Nuprl Lemma : set-subtype
Set{i:l} ⊆r (T:Type × (T ⟶ Set{i:l}))
Proof
Definitions occuring in Statement :
Set: Set{i:l},
subtype_rel: A ⊆r B,
function: x:A ⟶ B[x],
product: x:A × B[x],
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
guard: {T},
uimplies: b supposing a
Lemmas referenced :
set-ext,
subtype_rel_weakening,
Set_wf
Rules used in proof :
cut,
introduction,
extract_by_obid,
hypothesis,
thin,
instantiate,
sqequalHypSubstitution,
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isectElimination,
productEquality,
universeEquality,
functionEquality,
cumulativity,
hypothesisEquality,
independent_isectElimination
Latex:
Set\{i:l\} \msubseteq{}r (T:Type \mtimes{} (T {}\mrightarrow{} Set\{i:l\}))
Date html generated:
2018_05_22-PM-09_47_38
Last ObjectModification:
2018_05_16-PM-01_31_07
Theory : constructive!set!theory
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