Nuprl Lemma : rnexp0
∀[k:ℕ+]. (r0^k = r0)
Proof
Definitions occuring in Statement :
rnexp: x^k1,
req: x = y,
int-to-real: r(n),
nat_plus: ℕ+,
uall: ∀[x:A]. B[x],
natural_number: $n
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
subtype_rel: A ⊆r B,
implies: P ⇒ Q,
uiff: uiff(P;Q),
and: P ∧ Q,
uimplies: b supposing a,
squash: ↓T,
prop: ℙ,
true: True,
guard: {T},
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
rev_uimplies: rev_uimplies(P;Q)
Lemmas referenced :
req_witness,
rnexp_wf,
nat_plus_subtype_nat,
int-to-real_wf,
nat_plus_wf,
exp_wf2,
req-int,
equal_wf,
squash_wf,
true_wf,
exp-zero,
iff_weakening_equal,
req_functionality,
rnexp-int,
req_weakening
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
applyEquality,
hypothesis,
sqequalRule,
natural_numberEquality,
independent_functionElimination,
because_Cache,
productElimination,
independent_isectElimination,
lambdaEquality,
imageElimination,
equalityTransitivity,
equalitySymmetry,
universeEquality,
intEquality,
imageMemberEquality,
baseClosed
Latex:
\mforall{}[k:\mBbbN{}\msupplus{}]. (r0\^{}k = r0)
Date html generated:
2017_10_03-AM-08_22_00
Last ObjectModification:
2017_07_28-AM-07_22_05
Theory : reals
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