Nuprl Lemma : equal-iff-diff-zero

x,y:ℤ.  uiff(x y ∈ ℤ;(x y) 0 ∈ ℤ)


Proof




Definitions occuring in Statement :  uiff: uiff(P;Q) all: x:A. B[x] subtract: m natural_number: $n int: equal: t ∈ T
Definitions unfolded in proof :  all: x:A. B[x] uiff: uiff(P;Q) and: P ∧ Q uimplies: supposing a member: t ∈ T decidable: Dec(P) or: P ∨ Q uall: [x:A]. B[x] satisfiable_int_formula: satisfiable_int_formula(fmla) exists: x:A. B[x] false: False implies:  Q not: ¬A top: Top prop:
Lemmas referenced :  subtract_wf equal_wf int_formula_prop_wf int_term_value_constant_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 itermConstant_wf itermVar_wf itermSubtract_wf intformeq_wf intformnot_wf intformand_wf satisfiable-full-omega-tt decidable__equal_int
Rules used in proof :  sqequalSubstitution sqequalTransitivity computationStep sqequalReflexivity lambdaFormation independent_pairFormation isect_memberFormation 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

Latex:
\mforall{}x,y:\mBbbZ{}.    uiff(x  =  y;(x  -  y)  =  0)



Date html generated: 2016_05_14-AM-07_20_29
Last ObjectModification: 2016_01_07-PM-03_59_53

Theory : int_2


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