Nuprl Lemma : subtype_coSet
(T:Type × (T ⟶ coSet{i:l})) ⊆r coSet{i:l}
Proof
Definitions occuring in Statement :
coSet: coSet{i:l},
subtype_rel: A ⊆r B,
function: x:A ⟶ B[x],
product: x:A × B[x],
universe: Type
Definitions unfolded in proof :
and: P ∧ Q,
ext-eq: A ≡ B,
coSet: coSet{i:l},
so_apply: x[s],
so_lambda: λ2x.t[x],
member: t ∈ T,
uall: ∀[x:A]. B[x]
Lemmas referenced :
coW-ext
Rules used in proof :
productElimination,
hypothesis,
hypothesisEquality,
cumulativity,
lambdaEquality,
sqequalRule,
universeEquality,
thin,
isectElimination,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution,
sqequalHypSubstitution,
extract_by_obid,
introduction,
instantiate,
cut
Latex:
(T:Type \mtimes{} (T {}\mrightarrow{} coSet\{i:l\})) \msubseteq{}r coSet\{i:l\}
Date html generated:
2018_07_29-AM-09_49_25
Last ObjectModification:
2018_07_10-PM-10_21_05
Theory : constructive!set!theory
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