Nuprl Lemma : iroot-positive

[n,x:ℕ+].  (1 ≤ iroot(n;x))


Proof




Definitions occuring in Statement :  iroot: iroot(n;x) nat_plus: + uall: [x:A]. B[x] le: A ≤ B natural_number: $n
Definitions unfolded in proof :  uall: [x:A]. B[x] member: t ∈ T subtype_rel: A ⊆B all: x:A. B[x] decidable: Dec(P) or: P ∨ Q and: P ∧ Q le: A ≤ B not: ¬A implies:  Q false: False prop: nat: guard: {T} nat_plus: + ge: i ≥  uimplies: supposing a satisfiable_int_formula: satisfiable_int_formula(fmla) exists: x:A. B[x] top: Top sq_type: SQType(T) squash: T true: True iff: ⇐⇒ Q
Lemmas referenced :  int_formula_prop_less_lemma intformless_wf iff_weakening_equal exp-one true_wf squash_wf less_than_wf int_subtype_base subtype_base_sq int_formula_prop_wf int_formula_prop_le_lemma int_term_value_constant_lemma int_term_value_var_lemma int_formula_prop_eq_lemma int_formula_prop_not_lemma int_formula_prop_and_lemma intformle_wf itermConstant_wf itermVar_wf intformeq_wf intformnot_wf intformand_wf satisfiable-full-omega-tt decidable__equal_int nat_plus_properties le_wf nat_properties nat_plus_subtype_nat nat_plus_wf less_than'_wf iroot_wf decidable__le iroot-property
Rules used in proof :  sqequalSubstitution sqequalTransitivity computationStep sqequalReflexivity isect_memberFormation introduction cut lemma_by_obid sqequalHypSubstitution isectElimination thin hypothesisEquality applyEquality because_Cache hypothesis sqequalRule dependent_functionElimination natural_numberEquality unionElimination productElimination independent_pairEquality lambdaEquality axiomEquality equalityTransitivity equalitySymmetry isect_memberEquality voidElimination setElimination rename setEquality intEquality independent_isectElimination dependent_pairFormation int_eqEquality voidEquality independent_pairFormation computeAll instantiate cumulativity independent_functionElimination imageElimination imageMemberEquality baseClosed universeEquality

Latex:
\mforall{}[n,x:\mBbbN{}\msupplus{}].    (1  \mleq{}  iroot(n;x))



Date html generated: 2019_06_20-PM-02_34_51
Last ObjectModification: 2019_03_19-AM-10_49_36

Theory : num_thy_1


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