Nuprl Lemma : fix_wf_coSet
∀[G:⋂W:𝕌'. (W ⟶ (T:Type × (T ⟶ W)))]. (fix(G) ∈ coSet{i:l})
Proof
Definitions occuring in Statement :
coSet: coSet{i:l},
uall: ∀[x:A]. B[x],
member: t ∈ T,
fix: fix(F),
isect: ⋂x:A. B[x],
function: x:A ⟶ B[x],
product: x:A × B[x],
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
coSet: coSet{i:l},
so_lambda: λ2x.t[x],
so_apply: x[s]
Lemmas referenced :
fix_wf_coW
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
universeEquality,
lambdaEquality,
hypothesisEquality,
hypothesis,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
isectEquality,
cumulativity,
functionEquality,
productEquality
Latex:
\mforall{}[G:\mcap{}W:\mBbbU{}'. (W {}\mrightarrow{} (T:Type \mtimes{} (T {}\mrightarrow{} W)))]. (fix(G) \mmember{} coSet\{i:l\})
Date html generated:
2019_10_31-AM-06_32_58
Last ObjectModification:
2018_08_23-AM-11_26_27
Theory : constructive!set!theory
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