Nuprl Lemma : divides-add

x,y,z:ℤ.  ((z x)  (z y)  (z (x y)))


Proof




Definitions occuring in Statement :  divides: a all: x:A. B[x] implies:  Q add: m int:
Definitions unfolded in proof :  divides: a all: x:A. B[x] implies:  Q exists: x:A. B[x] member: t ∈ T decidable: Dec(P) or: P ∨ Q uall: [x:A]. B[x] uimplies: supposing a satisfiable_int_formula: satisfiable_int_formula(fmla) false: False not: ¬A top: Top and: P ∧ Q prop: so_lambda: λ2x.t[x] so_apply: x[s]
Lemmas referenced :  exists_wf equal_wf int_formula_prop_wf int_term_value_mul_lemma int_term_value_var_lemma int_term_value_add_lemma int_formula_prop_eq_lemma int_formula_prop_not_lemma int_formula_prop_and_lemma itermMultiply_wf itermVar_wf itermAdd_wf intformeq_wf intformnot_wf intformand_wf satisfiable-full-omega-tt decidable__equal_int
Rules used in proof :  sqequalSubstitution sqequalRule sqequalReflexivity sqequalTransitivity computationStep lambdaFormation sqequalHypSubstitution productElimination thin dependent_pairFormation addEquality hypothesisEquality cut lemma_by_obid dependent_functionElimination because_Cache hypothesis unionElimination isectElimination natural_numberEquality independent_isectElimination lambdaEquality int_eqEquality intEquality isect_memberEquality voidElimination voidEquality independent_pairFormation computeAll multiplyEquality

Latex:
\mforall{}x,y,z:\mBbbZ{}.    ((z  |  x)  {}\mRightarrow{}  (z  |  y)  {}\mRightarrow{}  (z  |  (x  +  y)))



Date html generated: 2016_05_14-PM-09_23_34
Last ObjectModification: 2016_01_14-PM-11_34_21

Theory : num_thy_1


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