Nuprl Lemma : csm+-comp-csm+
∀[H,K,X:j⊢]. ∀[A:{H ⊢ _}]. ∀[tau:K j⟶ H]. ∀[s:X j⟶ K]. (tau+ o s+ = tau o s+ ∈ X.((A)tau)s ij⟶ H.A)
Proof
Definitions occuring in Statement :
csm+: tau+,
cube-context-adjoin: X.A,
csm-ap-type: (AF)s,
cubical-type: {X ⊢ _},
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,
uimplies: b supposing a,
squash: ↓T,
true: True
Lemmas referenced :
csm+-comp-csm+-sq,
csm+_wf,
csm-comp_wf,
subtype_rel-equal,
cube_set_map_wf,
cube-context-adjoin_wf,
csm-ap-type_wf,
cubical-type-cumulativity2,
cubical_set_cumulativity-i-j,
csm-comp-type,
cubical-type_wf,
cubical_set_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation_alt,
sqequalRule,
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
Error :memTop,
hypothesis,
hypothesisEquality,
applyEquality,
instantiate,
because_Cache,
independent_isectElimination,
lambdaEquality_alt,
imageElimination,
equalityTransitivity,
equalitySymmetry,
natural_numberEquality,
imageMemberEquality,
baseClosed,
universeIsType,
inhabitedIsType
Latex:
\mforall{}[H,K,X:j\mvdash{}]. \mforall{}[A:\{H \mvdash{} \_\}]. \mforall{}[tau:K j{}\mrightarrow{} H]. \mforall{}[s:X j{}\mrightarrow{} K]. (tau+ o s+ = tau o s+)
Date html generated:
2020_05_20-PM-01_58_30
Last ObjectModification:
2020_04_21-AM-11_48_12
Theory : cubical!type!theory
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