Nuprl Lemma : set-ext
Set{i:l} ≡ T:Type × (T ⟶ Set{i:l})
Proof
Definitions occuring in Statement :
Set: Set{i:l},
ext-eq: A ≡ B,
function: x:A ⟶ B[x],
product: x:A × B[x],
universe: Type
Definitions unfolded in proof :
Set: Set{i:l},
uall: ∀[x:A]. B[x],
member: t ∈ T,
so_lambda: λ2x.t[x],
so_apply: x[s]
Lemmas referenced :
W-ext
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
cut,
instantiate,
introduction,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
universeEquality,
sqequalRule,
lambdaEquality,
cumulativity,
hypothesisEquality,
hypothesis
Latex:
Set\{i:l\} \mequiv{} T:Type \mtimes{} (T {}\mrightarrow{} Set\{i:l\})
Date html generated:
2018_05_22-PM-09_47_36
Last ObjectModification:
2018_05_16-PM-01_31_06
Theory : constructive!set!theory
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