Nuprl Lemma : length-copath-cons
∀[b:Top]. ∀[p:Top × Top]. (copath-length(copath-cons(b;p)) ~ copath-length(p) + 1)
Proof
Definitions occuring in Statement :
copath-cons: copath-cons(b;x),
copath-length: copath-length(p),
uall: ∀[x:A]. B[x],
top: Top,
product: x:A × B[x],
add: n + m,
natural_number: $n,
sqequal: s ~ t
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
copath-length: copath-length(p),
pi1: fst(t),
copath-cons: copath-cons(b;x)
Lemmas referenced :
top_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
productElimination,
thin,
sqequalRule,
hypothesis,
sqequalAxiom,
productEquality,
extract_by_obid,
sqequalHypSubstitution,
isect_memberEquality,
isectElimination,
hypothesisEquality,
because_Cache
Latex:
\mforall{}[b:Top]. \mforall{}[p:Top \mtimes{} Top]. (copath-length(copath-cons(b;p)) \msim{} copath-length(p) + 1)
Date html generated:
2018_07_25-PM-01_40_24
Last ObjectModification:
2018_06_01-AM-10_19_14
Theory : co-recursion
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