Nuprl Lemma : divides_subtract

x,y,z:ℤ.  ((x y)  (x z)  (x (y z)))


Proof




Definitions occuring in Statement :  divides: a all: x:A. B[x] implies:  Q subtract: m int:
Definitions unfolded in proof :  divides: a all: x:A. B[x] implies:  Q exists: x:A. B[x] member: t ∈ T uall: [x:A]. B[x] decidable: Dec(P) or: P ∨ Q 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_subtract_lemma int_formula_prop_eq_lemma int_formula_prop_not_lemma int_formula_prop_and_lemma itermMultiply_wf itermVar_wf itermSubtract_wf intformeq_wf intformnot_wf intformand_wf satisfiable-full-omega-tt decidable__equal_int subtract_wf
Rules used in proof :  sqequalSubstitution sqequalRule sqequalReflexivity sqequalTransitivity computationStep lambdaFormation sqequalHypSubstitution productElimination thin dependent_pairFormation cut lemma_by_obid isectElimination hypothesisEquality hypothesis dependent_functionElimination because_Cache unionElimination natural_numberEquality independent_isectElimination lambdaEquality int_eqEquality intEquality isect_memberEquality voidElimination voidEquality independent_pairFormation computeAll multiplyEquality

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



Date html generated: 2016_05_14-PM-04_16_28
Last ObjectModification: 2016_01_14-PM-11_42_28

Theory : num_thy_1


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