Nuprl Lemma : log_wf
∀[b:{i:ℤ| 1 < i} ]. ∀[x:ℤ]. (log(b;x) ∈ ℕ)
Proof
Definitions occuring in Statement :
log: log(b;n),
nat: ℕ,
less_than: a < b,
uall: ∀[x:A]. B[x],
member: t ∈ T,
set: {x:A| B[x]} ,
natural_number: $n,
int: ℤ
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
log: log(b;n),
so_lambda: λ2x.t[x],
so_apply: x[s],
uimplies: b supposing a,
all: ∀x:A. B[x],
nat_plus: ℕ+,
less_than: a < b,
squash: ↓T,
less_than': less_than'(a;b),
true: True,
and: P ∧ Q,
subtype_rel: A ⊆r B
Lemmas referenced :
genfact-inv_wf,
nat_plus_wf,
istype-less_than,
istype-int
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
Error :isect_memberFormation_alt,
introduction,
cut,
setElimination,
thin,
rename,
sqequalRule,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
Error :lambdaEquality_alt,
hypothesisEquality,
Error :universeIsType,
hypothesis,
independent_isectElimination,
Error :lambdaFormation_alt,
because_Cache,
Error :dependent_set_memberEquality_alt,
closedConclusion,
natural_numberEquality,
independent_pairFormation,
imageMemberEquality,
baseClosed,
applyEquality,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
Error :isect_memberEquality_alt,
Error :isectIsTypeImplies,
Error :inhabitedIsType,
Error :setIsType
Latex:
\mforall{}[b:\{i:\mBbbZ{}| 1 < i\} ]. \mforall{}[x:\mBbbZ{}]. (log(b;x) \mmember{} \mBbbN{})
Date html generated:
2019_06_20-PM-02_32_29
Last ObjectModification:
2019_03_06-AM-10_52_46
Theory : num_thy_1
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