Nuprl Lemma : fast-fib-ext
∀n:ℕ. (∃m:{ℕ| (m = fib(n) ∈ ℕ)})
Proof
Definitions occuring in Statement :
fib: fib(n),
nat: ℕ,
all: ∀x:A. B[x],
sq_exists: ∃x:{A| B[x]},
equal: s = t ∈ T
Definitions unfolded in proof :
member: t ∈ T,
fast-fib,
natrec: natrec,
genrec: genrec,
so_apply: x[s1;s2],
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,
guard: {T},
or: P ∨ Q,
squash: ↓T,
subtract: n - m,
genrec-ap: genrec-ap
Lemmas referenced :
fast-fib,
lifting-strict-int_eq,
top_wf,
equal_wf,
has-value_wf_base,
base_wf,
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,
isectElimination,
baseClosed,
isect_memberEquality,
voidElimination,
voidEquality,
independent_isectElimination,
independent_pairFormation,
lambdaFormation,
callbyvalueDecide,
hypothesisEquality,
equalityTransitivity,
equalitySymmetry,
unionEquality,
unionElimination,
sqleReflexivity,
dependent_functionElimination,
independent_functionElimination,
baseApply,
closedConclusion,
decideExceptionCases,
inrFormation,
because_Cache,
imageMemberEquality,
imageElimination,
exceptionSqequal,
inlFormation
Latex:
\mforall{}n:\mBbbN{}. (\mexists{}m:\{\mBbbN{}| (m = fib(n))\})
Date html generated:
2017_04_17-AM-09_44_18
Last ObjectModification:
2017_02_27-PM-05_38_28
Theory : num_thy_1
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