### Nuprl Lemma : square_non_neg

`∀x:ℤ. (0 ≤ (x * x))`

Proof

Definitions occuring in Statement :  le: `A ≤ B` all: `∀x:A. B[x]` multiply: `n * m` natural_number: `\$n` int: `ℤ`
Definitions unfolded in proof :  all: `∀x:A. B[x]` uall: `∀[x:A]. B[x]` member: `t ∈ T` subtype_rel: `A ⊆r B` nat: `ℕ` uimplies: `b supposing a` prop: `ℙ` squash: `↓T` decidable: `Dec(P)` or: `P ∨ Q` false: `False` le: `A ≤ B` and: `P ∧ Q` uiff: `uiff(P;Q)` satisfiable_int_formula: `satisfiable_int_formula(fmla)` exists: `∃x:A. B[x]` implies: `P `` Q` not: `¬A` top: `Top` true: `True` bool: `𝔹` unit: `Unit` it: `⋅` btrue: `tt` less_than: `a < b` less_than': `less_than'(a;b)` bfalse: `ff` sq_type: `SQType(T)` guard: `{T}` bnot: `¬bb` ifthenelse: `if b then t else f fi ` assert: `↑b`
Lemmas referenced :  mul_preserves_le absval_wf nat_wf absval-non-neg le_wf squash_wf true_wf decidable__equal_int multiply-is-int-iff satisfiable-full-omega-tt intformnot_wf intformeq_wf itermConstant_wf itermMultiply_wf itermVar_wf int_formula_prop_not_lemma int_formula_prop_eq_lemma int_term_value_constant_lemma int_term_value_mul_lemma int_term_value_var_lemma int_formula_prop_wf false_wf 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 itermMinus_wf int_term_value_minus_lemma absval_unfold
Rules used in proof :  sqequalSubstitution sqequalTransitivity computationStep sqequalReflexivity lambdaFormation cut introduction extract_by_obid sqequalHypSubstitution isectElimination thin natural_numberEquality hypothesisEquality hypothesis applyEquality lambdaEquality setElimination rename sqequalRule independent_isectElimination because_Cache hyp_replacement equalitySymmetry imageElimination equalityTransitivity intEquality dependent_functionElimination unionElimination pointwiseFunctionality promote_hyp productElimination baseApply closedConclusion baseClosed dependent_pairFormation int_eqEquality isect_memberEquality voidElimination voidEquality computeAll imageMemberEquality minusEquality equalityElimination lessCases isect_memberFormation sqequalAxiom independent_pairFormation independent_functionElimination multiplyEquality instantiate cumulativity

Latex:
\mforall{}x:\mBbbZ{}.  (0  \mleq{}  (x  *  x))

Date html generated: 2017_04_14-AM-09_15_33
Last ObjectModification: 2017_02_27-PM-03_53_21

Theory : int_2

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