Nuprl Lemma : csm-p-composition-exists
∀[X:j⊢]. ∀[A,T:{X ⊢ _}]. (X ⊢ CompOp(A) ⇒ X.T ⊢ CompOp((A)p))
Proof
Definitions occuring in Statement :
composition-op: Gamma ⊢ CompOp(A),
cc-fst: p,
cube-context-adjoin: X.A,
csm-ap-type: (AF)s,
cubical-type: {X ⊢ _},
cubical_set: CubicalSet,
uall: ∀[x:A]. B[x],
implies: P ⇒ Q
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
implies: P ⇒ Q,
member: t ∈ T,
subtype_rel: A ⊆r B
Lemmas referenced :
csm-composition_wf,
cube-context-adjoin_wf,
cubical-type-cumulativity2,
cubical_set_cumulativity-i-j,
cc-fst_wf,
composition-op_wf,
cubical-type_wf,
cubical_set_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation_alt,
lambdaFormation_alt,
rename,
introduction,
cut,
thin,
instantiate,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
hypothesisEquality,
applyEquality,
because_Cache,
hypothesis,
sqequalRule,
universeIsType,
inhabitedIsType
Latex:
\mforall{}[X:j\mvdash{}]. \mforall{}[A,T:\{X \mvdash{} \_\}]. (X \mvdash{} CompOp(A) {}\mRightarrow{} X.T \mvdash{} CompOp((A)p))
Date html generated:
2020_05_20-PM-03_51_36
Last ObjectModification:
2020_04_09-PM-01_11_37
Theory : cubical!type!theory
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