Nuprl Lemma : strong-continuity2-half-squash-ext
∀[T:Type]. ∀F:(ℕ ⟶ T) ⟶ ℕ. ⇃(strong-continuity2(T;F)) supposing (T ⊆r ℕ) ∧ (↓T)
Proof
Definitions occuring in Statement :
strong-continuity2: strong-continuity2(T;F),
quotient: x,y:A//B[x; y],
nat: ℕ,
uimplies: b supposing a,
subtype_rel: A ⊆r B,
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
squash: ↓T,
and: P ∧ Q,
true: True,
function: x:A ⟶ B[x],
universe: Type
Definitions unfolded in proof :
member: t ∈ T,
bfalse: ff,
it: ⋅,
strong-continuity2-half-squash,
implies-quotient-true2,
trivial-quotient-true,
basic-implies-strong-continuity2-ext,
implies-quotient-true
Lemmas referenced :
strong-continuity2-half-squash,
implies-quotient-true2,
trivial-quotient-true,
basic-implies-strong-continuity2-ext,
implies-quotient-true
Rules used in proof :
introduction,
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
cut,
instantiate,
extract_by_obid,
hypothesis,
sqequalRule,
thin,
sqequalHypSubstitution,
equalityTransitivity,
equalitySymmetry
Latex:
\mforall{}[T:Type]. \mforall{}F:(\mBbbN{} {}\mrightarrow{} T) {}\mrightarrow{} \mBbbN{}. \00D9(strong-continuity2(T;F)) supposing (T \msubseteq{}r \mBbbN{}) \mwedge{} (\mdownarrow{}T)
Date html generated:
2019_06_20-PM-02_51_18
Last ObjectModification:
2019_03_26-AM-06_46_06
Theory : continuity
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