Nuprl Lemma : strong-continuity2-no-inner-squash-cantor5

F:(ℕ ⟶ 𝔹) ⟶ ℤ
  ⇃(∃M:n:ℕ ⟶ (ℕn ⟶ 𝔹) ⟶ (ℤ?)
     ∀f:ℕ ⟶ 𝔹((∃n:ℕ((M f) (inl (F f)) ∈ (ℤ?))) ∧ (∀n:ℕ(M f) (inl (F f)) ∈ (ℤ?) supposing ↑isl(M f))))


Proof




Definitions occuring in Statement :  quotient: x,y:A//B[x; y] int_seg: {i..j-} nat: assert: b isl: isl(x) bool: 𝔹 uimplies: supposing a all: x:A. B[x] exists: x:A. B[x] and: P ∧ Q true: True unit: Unit apply: a function: x:A ⟶ B[x] inl: inl x union: left right natural_number: $n int: equal: t ∈ T
Definitions unfolded in proof :  so_apply: x[s] so_lambda: λ2x.t[x] prop: exists: x:A. B[x] implies:  Q member: t ∈ T uall: [x:A]. B[x] all: x:A. B[x]
Lemmas referenced :  equal_wf all_wf biject-int-nat surject-nat-bool subtype_rel_self nat_wf bool_wf strong-continuity2-half-squash-surject-biject
Rules used in proof :  functionExtensionality applyEquality sqequalRule lambdaEquality dependent_pairFormation functionEquality hypothesisEquality dependent_functionElimination because_Cache independent_functionElimination intEquality hypothesis thin isectElimination sqequalHypSubstitution extract_by_obid introduction cut lambdaFormation sqequalReflexivity computationStep sqequalTransitivity sqequalSubstitution

Latex:
\mforall{}F:(\mBbbN{}  {}\mrightarrow{}  \mBbbB{})  {}\mrightarrow{}  \mBbbZ{}
    \00D9(\mexists{}M:n:\mBbbN{}  {}\mrightarrow{}  (\mBbbN{}n  {}\mrightarrow{}  \mBbbB{})  {}\mrightarrow{}  (\mBbbZ{}?)
          \mforall{}f:\mBbbN{}  {}\mrightarrow{}  \mBbbB{}
              ((\mexists{}n:\mBbbN{}.  ((M  n  f)  =  (inl  (F  f))))  \mwedge{}  (\mforall{}n:\mBbbN{}.  (M  n  f)  =  (inl  (F  f))  supposing  \muparrow{}isl(M  n  f))))



Date html generated: 2017_09_29-PM-06_06_59
Last ObjectModification: 2017_09_04-AM-11_21_22

Theory : continuity


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