Nuprl Lemma : coW-subtype1
∀[A:Type]. ∀[B:A ⟶ Type]. ((a:A × (B[a] ⟶ coW(A;a.B[a]))) ⊆r coW(A;a.B[a]))
Proof
Definitions occuring in Statement :
coW: coW(A;a.B[a]),
subtype_rel: A ⊆r B,
uall: ∀[x:A]. B[x],
so_apply: x[s],
function: x:A ⟶ B[x],
product: x:A × B[x],
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
ext-eq: A ≡ B,
and: P ∧ Q
Lemmas referenced :
coW-ext,
istype-universe
Rules used in proof :
cut,
introduction,
extract_by_obid,
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
Error :isect_memberFormation_alt,
hypothesis,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
Error :functionIsType,
Error :universeIsType,
because_Cache,
instantiate,
universeEquality,
productElimination
Latex:
\mforall{}[A:Type]. \mforall{}[B:A {}\mrightarrow{} Type]. ((a:A \mtimes{} (B[a] {}\mrightarrow{} coW(A;a.B[a]))) \msubseteq{}r coW(A;a.B[a]))
Date html generated:
2019_06_20-PM-00_56_03
Last ObjectModification:
2019_01_02-PM-01_32_39
Theory : co-recursion-2
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