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 :
uall: ∀[x:A]. B[x],
member: t ∈ T,
subtype_rel: A ⊆r B,
W: W(A;a.B[a]),
param-W: pW,
so_lambda: λ2x.t[x],
so_apply: x[s],
coW: coW(A;a.B[a])
Lemmas referenced :
W_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
lambdaEquality,
sqequalHypSubstitution,
setElimination,
thin,
rename,
hypothesis,
instantiate,
extract_by_obid,
isectElimination,
hypothesisEquality,
sqequalRule,
cumulativity,
applyEquality,
axiomEquality,
functionEquality,
universeEquality,
isect_memberEquality,
because_Cache
Latex:
\mforall{}[A:\mBbbU{}']. \mforall{}[B:A {}\mrightarrow{} Type]. (W(A;a.B[a]) \msubseteq{}r coW(A;a.B[a]))
Date html generated:
2019_06_20-PM-00_56_01
Last ObjectModification:
2019_01_02-PM-01_32_37
Theory : co-recursion-2
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