Nuprl Lemma : cc-fst+-comp-1
∀[G:j⊢]. (p+ o [1(𝕀)] = [1(𝕀)] o p ∈ G.𝕀 ij⟶ G.𝕀)
Proof
Definitions occuring in Statement :
interval-1: 1(𝕀),
interval-type: 𝕀,
csm+: tau+,
csm-id-adjoin: [u],
cc-fst: p,
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],
interval-1: 1(𝕀),
csm-id-adjoin: [u],
cc-fst: p,
interval-type: 𝕀,
csm-comp: G o F,
csm+: tau+,
csm-id: 1(X),
csm-adjoin: (s;u),
compose: f o g,
constant-cubical-type: (X),
cc-snd: q,
csm-ap-type: (AF)s,
pi2: snd(t),
csm-ap: (s)x,
pi1: fst(t),
member: t ∈ T,
subtype_rel: A ⊆r B
Lemmas referenced :
csm-comp_wf,
cube-context-adjoin_wf,
cubical_set_cumulativity-i-j,
interval-type_wf,
cc-fst_wf,
csm-id-adjoin_wf-interval-1,
cubical_set_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation_alt,
sqequalRule,
cut,
thin,
instantiate,
introduction,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
hypothesisEquality,
applyEquality,
hypothesis,
because_Cache,
universeIsType
Latex:
\mforall{}[G:j\mvdash{}]. (p+ o [1(\mBbbI{})] = [1(\mBbbI{})] o p)
Date html generated:
2020_05_20-PM-04_43_50
Last ObjectModification:
2020_04_10-AM-11_25_52
Theory : cubical!type!theory
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