Nuprl Lemma : W-subtype-coW
∀[A:𝕌']. ∀[B:A ⟶ Type]. (W(A;a.B[a]) ⊆r coW(A;a.B[a]))
Proof
Definitions occuring in Statement :
coW: coW(A;a.B[a]),
W: W(A;a.B[a]),
subtype_rel: A ⊆r B,
uall: ∀[x:A]. B[x],
so_apply: x[s],
function: x:A ⟶ B[x],
universe: Type
Definitions unfolded in proof :
coW: coW(A;a.B[a]),
so_apply: x[s],
so_lambda: λ2x.t[x],
param-W: pW,
W: W(A;a.B[a]),
subtype_rel: A ⊆r B,
member: t ∈ T,
uall: ∀[x:A]. B[x]
Lemmas referenced :
W_wf
Rules used in proof :
because_Cache,
isect_memberEquality,
universeEquality,
functionEquality,
axiomEquality,
applyEquality,
cumulativity,
sqequalRule,
hypothesisEquality,
isectElimination,
extract_by_obid,
instantiate,
hypothesis,
rename,
thin,
setElimination,
sqequalHypSubstitution,
lambdaEquality,
cut,
introduction,
isect_memberFormation,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution
Latex:
\mforall{}[A:\mBbbU{}']. \mforall{}[B:A {}\mrightarrow{} Type]. (W(A;a.B[a]) \msubseteq{}r coW(A;a.B[a]))
Date html generated:
2018_07_25-PM-01_37_12
Last ObjectModification:
2018_07_19-AM-09_49_32
Theory : co-recursion
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