Nuprl Lemma : csm-sigma_comp2
∀[X,H,cA,cB,A,tau:Top]. ((sigma_comp(cA;cB))tau ~ sigma_comp((cA)tau;(cB)tau+))
Proof
Definitions occuring in Statement :
sigma_comp: sigma_comp(cA;cB)
,
csm-comp-structure: (cA)tau
,
csm+: tau+
,
cube-context-adjoin: X.A
,
csm-ap-type: (AF)s
,
uall: ∀[x:A]. B[x]
,
top: Top
,
sqequal: s ~ t
Definitions unfolded in proof :
uall: ∀[x:A]. B[x]
,
csm-comp-structure: (cA)tau
,
sigma_comp: sigma_comp(cA;cB)
,
let: let,
csm+: tau+
,
csm-ap-type: (AF)s
,
csm-comp: G o F
,
csm-id-adjoin: [u]
,
interval-1: 1(𝕀)
,
csm-ap-term: (t)s
,
compose: f o g
,
csm-id: 1(X)
,
csm-adjoin: (s;u)
,
cc-snd: q
,
cc-fst: p
,
csm-ap: (s)x
,
pi2: snd(t)
,
pi1: fst(t)
,
member: t ∈ T
Lemmas referenced :
top_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
sqequalRule,
because_Cache,
cut,
introduction,
extract_by_obid,
hypothesis
Latex:
\mforall{}[X,H,cA,cB,A,tau:Top]. ((sigma\_comp(cA;cB))tau \msim{} sigma\_comp((cA)tau;(cB)tau+))
Date html generated:
2017_01_10-AM-09_54_02
Last ObjectModification:
2016_12_24-AM-11_28_45
Theory : cubical!type!theory
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