Nuprl Definition : strong-continuity2
strong-continuity2(T;F) ==
∃M:n:ℕ ⟶ (ℕn ⟶ T) ⟶ (ℕ?)
∀f:ℕ ⟶ T. ((∃n:ℕ. ((M n f) = (inl (F f)) ∈ (ℕ?))) ∧ (∀n:ℕ. (M n f) = (inl (F f)) ∈ (ℕ?) supposing ↑isl(M n f)))
Definitions occuring in Statement :
int_seg: {i..j-},
nat: ℕ,
assert: ↑b,
isl: isl(x),
uimplies: b supposing a,
all: ∀x:A. B[x],
exists: ∃x:A. B[x],
and: P ∧ Q,
unit: Unit,
apply: f a,
function: x:A ⟶ B[x],
inl: inl x,
union: left + right,
natural_number: $n,
equal: s = t ∈ T
Definitions occuring in definition :
apply: f a,
inl: inl x,
unit: Unit,
nat: ℕ,
union: left + right,
equal: s = t ∈ T,
isl: isl(x),
assert: ↑b,
uimplies: b supposing a,
all: ∀x:A. B[x],
exists: ∃x:A. B[x],
and: P ∧ Q,
function: x:A ⟶ B[x],
natural_number: $n,
int_seg: {i..j-}
FDL editor aliases :
strong-continuity2
Latex:
strong-continuity2(T;F) ==
\mexists{}M:n:\mBbbN{} {}\mrightarrow{} (\mBbbN{}n {}\mrightarrow{} T) {}\mrightarrow{} (\mBbbN{}?)
\mforall{}f:\mBbbN{} {}\mrightarrow{} T
((\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:
2016_12_12-AM-09_22_24
Last ObjectModification:
2016_11_22-AM-11_36_59
Theory : continuity
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