Nuprl Lemma : mon_nat_op_id
∀[g:IMonoid]. ∀[n:ℕ]. ((n ⋅ e) = e ∈ |g|)
Proof
Definitions occuring in Statement :
mon_nat_op: n ⋅ e,
imon: IMonoid,
grp_id: e,
grp_car: |g|,
nat: ℕ,
uall: ∀[x:A]. B[x],
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
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,
all: ∀x:A. B[x],
top: Top,
and: P ∧ Q,
prop: ℙ,
squash: ↓T,
imon: IMonoid,
true: True,
subtype_rel: A ⊆r B,
guard: {T},
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
decidable: Dec(P),
or: P ∨ Q,
mon_nat_op: n ⋅ e,
nat_op: n x(op;id) e,
so_lambda: λ2x.t[x],
so_apply: x[s]
Lemmas referenced :
nat_wf,
imon_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,
equal_wf,
squash_wf,
true_wf,
grp_car_wf,
mon_nat_op_zero,
grp_id_wf,
iff_weakening_equal,
decidable__le,
subtract_wf,
intformnot_wf,
itermSubtract_wf,
int_formula_prop_not_lemma,
int_term_value_subtract_lemma,
itop_unroll_hi,
int_seg_wf,
mon_ident,
itop_wf,
grp_op_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
extract_by_obid,
hypothesis,
sqequalRule,
sqequalHypSubstitution,
isect_memberEquality,
isectElimination,
thin,
hypothesisEquality,
axiomEquality,
because_Cache,
setElimination,
rename,
intWeakElimination,
lambdaFormation,
natural_numberEquality,
independent_isectElimination,
dependent_pairFormation,
lambdaEquality,
int_eqEquality,
intEquality,
dependent_functionElimination,
voidElimination,
voidEquality,
independent_pairFormation,
computeAll,
independent_functionElimination,
applyEquality,
imageElimination,
equalityTransitivity,
equalitySymmetry,
universeEquality,
imageMemberEquality,
baseClosed,
productElimination,
unionElimination
Latex:
\mforall{}[g:IMonoid]. \mforall{}[n:\mBbbN{}]. ((n \mcdot{} e) = e)
Date html generated:
2017_10_01-AM-08_16_31
Last ObjectModification:
2017_02_28-PM-02_01_08
Theory : groups_1
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