### Nuprl Lemma : strong-continuity2-no-inner-squash-unique-bool

`∀F:(ℕ ⟶ 𝔹) ⟶ ℕ`
`  ⇃(∃M:n:ℕ ⟶ (ℕn ⟶ 𝔹) ⟶ (ℕ?)`
`     ∀f:ℕ ⟶ 𝔹. ∃n:ℕ. (((M n f) = (inl (F f)) ∈ (ℕ?)) ∧ (∀m:ℕ. ((↑isl(M m f)) `` (m = n ∈ ℕ)))))`

Proof

Definitions occuring in Statement :  quotient: `x,y:A//B[x; y]` int_seg: `{i..j-}` nat: `ℕ` assert: `↑b` isl: `isl(x)` bool: `𝔹` all: `∀x:A. B[x]` exists: `∃x:A. B[x]` implies: `P `` Q` and: `P ∧ Q` true: `True` unit: `Unit` apply: `f a` function: `x:A ⟶ B[x]` inl: `inl x` union: `left + right` natural_number: `\$n` equal: `s = t ∈ T`
Definitions unfolded in proof :  implies: `P `` Q` member: `t ∈ T` uall: `∀[x:A]. B[x]` strong-continuity3: `strong-continuity3(T;F)` all: `∀x:A. B[x]`
Lemmas referenced :  nat_wf surject-nat-bool bool_wf strong-continuity3-half-squash-surject
Rules used in proof :  functionEquality hypothesisEquality dependent_functionElimination independent_functionElimination hypothesis thin isectElimination sqequalHypSubstitution extract_by_obid introduction cut lambdaFormation sqequalReflexivity computationStep sqequalTransitivity sqequalSubstitution

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

Date html generated: 2017_09_29-PM-06_05_39
Last ObjectModification: 2017_09_04-PM-00_13_19

Theory : continuity

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