Nuprl Lemma : csm+-p-type
∀[C,H,K,A,B,tau:Top]. (((A)p)(tau+ o p;q) ~ ((A)tau+)p)
Proof
Definitions occuring in Statement :
csm+: tau+,
csm-adjoin: (s;u),
cc-snd: q,
cc-fst: p,
cube-context-adjoin: X.A,
csm-ap-type: (AF)s,
csm-comp: G o F,
uall: ∀[x:A]. B[x],
top: Top,
sqequal: s ~ t
Definitions unfolded in proof :
csm-ap-type: (AF)s,
uall: ∀[x:A]. B[x],
so_lambda: so_lambda(x,y,z,w.t[x; y; z; w]),
member: t ∈ T,
so_apply: x[s1;s2;s3;s4],
so_lambda: λ2x y.t[x; y],
top: Top,
so_apply: x[s1;s2],
uimplies: b supposing a,
csm-ap: (s)x,
cc-fst: p,
pi1: fst(t),
csm-adjoin: (s;u),
csm-comp: G o F,
compose: f o g,
csm+: tau+,
cc-snd: q,
pi2: snd(t)
Lemmas referenced :
lifting-strict-spread,
strict4-spread,
top_wf
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
baseClosed,
isect_memberEquality,
voidElimination,
voidEquality,
independent_isectElimination,
hypothesis,
because_Cache,
isect_memberFormation,
sqequalAxiom,
hypothesisEquality
Latex:
\mforall{}[C,H,K,A,B,tau:Top]. (((A)p)(tau+ o p;q) \msim{} ((A)tau+)p)
Date html generated:
2017_01_09-AM-09_14_50
Last ObjectModification:
2016_12_15-PM-03_07_14
Theory : cubical!type!theory
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