### Nuprl Lemma : exp-2-3-fact

`∀n:ℕ. ((2 ≤ n) `` 2 * 2^n < 3^n)`

Proof

Definitions occuring in Statement :  exp: `i^n` nat: `ℕ` less_than: `a < b` le: `A ≤ B` all: `∀x:A. B[x]` implies: `P `` Q` multiply: `n * m` natural_number: `\$n`
Definitions unfolded in proof :  all: `∀x:A. B[x]` uall: `∀[x:A]. B[x]` member: `t ∈ T` nat: `ℕ` implies: `P `` Q` false: `False` ge: `i ≥ j ` uimplies: `b supposing a` satisfiable_int_formula: `satisfiable_int_formula(fmla)` exists: `∃x:A. B[x]` not: `¬A` top: `Top` and: `P ∧ Q` prop: `ℙ` le: `A ≤ B` less_than': `less_than'(a;b)` true: `True` less_than: `a < b` squash: `↓T` exp: `i^n` primrec: `primrec(n;b;c)` decidable: `Dec(P)` or: `P ∨ Q` nat_plus: `ℕ+` sq_type: `SQType(T)` guard: `{T}` subtract: `n - m`
Lemmas referenced :  int_term_value_mul_lemma itermMultiply_wf nat_plus_properties exp_wf_nat_plus decidable__lt int_formula_prop_eq_lemma intformeq_wf int_subtype_base subtype_base_sq decidable__equal_int exp_step nat_wf int_term_value_subtract_lemma int_formula_prop_not_lemma itermSubtract_wf intformnot_wf subtract_wf decidable__le le_wf exp_wf2 member-less_than less_than_wf ge_wf int_formula_prop_wf int_formula_prop_less_lemma int_term_value_var_lemma int_term_value_constant_lemma int_formula_prop_le_lemma int_formula_prop_and_lemma intformless_wf itermVar_wf itermConstant_wf intformle_wf intformand_wf satisfiable-full-omega-tt nat_properties
Rules used in proof :  sqequalSubstitution sqequalTransitivity computationStep sqequalReflexivity lambdaFormation cut lemma_by_obid sqequalHypSubstitution isectElimination thin hypothesisEquality hypothesis setElimination rename introduction intWeakElimination natural_numberEquality independent_isectElimination dependent_pairFormation lambdaEquality int_eqEquality intEquality dependent_functionElimination isect_memberEquality voidElimination voidEquality sqequalRule independent_pairFormation computeAll independent_functionElimination multiplyEquality productElimination because_Cache imageElimination unionElimination dependent_set_memberEquality instantiate cumulativity imageMemberEquality baseClosed equalityTransitivity equalitySymmetry applyEquality setEquality

Latex:
\mforall{}n:\mBbbN{}.  ((2  \mleq{}  n)  {}\mRightarrow{}  2  *  2\^{}n  <  3\^{}n)

Date html generated: 2016_05_18-AM-09_35_50
Last ObjectModification: 2016_01_17-AM-02_47_09

Theory : reals

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