Nuprl Lemma : csm-path-term
∀[phi,r,s,a,b,w:Top]. ((path-term(phi;w;a;b;r))s ~ path-term((phi)s;(w)s;(a)s;(b)s;(r)s))
Proof
Definitions occuring in Statement :
path-term: path-term(phi;w;a;b;r),
csm-ap-term: (t)s,
uall: ∀[x:A]. B[x],
top: Top,
sqequal: s ~ t
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
path-term: path-term(phi;w;a;b;r),
member: t ∈ T,
top: Top
Lemmas referenced :
top_wf,
csm-case-term,
csm-cubical-path-app,
csm-face-zero
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
because_Cache,
cut,
introduction,
extract_by_obid,
hypothesis,
hypothesisEquality,
isect_memberEquality,
voidElimination,
voidEquality,
sqequalRule,
sqequalHypSubstitution,
isectElimination,
thin
Latex:
\mforall{}[phi,r,s,a,b,w:Top]. ((path-term(phi;w;a;b;r))s \msim{} path-term((phi)s;(w)s;(a)s;(b)s;(r)s))
Date html generated:
2018_05_23-AM-10_59_56
Last ObjectModification:
2018_05_20-PM-08_03_12
Theory : cubical!type!theory
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