Nuprl Lemma : copath-length_wf
∀[A:𝕌']. ∀[B:A ⟶ Type]. ∀[w:coW(A;a.B[a])]. ∀[p:copath(a.B[a];w)]. (copath-length(p) ∈ ℕ)
Proof
Definitions occuring in Statement :
copath-length: copath-length(p),
copath: copath(a.B[a];w),
coW: coW(A;a.B[a]),
nat: ℕ,
uall: ∀[x:A]. B[x],
so_apply: x[s],
member: t ∈ T,
function: x:A ⟶ B[x],
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
copath-length: copath-length(p),
copath: copath(a.B[a];w),
pi1: fst(t),
so_lambda: λ2x.t[x],
so_apply: x[s]
Lemmas referenced :
copath_wf,
coW_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
sqequalHypSubstitution,
productElimination,
thin,
hypothesisEquality,
hypothesis,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
extract_by_obid,
isectElimination,
lambdaEquality,
applyEquality,
isect_memberEquality,
because_Cache,
instantiate,
cumulativity,
functionEquality,
universeEquality
Latex:
\mforall{}[A:\mBbbU{}']. \mforall{}[B:A {}\mrightarrow{} Type]. \mforall{}[w:coW(A;a.B[a])]. \mforall{}[p:copath(a.B[a];w)]. (copath-length(p) \mmember{} \mBbbN{})
Date html generated:
2018_07_25-PM-01_39_22
Last ObjectModification:
2018_06_01-AM-08_46_02
Theory : co-recursion
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