Nuprl Lemma : genfact-unbounded-ext

f:ℕ+ ⟶ ℤ. ∀b:ℕ+. ∀N:ℤ.  (∃n:ℕ [(N ≤ genfact(n;b;m.f[m]))]) supposing ∀m:ℕ+1 < f[m]


Proof




Definitions occuring in Statement :  genfact: genfact(n;b;m.f[m]) nat_plus: + nat: less_than: a < b uimplies: supposing a so_apply: x[s] le: A ≤ B all: x:A. B[x] sq_exists: x:A [B[x]] function: x:A ⟶ B[x] natural_number: $n int:
Definitions unfolded in proof :  member: t ∈ T so_apply: x[s] genrec-ap: genrec-ap genfact-unbounded uniform-comp-nat-induction decidable__le decidable__and decidable__not decidable__less_than' decidable__implies decidable__false any: any x 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 uimplies: supposing a
Lemmas referenced :  genfact-unbounded lifting-strict-decide istype-void strict4-decide lifting-strict-less uniform-comp-nat-induction decidable__le decidable__and decidable__not decidable__less_than' decidable__implies decidable__false
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

Latex:
\mforall{}f:\mBbbN{}\msupplus{}  {}\mrightarrow{}  \mBbbZ{}.  \mforall{}b:\mBbbN{}\msupplus{}.  \mforall{}N:\mBbbZ{}.    (\mexists{}n:\mBbbN{}  [(N  \mleq{}  genfact(n;b;m.f[m]))])  supposing  \mforall{}m:\mBbbN{}\msupplus{}.  1  <  f[m]



Date html generated: 2019_06_20-PM-02_25_54
Last ObjectModification: 2019_03_26-AM-07_43_38

Theory : num_thy_1


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