### Nuprl Lemma : exp-positive

`∀[n,x:ℕ+].  0 < x^n`

Proof

Definitions occuring in Statement :  exp: `i^n` 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` nat_plus: `ℕ+` less_than: `a < b` squash: `↓T` less_than': `less_than'(a;b)` true: `True` and: `P ∧ Q` prop: `ℙ` nat: `ℕ` le: `A ≤ B` subtract: `n - m` false: `False` not: `¬A` implies: `P `` Q` all: `∀x:A. B[x]` decidable: `Dec(P)` or: `P ∨ Q` uimplies: `b supposing a` satisfiable_int_formula: `satisfiable_int_formula(fmla)` exists: `∃x:A. B[x]` top: `Top` guard: `{T}` so_lambda: `λ2x.t[x]` so_apply: `x[s]` subtype_rel: `A ⊆r B`
Lemmas referenced :  nat_plus_subtype_nat member-less_than primrec-wf-nat-plus uall_wf nat_plus_wf int_formula_prop_wf int_formula_prop_less_lemma int_term_value_var_lemma int_term_value_add_lemma int_term_value_constant_lemma int_formula_prop_le_lemma int_formula_prop_not_lemma int_formula_prop_and_lemma intformless_wf itermVar_wf itermAdd_wf itermConstant_wf intformle_wf intformnot_wf intformand_wf satisfiable-full-omega-tt decidable__le exp_wf2 decidable__lt nat_plus_properties le_wf false_wf subtract_wf exp_wf_nat_plus mul_bounds_1b less_than_wf exp_step
Rules used in proof :  sqequalSubstitution sqequalTransitivity computationStep sqequalReflexivity isect_memberFormation introduction cut sqequalRule lemma_by_obid sqequalHypSubstitution isectElimination thin dependent_set_memberEquality natural_numberEquality independent_pairFormation imageMemberEquality hypothesisEquality baseClosed hypothesis setElimination rename lambdaFormation because_Cache dependent_functionElimination addEquality unionElimination independent_isectElimination dependent_pairFormation lambdaEquality int_eqEquality intEquality isect_memberEquality voidElimination voidEquality computeAll equalityTransitivity equalitySymmetry applyEquality independent_functionElimination

Latex:
\mforall{}[n,x:\mBbbN{}\msupplus{}].    0  <  x\^{}n

Date html generated: 2016_05_14-PM-04_26_47
Last ObjectModification: 2016_01_14-PM-11_36_35

Theory : num_thy_1

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