Nuprl Lemma : coWsup_wf
∀[A:𝕌']. ∀[B:A ⟶ Type]. ∀[a:A]. ∀[f:B[a] ⟶ coW(A;a.B[a])]. (coWsup(a;f) ∈ coW(A;a.B[a]))
Proof
Definitions occuring in Statement :
coWsup: coWsup(a;f),
coW: coW(A;a.B[a]),
uall: ∀[x:A]. B[x],
so_apply: x[s],
member: t ∈ T,
function: x:A ⟶ B[x],
universe: Type
Definitions unfolded in proof :
and: P ∧ Q,
ext-eq: A ≡ B,
subtype_rel: A ⊆r B,
so_lambda: λ2x.t[x],
so_apply: x[s],
coWsup: coWsup(a;f),
member: t ∈ T,
uall: ∀[x:A]. B[x]
Lemmas referenced :
coW-ext,
coW_wf
Rules used in proof :
productElimination,
universeEquality,
isect_memberEquality,
equalitySymmetry,
equalityTransitivity,
axiomEquality,
because_Cache,
hypothesis,
lambdaEquality,
isectElimination,
sqequalHypSubstitution,
extract_by_obid,
instantiate,
thin,
applyEquality,
cumulativity,
functionEquality,
hypothesisEquality,
dependent_pairEquality,
sqequalRule,
cut,
introduction,
isect_memberFormation,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution
Latex:
\mforall{}[A:\mBbbU{}']. \mforall{}[B:A {}\mrightarrow{} Type]. \mforall{}[a:A]. \mforall{}[f:B[a] {}\mrightarrow{} coW(A;a.B[a])]. (coWsup(a;f) \mmember{} coW(A;a.B[a]))
Date html generated:
2018_07_25-PM-01_37_41
Last ObjectModification:
2018_07_21-PM-04_45_41
Theory : co-recursion
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