Nuprl Lemma : copath-at_wf
∀[A:𝕌']. ∀[B:A ⟶ Type]. ∀[w:coW(A;a.B[a])]. ∀[p:copath(a.B[a];w)]. (copath-at(w;p) ∈ coW(A;a.B[a]))
Proof
Definitions occuring in Statement :
copath-at: copath-at(w;p),
copath: copath(a.B[a];w),
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 :
so_apply: x[s],
so_lambda: λ2x.t[x],
copath: copath(a.B[a];w),
copath-at: copath-at(w;p),
member: t ∈ T,
uall: ∀[x:A]. B[x]
Lemmas referenced :
coW_wf,
copath_wf,
coPath-at_wf,
coPath_wf
Rules used in proof :
universeEquality,
functionEquality,
cumulativity,
instantiate,
because_Cache,
isect_memberEquality,
equalitySymmetry,
equalityTransitivity,
axiomEquality,
hypothesis,
applyEquality,
lambdaEquality,
isectElimination,
extract_by_obid,
hypothesisEquality,
dependent_pairEquality,
thin,
productElimination,
sqequalHypSubstitution,
spreadEquality,
sqequalRule,
cut,
introduction,
isect_memberFormation,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution
Latex:
\mforall{}[A:\mBbbU{}']. \mforall{}[B:A {}\mrightarrow{} Type]. \mforall{}[w:coW(A;a.B[a])]. \mforall{}[p:copath(a.B[a];w)].
(copath-at(w;p) \mmember{} coW(A;a.B[a]))
Date html generated:
2018_07_25-PM-01_38_57
Last ObjectModification:
2018_07_18-PM-05_21_13
Theory : co-recursion
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