Nuprl Lemma : weak-continuity-skolem-truncated
∀[T:{T:Type| (T ⊆r ℕ) ∧ (↓T)} ]. ∀F:(ℕ ⟶ T) ⟶ ℕ. ⇃(weak-continuity-skolem(T;F))
Proof
Definitions occuring in Statement :
weak-continuity-skolem: weak-continuity-skolem(T;F),
quotient: x,y:A//B[x; y],
nat: ℕ,
subtype_rel: A ⊆r B,
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
squash: ↓T,
and: P ∧ Q,
true: True,
set: {x:A| B[x]} ,
function: x:A ⟶ B[x],
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
member: t ∈ T,
subtype_rel: A ⊆r B,
sq-basic-strong-continuity: sq-basic-strong-continuity(T;F),
sq_exists: ∃x:A [B[x]],
basic-strong-continuity: basic-strong-continuity(T;F),
prop: ℙ,
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
uimplies: b supposing a,
implies: P ⇒ Q,
guard: {T},
and: P ∧ Q
Lemmas referenced :
Kleene-M_wf,
subtype_rel_self,
quotient_wf,
basic-strong-continuity_wf,
true_wf,
equiv_rel_true,
implies-quotient-true,
weak-continuity-skolem_wf,
strong-continuity2-weak-skolem,
basic-implies-strong-continuity2,
istype-nat,
istype-universe,
subtype_rel_wf,
nat_wf,
squash_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
Error :isect_memberFormation_alt,
Error :lambdaFormation_alt,
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
applyEquality,
sqequalRule,
because_Cache,
Error :lambdaEquality_alt,
Error :inhabitedIsType,
Error :universeIsType,
setElimination,
rename,
independent_isectElimination,
independent_functionElimination,
Error :functionIsType,
Error :setIsType,
instantiate,
universeEquality,
Error :productIsType
Latex:
\mforall{}[T:\{T:Type| (T \msubseteq{}r \mBbbN{}) \mwedge{} (\mdownarrow{}T)\} ]. \mforall{}F:(\mBbbN{} {}\mrightarrow{} T) {}\mrightarrow{} \mBbbN{}. \00D9(weak-continuity-skolem(T;F))
Date html generated:
2019_06_20-PM-02_51_14
Last ObjectModification:
2019_02_09-PM-11_56_39
Theory : continuity
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