Nuprl Lemma : basic-implies-strong-continuity2-ext
∀[T:Type]. ∀[F:(ℕ ⟶ T) ⟶ ℕ]. (basic-strong-continuity(T;F) ⇒ strong-continuity2(T;F))
Proof
Definitions occuring in Statement :
strong-continuity2: strong-continuity2(T;F),
basic-strong-continuity: basic-strong-continuity(T;F),
nat: ℕ,
uall: ∀[x:A]. B[x],
implies: P ⇒ Q,
function: x:A ⟶ B[x],
universe: Type
Definitions unfolded in proof :
member: t ∈ T,
int?: int?(x),
it: ⋅,
isl: isl(x),
btrue: tt,
bfalse: ff,
is_int: is_int(x),
basic-implies-strong-continuity2,
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,
so_apply: x[s],
uimplies: b supposing a
Lemmas referenced :
basic-implies-strong-continuity2,
lifting-strict-callbyvalue,
istype-void,
strict4-decide,
lifting-strict-decide,
lifting-strict-isint
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{}[T:Type]. \mforall{}[F:(\mBbbN{} {}\mrightarrow{} T) {}\mrightarrow{} \mBbbN{}]. (basic-strong-continuity(T;F) {}\mRightarrow{} strong-continuity2(T;F))
Date html generated:
2019_06_20-PM-02_50_27
Last ObjectModification:
2019_03_26-AM-07_45_02
Theory : continuity
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