### Nuprl Lemma : exp-ge-1

`∀[b:{2...}]. ∀[j:ℕ+].  1 < b^j`

Proof

Definitions occuring in Statement :  exp: `i^n` int_upper: `{i...}` nat_plus: `ℕ+` less_than: `a < b` uall: `∀[x:A]. B[x]` natural_number: `\$n`
Definitions unfolded in proof :  uall: `∀[x:A]. B[x]` member: `t ∈ T` all: `∀x:A. B[x]` nat_plus: `ℕ+` implies: `P `` Q` prop: `ℙ` nat: `ℕ` guard: `{T}` int_upper: `{i...}` decidable: `Dec(P)` or: `P ∨ Q` uimplies: `b supposing a` satisfiable_int_formula: `satisfiable_int_formula(fmla)` exists: `∃x:A. B[x]` false: `False` not: `¬A` top: `Top` and: `P ∧ Q` so_lambda: `λ2x.t[x]` subtype_rel: `A ⊆r B` so_apply: `x[s]` le: `A ≤ B` less_than': `less_than'(a;b)` iff: `P `⇐⇒` Q` rev_implies: `P `` Q` uiff: `uiff(P;Q)` true: `True` squash: `↓T` sq_type: `SQType(T)` subtract: `n - m` less_than: `a < b`
Lemmas referenced :  nat_plus_properties less_than_wf exp_wf2 int_upper_properties decidable__le satisfiable-full-omega-tt intformand_wf intformnot_wf intformle_wf itermConstant_wf itermVar_wf intformless_wf int_formula_prop_and_lemma int_formula_prop_not_lemma int_formula_prop_le_lemma int_term_value_constant_lemma int_term_value_var_lemma int_formula_prop_less_lemma int_formula_prop_wf le_wf primrec-wf-nat-plus nat_plus_wf member-less_than nat_plus_subtype_nat int_upper_wf subtype_base_sq set_subtype_base int_subtype_base decidable__lt false_wf exp_wf_nat_plus not-lt-2 add_functionality_wrt_le add-commutes zero-add le-add-cancel equal_wf squash_wf true_wf exp1 iff_weakening_equal exp_step less-iff-le condition-implies-le minus-add minus-one-mul minus-one-mul-top add-associates add-zero add-subtract-cancel mul_preserves_lt itermMultiply_wf int_term_value_mul_lemma
Rules used in proof :  sqequalSubstitution sqequalTransitivity computationStep sqequalReflexivity isect_memberFormation introduction cut thin lambdaFormation rename extract_by_obid sqequalHypSubstitution isectElimination hypothesisEquality hypothesis setElimination natural_numberEquality dependent_set_memberEquality dependent_functionElimination unionElimination independent_isectElimination dependent_pairFormation lambdaEquality int_eqEquality intEquality isect_memberEquality voidElimination voidEquality sqequalRule independent_pairFormation computeAll because_Cache applyEquality instantiate cumulativity productElimination independent_functionElimination equalityTransitivity equalitySymmetry applyLambdaEquality imageElimination universeEquality imageMemberEquality baseClosed addEquality minusEquality multiplyEquality

Latex:
\mforall{}[b:\{2...\}].  \mforall{}[j:\mBbbN{}\msupplus{}].    1  <  b\^{}j

Date html generated: 2017_04_14-AM-09_22_31
Last ObjectModification: 2017_02_27-PM-03_58_00

Theory : int_2

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