Nuprl Rule : Continuity
This rule proved as lemma rule_continuity_true3 in file continuity/continuity_rule_gen.v
at https://github.com/vrahli/NuprlInCoq
H ⊢ ↓∃n:ℕ. ∀[g:ℤ ⟶ ℤ]. (F f) = (F g) ∈ ℤ supposing ∀[i:ℤ]. (f i) = (g i) ∈ ℤ supposing |i| < n
BY Continuity ()
H ⊢ F ∈ (ℤ ⟶ ℤ) ⟶ ℤ
H ⊢ f ∈ ℤ ⟶ ℤ
Definitions occuring in rule :
squash: ↓T,
exists: ∃x:A. B[x],
nat: ℕ,
uall: ∀[x:A]. B[x],
uimplies: b supposing a,
less_than: a < b,
absval: |i|,
equal: s = t ∈ T,
apply: f a,
member: t ∈ T,
function: x:A ⟶ B[x],
int: ℤ,
axiom: Ax
Latex:
H \mvdash{} \mdownarrow{}\mexists{}n:\mBbbN{}. \mforall{}[g:\mBbbZ{} {}\mrightarrow{} \mBbbZ{}]. (F f) = (F g) supposing \mforall{}[i:\mBbbZ{}]. (f i) = (g i) supposing |i| < n
BY Continuity ()
H \mvdash{} F \mmember{} (\mBbbZ{} {}\mrightarrow{} \mBbbZ{}) {}\mrightarrow{} \mBbbZ{}
H \mvdash{} f \mmember{} \mBbbZ{} {}\mrightarrow{} \mBbbZ{}
Date html generated:
2019_06_20-PM-04_12_03
Last ObjectModification:
2016_07_08-PM-03_49_09
Theory : rules
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