Nuprl Lemma : csm+-comp-m
∀[H,K:j⊢]. ∀[tau:K j⟶ H]. (m o tau++ = tau+ o m ∈ K.𝕀.𝕀 ij⟶ H.𝕀)
Proof
Definitions occuring in Statement :
csm-m: m,
interval-type: 𝕀,
csm+: tau+,
cube-context-adjoin: X.A,
csm-comp: G o F,
cube_set_map: A ⟶ B,
cubical_set: CubicalSet,
uall: ∀[x:A]. B[x],
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
subtype_rel: A ⊆r B,
cube_set_map: A ⟶ B,
psc_map: A ⟶ B,
nat-trans: nat-trans(C;D;F;G),
cat-ob: cat-ob(C),
pi1: fst(t),
op-cat: op-cat(C),
spreadn: spread4,
cube-cat: CubeCat,
fset: fset(T),
quotient: x,y:A//B[x; y],
cat-arrow: cat-arrow(C),
pi2: snd(t),
type-cat: TypeCat,
all: ∀x:A. B[x],
names-hom: I ⟶ J,
cat-comp: cat-comp(C),
compose: f o g,
uimplies: b supposing a,
cubical_set: CubicalSet,
ps_context: __⊢,
cat-functor: Functor(C1;C2),
I_cube: A(I),
cube-context-adjoin: X.A,
interval-type: 𝕀,
csm+: tau+,
csm-m: m,
csm-comp: G o F,
csm-adjoin: (s;u),
csm-ap: (s)x,
cc-adjoin-cube: (v;u),
cc-snd: q,
cc-fst: p,
constant-cubical-type: (X),
csm-ap-type: (AF)s
Lemmas referenced :
csm-equal,
cube-context-adjoin_wf,
cubical_set_cumulativity-i-j,
interval-type_wf,
csm-comp_wf,
csm+_wf_interval,
subtype_rel_self,
cube_set_map_wf,
csm-m_wf,
cube-set-map-subtype,
I_cube_wf,
fset_wf,
nat_wf,
functor-ob_wf,
op-cat_wf,
cube-cat_wf,
type-cat_wf,
cat-functor_wf,
cat-ob_wf,
I_cube_pair_redex_lemma
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation_alt,
introduction,
cut,
thin,
instantiate,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
hypothesisEquality,
applyEquality,
hypothesis,
sqequalRule,
because_Cache,
independent_isectElimination,
functionExtensionality,
universeIsType,
isect_memberEquality_alt,
axiomEquality,
isectIsTypeImplies,
inhabitedIsType,
lambdaEquality_alt,
setElimination,
rename,
equalityTransitivity,
equalitySymmetry,
functionEquality,
universeEquality,
dependent_functionElimination,
Error :memTop,
productElimination
Latex:
\mforall{}[H,K:j\mvdash{}]. \mforall{}[tau:K j{}\mrightarrow{} H]. (m o tau++ = tau+ o m)
Date html generated:
2020_05_20-PM-04_43_07
Last ObjectModification:
2020_04_10-AM-11_25_32
Theory : cubical!type!theory
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