Nuprl Lemma : csm-sigma_comp3
∀[H,A',X,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-comp: G o F,
csm-id-adjoin: [u],
csm-ap-type: (AF)s,
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{}[H,A',X,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_17
Last ObjectModification:
2016_12_24-PM-00_40_36
Theory : cubical!type!theory
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