### Nuprl Lemma : mul-imin

`∀[n:ℕ]. ∀[a,b:ℤ].  ((n * imin(a;b)) = imin(n * a;n * b) ∈ ℤ)`

Proof

Definitions occuring in Statement :  imin: `imin(a;b)` nat: `ℕ` uall: `∀[x:A]. B[x]` multiply: `n * m` int: `ℤ` equal: `s = t ∈ T`
Definitions unfolded in proof :  uall: `∀[x:A]. B[x]` member: `t ∈ T` squash: `↓T` prop: `ℙ` nat: `ℕ` true: `True` subtype_rel: `A ⊆r B` uimplies: `b supposing a` guard: `{T}` iff: `P `⇐⇒` Q` and: `P ∧ Q` rev_implies: `P `` Q` implies: `P `` Q` all: `∀x:A. B[x]` bool: `𝔹` unit: `Unit` it: `⋅` btrue: `tt` uiff: `uiff(P;Q)` ifthenelse: `if b then t else f fi ` bfalse: `ff` exists: `∃x:A. B[x]` or: `P ∨ Q` sq_type: `SQType(T)` bnot: `¬bb` assert: `↑b` false: `False` not: `¬A` ge: `i ≥ j ` decidable: `Dec(P)` satisfiable_int_formula: `satisfiable_int_formula(fmla)` top: `Top`
Lemmas referenced :  equal_wf squash_wf true_wf imin_unfold iff_weakening_equal le_int_wf bool_wf eqtt_to_assert assert_of_le_int eqff_to_assert bool_cases_sqequal subtype_base_sq bool_subtype_base assert-bnot le_wf nat_wf mul_preserves_le nat_properties decidable__le satisfiable-full-omega-tt intformand_wf intformnot_wf intformle_wf itermVar_wf int_formula_prop_and_lemma int_formula_prop_not_lemma int_formula_prop_le_lemma int_term_value_var_lemma int_formula_prop_wf decidable__equal_int intformeq_wf itermMultiply_wf int_formula_prop_eq_lemma int_term_value_mul_lemma
Rules used in proof :  sqequalSubstitution sqequalTransitivity computationStep sqequalReflexivity isect_memberFormation introduction cut applyEquality thin lambdaEquality sqequalHypSubstitution imageElimination extract_by_obid isectElimination hypothesisEquality equalityTransitivity hypothesis equalitySymmetry universeEquality because_Cache multiplyEquality setElimination rename natural_numberEquality sqequalRule imageMemberEquality baseClosed independent_isectElimination productElimination independent_functionElimination lambdaFormation unionElimination equalityElimination dependent_pairFormation promote_hyp dependent_functionElimination instantiate voidElimination cumulativity intEquality isect_memberEquality axiomEquality int_eqEquality voidEquality independent_pairFormation computeAll

Latex:
\mforall{}[n:\mBbbN{}].  \mforall{}[a,b:\mBbbZ{}].    ((n  *  imin(a;b))  =  imin(n  *  a;n  *  b))

Date html generated: 2017_04_14-AM-09_13_41
Last ObjectModification: 2017_02_27-PM-03_51_09

Theory : int_2

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