### Nuprl Lemma : minus_thru_mul

[a,b:ℤ].  ((-(a b)) ((-a) b) ∈ ℤ)

Proof

Definitions occuring in Statement :  uall: [x:A]. B[x] multiply: m minus: -n int: equal: t ∈ T
Definitions unfolded in proof :  uall: [x:A]. B[x] member: t ∈ T all: x:A. B[x] decidable: Dec(P) or: P ∨ Q uimplies: supposing a satisfiable_int_formula: satisfiable_int_formula(fmla) exists: x:A. B[x] false: False implies:  Q not: ¬A top: Top prop:
Lemmas referenced :  int_formula_prop_wf int_term_value_var_lemma int_term_value_mul_lemma int_term_value_minus_lemma int_formula_prop_eq_lemma int_formula_prop_not_lemma itermVar_wf itermMultiply_wf itermMinus_wf intformeq_wf intformnot_wf satisfiable-full-omega-tt decidable__equal_int
Rules used in proof :  sqequalSubstitution sqequalTransitivity computationStep sqequalReflexivity isect_memberFormation introduction cut lemma_by_obid sqequalHypSubstitution dependent_functionElimination thin because_Cache hypothesis unionElimination isectElimination natural_numberEquality independent_isectElimination dependent_pairFormation lambdaEquality int_eqEquality hypothesisEquality intEquality isect_memberEquality voidElimination voidEquality sqequalRule computeAll axiomEquality

Latex:
\mforall{}[a,b:\mBbbZ{}].    ((-(a  *  b))  =  ((-a)  *  b))

Date html generated: 2016_05_14-AM-07_20_27
Last ObjectModification: 2016_01_07-PM-03_59_49

Theory : int_2

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