Nuprl Lemma : length-copath-extend
∀[A:𝕌']. ∀[B:A ⟶ Type]. ∀[w:coW(A;a.B[a])]. ∀[p:copath(a.B[a];w)]. ∀[t:Top].
(copath-length(copath-extend(p;t)) = (copath-length(p) + 1) ∈ ℤ)
Proof
Definitions occuring in Statement :
copath-length: copath-length(p),
copath-extend: copath-extend(q;t),
copath: copath(a.B[a];w),
coW: coW(A;a.B[a]),
uall: ∀[x:A]. B[x],
top: Top,
so_apply: x[s],
function: x:A ⟶ B[x],
add: n + m,
natural_number: $n,
int: ℤ,
universe: Type,
equal: s = t ∈ T
Definitions unfolded in proof :
so_apply: x[s],
so_lambda: λ2x.t[x],
nat: ℕ,
pi1: fst(t),
copath-extend: copath-extend(q;t),
copath-length: copath-length(p),
copath: copath(a.B[a];w),
member: t ∈ T,
uall: ∀[x:A]. B[x]
Lemmas referenced :
coW_wf,
copath_wf,
top_wf
Rules used in proof :
universeEquality,
functionEquality,
cumulativity,
instantiate,
applyEquality,
lambdaEquality,
because_Cache,
axiomEquality,
isectElimination,
isect_memberEquality,
extract_by_obid,
natural_numberEquality,
hypothesis,
hypothesisEquality,
rename,
setElimination,
addEquality,
sqequalRule,
thin,
productElimination,
sqequalHypSubstitution,
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)]. \mforall{}[t:Top].
(copath-length(copath-extend(p;t)) = (copath-length(p) + 1))
Date html generated:
2018_07_25-PM-01_40_12
Last ObjectModification:
2018_07_24-PM-05_40_26
Theory : co-recursion
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