Nuprl Lemma : less-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 :
member: t ∈ T,
remainder: n rem m,
divide: n ÷ m,
so_apply: x[s1;s2],
natrec: natrec,
genrec: genrec,
less-efficient-exp,
decidable__equal_int,
decidable__int_equal,
uall: ∀[x:A]. B[x],
so_lambda: so_lambda(x,y,z,w.t[x; y; z; w]),
so_apply: x[s1;s2;s3;s4],
so_lambda: λ2x.t[x],
top: Top,
so_apply: x[s],
uimplies: b supposing a,
strict4: strict4(F),
and: P ∧ Q,
all: ∀x:A. B[x],
implies: P ⇒ Q,
has-value: (a)↓,
prop: ℙ,
or: P ∨ Q,
squash: ↓T,
so_lambda: λ2x y.t[x; y]
Lemmas referenced :
less-efficient-exp,
lifting-strict-int_eq,
istype-void,
strict4-decide,
lifting-strict-spread,
value-type-has-value,
int-value-type,
has-value_wf_base,
istype-base,
is-exception_wf,
decidable__equal_int,
decidable__int_equal
Rules used in proof :
introduction,
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
cut,
instantiate,
extract_by_obid,
hypothesis,
sqequalRule,
thin,
sqequalHypSubstitution,
equalityTransitivity,
equalitySymmetry,
isectElimination,
baseClosed,
Error :isect_memberEquality_alt,
voidElimination,
independent_isectElimination,
independent_pairFormation,
Error :lambdaFormation_alt,
callbyvalueIntEq,
baseApply,
closedConclusion,
hypothesisEquality,
productElimination,
intEquality,
Error :universeIsType,
int_eqExceptionCases,
Error :inrFormation_alt,
imageMemberEquality,
imageElimination,
exceptionSqequal,
Error :inlFormation_alt,
Error :inhabitedIsType,
sqequalSqle,
divergentSqle,
callbyvalueSpread,
sqleReflexivity,
Error :equalityIstype,
dependent_functionElimination,
independent_functionElimination,
spreadExceptionCases,
axiomSqleEquality
Latex:
\mforall{}i:\mBbbZ{}. \mforall{}n:\mBbbN{}. (\mexists{}j:\mBbbZ{} [(j = i\^{}n)])
Date html generated:
2019_06_20-PM-02_31_45
Last ObjectModification:
2019_03_10-PM-02_37_37
Theory : num_thy_1
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