Nuprl Lemma : qexp_wf
∀[r:ℚ]. ∀[n:ℕ]. (r ↑ n ∈ ℚ)
Proof
Definitions occuring in Statement :
qexp: r ↑ n,
rationals: ℚ,
nat: ℕ,
uall: ∀[x:A]. B[x],
member: t ∈ T
Definitions unfolded in proof :
qexp: r ↑ n,
uall: ∀[x:A]. B[x],
member: t ∈ T,
has-value: (a)↓,
uimplies: b supposing a,
nat: ℕ,
so_lambda: λ2x.t[x],
so_apply: x[s],
nat_plus: ℕ+,
subtype_rel: A ⊆r B,
int_nzero: ℤ-o,
prop: ℙ,
all: ∀x:A. B[x],
implies: P ⇒ Q,
nequal: a ≠ b ∈ T ,
not: ¬A,
false: False,
guard: {T},
ge: i ≥ j ,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
top: Top,
and: P ∧ Q
Lemmas referenced :
equal_wf,
int_formula_prop_wf,
int_formula_prop_less_lemma,
int_term_value_constant_lemma,
int_term_value_var_lemma,
int_formula_prop_eq_lemma,
int_formula_prop_and_lemma,
intformless_wf,
itermConstant_wf,
itermVar_wf,
intformeq_wf,
intformand_wf,
satisfiable-full-omega-tt,
nat_properties,
nat_plus_properties,
nequal_wf,
less_than_wf,
subtype_rel_sets,
exp_wf3,
exp-fastexp,
rationals_wf,
mk-rational_wf,
qrep_wf,
int-value-type,
le_wf,
set-value-type,
nat_wf,
value-type-has-value
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
isect_memberFormation,
introduction,
cut,
callbyvalueReduce,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesis,
independent_isectElimination,
intEquality,
lambdaEquality,
natural_numberEquality,
hypothesisEquality,
spreadEquality,
because_Cache,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
isect_memberEquality,
setElimination,
rename,
applyEquality,
setEquality,
lambdaFormation,
dependent_pairFormation,
int_eqEquality,
dependent_functionElimination,
voidElimination,
voidEquality,
independent_pairFormation,
computeAll,
independent_functionElimination
Latex:
\mforall{}[r:\mBbbQ{}]. \mforall{}[n:\mBbbN{}]. (r \muparrow{} n \mmember{} \mBbbQ{})
Date html generated:
2016_05_15-PM-11_06_36
Last ObjectModification:
2016_01_16-PM-09_27_30
Theory : rationals
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