Nuprl Lemma : efficient-exp-ext
∀i:ℤ. ∀n:ℕ. (∃j:{ℤ| (j = i^n ∈ ℤ)})
Proof
Definitions occuring in Statement :
exp: i^n,
nat: ℕ,
all: ∀x:A. B[x],
sq_exists: ∃x:{A| B[x]},
int: ℤ,
equal: s = t ∈ T
Definitions unfolded in proof :
squash: ↓T,
or: P ∨ Q,
guard: {T},
prop: ℙ,
has-value: (a)↓,
implies: P ⇒ Q,
all: ∀x:A. B[x],
and: P ∧ Q,
strict4: strict4(F),
uimplies: b supposing a,
so_apply: x[s],
top: Top,
so_lambda: λ2x.t[x],
so_apply: x[s1;s2;s3;s4],
so_lambda: so_lambda(x,y,z,w.t[x; y; z; w]),
uall: ∀[x:A]. B[x],
decidable__int_equal,
decidable__equal_int,
so_apply: x[s1;s2],
genrec: genrec,
natrec: natrec,
efficient-exp,
member: t ∈ T
Lemmas referenced :
decidable__int_equal,
decidable__equal_int,
efficient-exp
Rules used in proof :
inlFormation,
exceptionSqequal,
imageElimination,
imageMemberEquality,
because_Cache,
inrFormation,
decideExceptionCases,
closedConclusion,
baseApply,
independent_functionElimination,
dependent_functionElimination,
equalityEquality,
sqleReflexivity,
unionElimination,
unionEquality,
equalitySymmetry,
equalityTransitivity,
hypothesisEquality,
callbyvalueDecide,
lambdaFormation,
independent_pairFormation,
independent_isectElimination,
voidEquality,
voidElimination,
isect_memberEquality,
baseClosed,
isectElimination,
sqequalHypSubstitution,
thin,
sqequalRule,
hypothesis,
extract_by_obid,
instantiate,
cut,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution,
introduction
Latex:
\mforall{}i:\mBbbZ{}. \mforall{}n:\mBbbN{}. (\mexists{}j:\{\mBbbZ{}| (j = i\^{}n)\})
Date html generated:
2016_07_08-PM-05_04_41
Last ObjectModification:
2016_07_05-PM-02_43_35
Theory : general
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