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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