBbbZ{}]. \mforall{}[E:\{p..q\msupminus{}\} {}\mrightarrow{} A]. (\mPi{}(op,id) p \mleq{} i < q. E[i] \mmember{} A)
Date html generated:
2017_10_01-AM-08_15_30
Last ObjectModification:
2017_02_28-PM-02_00_35
Theory : groups_1
Home
Index