Nuprl Lemma : term-p+1
∀[X,Y,Z,W,t,A:Top]. (((t)p+)[1(𝕀)] ~ ((t)[1(𝕀)])p)
Proof
Definitions occuring in Statement :
interval-1: 1(𝕀),
csm+: tau+,
csm-id-adjoin: [u],
cc-fst: p,
cube-context-adjoin: X.A,
csm-ap-term: (t)s,
uall: ∀[x:A]. B[x],
top: Top,
sqequal: s ~ t
Definitions unfolded in proof :
interval-1: 1(𝕀),
csm-id-adjoin: [u],
csm-ap-term: (t)s,
cc-fst: p,
csm+: tau+,
csm-ap: (s)x,
csm-id: 1(X),
csm-adjoin: (s;u),
cc-snd: q,
csm-ap-type: (AF)s,
csm-comp: G o F,
pi2: snd(t),
compose: f o g,
pi1: fst(t),
uall: ∀[x:A]. B[x],
member: t ∈ T
Lemmas referenced :
top_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
sqequalRule,
isect_memberFormation,
introduction,
cut,
sqequalAxiom,
extract_by_obid,
hypothesis,
sqequalHypSubstitution,
isect_memberEquality,
isectElimination,
thin,
hypothesisEquality,
because_Cache
Latex:
\mforall{}[X,Y,Z,W,t,A:Top]. (((t)p+)[1(\mBbbI{})] \msim{} ((t)[1(\mBbbI{})])p)
Date html generated:
2018_05_23-AM-09_29_58
Last ObjectModification:
2018_05_20-PM-06_28_53
Theory : cubical!type!theory
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