Nuprl Lemma : contractible-comp-exists
∀X:j⊢. ∀A:{X ⊢ _}. (X ⊢ CompOp(A) ⇒ X ⊢ CompOp(Contractible(A)))
Proof
Definitions occuring in Statement :
composition-op: Gamma ⊢ CompOp(A),
contractible-type: Contractible(A),
cubical-type: {X ⊢ _},
cubical_set: CubicalSet,
all: ∀x:A. B[x],
implies: P ⇒ Q
Definitions unfolded in proof :
all: ∀x:A. B[x],
implies: P ⇒ Q,
member: t ∈ T,
uall: ∀[x:A]. B[x],
subtype_rel: A ⊆r B
Lemmas referenced :
contractible-comp_wf,
cubical-type-cumulativity2,
cubical_set_cumulativity-i-j,
composition-op_wf,
cubical-type_wf,
cubical_set_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation_alt,
rename,
introduction,
cut,
thin,
instantiate,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
hypothesisEquality,
applyEquality,
because_Cache,
hypothesis,
sqequalRule,
universeIsType
Latex:
\mforall{}X:j\mvdash{}. \mforall{}A:\{X \mvdash{} \_\}. (X \mvdash{} CompOp(A) {}\mRightarrow{} X \mvdash{} CompOp(Contractible(A)))
Date html generated:
2020_05_20-PM-05_14_31
Last ObjectModification:
2020_04_10-AM-11_46_21
Theory : cubical!type!theory
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