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: uall: [x:A]. B[x] equal: t ∈ T
Definitions unfolded in proof :  uall: [x:A]. B[x] member: t ∈ T nat: implies:  Q false: False ge: i ≥  uimplies: 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: squash: T imon: IMonoid true: True subtype_rel: A ⊆B guard: {T} iff: ⇐⇒ Q rev_implies:  Q decidable: Dec(P) or: P ∨ Q mon_nat_op: n ⋅ e nat_op: 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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