Nuprl Lemma : csm-universe-comp-fun
∀[s,A,G,H:Top]. ((CompFun(A))s ~ CompFun((A)s))
Proof
Definitions occuring in Statement :
universe-comp-fun: CompFun(A),
csm-comp-structure: (cA)tau,
csm-ap-term: (t)s,
uall: ∀[x:A]. B[x],
top: Top,
sqequal: s ~ t
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
universe-comp-fun: CompFun(A),
all: ∀x:A. B[x],
implies: P ⇒ Q,
csm-composition: (comp)sigma,
comp-op-to-comp-fun: cop-to-cfun(cA),
composition-term: comp cA [phi ⊢→ u] a0,
csm-comp-structure: (cA)tau,
cubical-term-at: u(a),
cc-adjoin-cube: (v;u),
interval-type: 𝕀,
subset-iota: iota,
csm-comp: G o F,
csm-ap-term: (t)s,
csm-ap: (s)x,
compose: f o g,
constant-cubical-type: (X)
Lemmas referenced :
csm-universe-comp-op,
istype-top
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation_alt,
introduction,
cut,
sqequalRule,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
Error :memTop,
inhabitedIsType,
lambdaFormation_alt,
equalityIstype,
equalityTransitivity,
equalitySymmetry,
dependent_functionElimination,
independent_functionElimination,
axiomSqEquality,
isect_memberEquality_alt,
isectIsTypeImplies
Latex:
\mforall{}[s,A,G,H:Top]. ((CompFun(A))s \msim{} CompFun((A)s))
Date html generated:
2020_05_20-PM-07_18_06
Last ObjectModification:
2020_04_25-PM-09_44_58
Theory : cubical!type!theory
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