### Nuprl Lemma : absval_square

`∀[x:ℤ]. (|x * x| = (x * x) ∈ ℤ)`

Proof

Definitions occuring in Statement :  absval: `|i|` uall: `∀[x:A]. B[x]` multiply: `n * m` int: `ℤ` equal: `s = t ∈ T`
Definitions unfolded in proof :  uall: `∀[x:A]. B[x]` all: `∀x:A. B[x]` member: `t ∈ T` implies: `P `` Q` bool: `𝔹` unit: `Unit` it: `⋅` btrue: `tt` uiff: `uiff(P;Q)` and: `P ∧ Q` uimplies: `b supposing a` less_than: `a < b` less_than': `less_than'(a;b)` top: `Top` true: `True` squash: `↓T` not: `¬A` false: `False` prop: `ℙ` bfalse: `ff` exists: `∃x:A. B[x]` or: `P ∨ Q` sq_type: `SQType(T)` guard: `{T}` bnot: `¬bb` ifthenelse: `if b then t else f fi ` assert: `↑b` satisfiable_int_formula: `satisfiable_int_formula(fmla)`
Lemmas referenced :  square_non_neg absval_unfold lt_int_wf bool_wf eqtt_to_assert assert_of_lt_int top_wf less_than_wf eqff_to_assert equal_wf bool_cases_sqequal subtype_base_sq bool_subtype_base assert-bnot satisfiable-full-omega-tt intformand_wf intformle_wf itermConstant_wf itermMultiply_wf itermVar_wf intformnot_wf intformless_wf int_formula_prop_and_lemma int_formula_prop_le_lemma int_term_value_constant_lemma int_term_value_mul_lemma int_term_value_var_lemma int_formula_prop_not_lemma int_formula_prop_less_lemma int_formula_prop_wf
Rules used in proof :  cut introduction extract_by_obid sqequalSubstitution sqequalTransitivity computationStep sqequalReflexivity isect_memberFormation hypothesis sqequalHypSubstitution dependent_functionElimination thin hypothesisEquality sqequalRule isectElimination multiplyEquality minusEquality natural_numberEquality lambdaFormation unionElimination equalityElimination equalityTransitivity equalitySymmetry productElimination independent_isectElimination because_Cache lessCases sqequalAxiom isect_memberEquality independent_pairFormation voidElimination voidEquality imageMemberEquality baseClosed imageElimination independent_functionElimination dependent_pairFormation promote_hyp instantiate cumulativity lambdaEquality int_eqEquality intEquality computeAll

Latex:
\mforall{}[x:\mBbbZ{}].  (|x  *  x|  =  (x  *  x))

Date html generated: 2017_04_14-AM-09_15_35
Last ObjectModification: 2017_02_27-PM-03_53_07

Theory : int_2

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