Nuprl Lemma : is-power_wf
∀[n:ℕ+]. ∀[x:ℕ]. (is-power(n;x) ∈ 𝔹)
Proof
Definitions occuring in Statement :
is-power: is-power(n;x),
nat_plus: ℕ+,
nat: ℕ,
bool: 𝔹,
uall: ∀[x:A]. B[x],
member: t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
is-power: is-power(n;x),
has-value: (a)↓,
uimplies: b supposing a,
nat: ℕ,
so_lambda: λ2x.t[x],
so_apply: x[s],
subtype_rel: A ⊆r B
Lemmas referenced :
value-type-has-value,
nat_wf,
set-value-type,
le_wf,
istype-int,
int-value-type,
iroot_wf,
eq_int_wf,
fastexp_wf,
nat_plus_subtype_nat,
istype-nat,
nat_plus_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
Error :isect_memberFormation_alt,
introduction,
cut,
sqequalRule,
callbyvalueReduce,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesis,
independent_isectElimination,
intEquality,
Error :lambdaEquality_alt,
natural_numberEquality,
hypothesisEquality,
applyEquality,
setElimination,
rename,
because_Cache,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
Error :isect_memberEquality_alt,
Error :isectIsTypeImplies,
Error :inhabitedIsType,
Error :universeIsType
Latex:
\mforall{}[n:\mBbbN{}\msupplus{}]. \mforall{}[x:\mBbbN{}]. (is-power(n;x) \mmember{} \mBbbB{})
Date html generated:
2019_06_20-PM-02_34_14
Last ObjectModification:
2019_03_19-AM-10_49_24
Theory : num_thy_1
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