Nuprl Lemma : int_op_wf
∀[g:Group{i}]. ∀[a:ℤ]. ∀[e:|g|]. (a x(*;e;~) e ∈ |g|)
Proof
Definitions occuring in Statement :
int_op: i x(op;id;inv) e,
grp: Group{i},
grp_inv: ~,
grp_id: e,
grp_op: *,
grp_car: |g|,
uall: ∀[x:A]. B[x],
member: t ∈ T,
int: ℤ
Definitions unfolded in proof :
int_op: i x(op;id;inv) e,
uall: ∀[x:A]. B[x],
member: t ∈ T,
grp: Group{i},
mon: Mon,
all: ∀x:A. B[x],
implies: P ⇒ Q,
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
subtype_rel: A ⊆r B,
uiff: uiff(P;Q),
and: P ∧ Q,
uimplies: b supposing a,
ifthenelse: if b then t else f fi ,
bfalse: ff,
guard: {T},
prop: ℙ,
imon: IMonoid,
nat: ℕ,
decidable: Dec(P),
or: P ∨ Q,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
false: False,
not: ¬A,
top: Top
Lemmas referenced :
grp_car_wf,
grp_wf,
le_int_wf,
bool_wf,
uiff_transitivity,
equal-wf-base,
int_subtype_base,
assert_wf,
le_wf,
eqtt_to_assert,
assert_of_le_int,
lt_int_wf,
less_than_wf,
bnot_wf,
eqff_to_assert,
assert_functionality_wrt_uiff,
bnot_of_le_int,
assert_of_lt_int,
equal_wf,
nat_op_wf,
grp_sig_wf,
monoid_p_wf,
grp_op_wf,
grp_id_wf,
inverse_wf,
grp_inv_wf,
decidable__le,
satisfiable-full-omega-tt,
intformand_wf,
intformnot_wf,
intformle_wf,
itermConstant_wf,
itermMinus_wf,
itermVar_wf,
intformless_wf,
int_formula_prop_and_lemma,
int_formula_prop_not_lemma,
int_formula_prop_le_lemma,
int_term_value_constant_lemma,
int_term_value_minus_lemma,
int_term_value_var_lemma,
int_formula_prop_less_lemma,
int_formula_prop_wf
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
isect_memberFormation,
introduction,
cut,
sqequalHypSubstitution,
hypothesis,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
extract_by_obid,
isectElimination,
thin,
setElimination,
rename,
hypothesisEquality,
isect_memberEquality,
because_Cache,
intEquality,
natural_numberEquality,
lambdaFormation,
unionElimination,
equalityElimination,
baseApply,
closedConclusion,
baseClosed,
applyEquality,
independent_functionElimination,
productElimination,
independent_isectElimination,
dependent_functionElimination,
lambdaEquality,
setEquality,
cumulativity,
dependent_set_memberEquality,
minusEquality,
dependent_pairFormation,
int_eqEquality,
voidElimination,
voidEquality,
independent_pairFormation,
computeAll
Latex:
\mforall{}[g:Group\{i\}]. \mforall{}[a:\mBbbZ{}]. \mforall{}[e:|g|]. (a x(*;e;\msim{}) e \mmember{} |g|)
Date html generated:
2017_10_01-AM-08_16_09
Last ObjectModification:
2017_02_28-PM-02_00_56
Theory : groups_1
Home
Index