Nuprl Lemma : composition-implies-filling-structure
∀Gamma:j⊢. ∀A:{Gamma ⊢ _}. (Gamma ⊢ Compositon(A) ⇒ Gamma ⊢ Filling(A))
Proof
Definitions occuring in Statement :
filling-structure: Gamma ⊢ Filling(A),
composition-structure: Gamma ⊢ Compositon(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]
Lemmas referenced :
comp-to-fill_wf2,
composition-structure_wf,
cubical-type_wf,
cubical_set_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation_alt,
rename,
introduction,
cut,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
universeIsType,
instantiate
Latex:
\mforall{}Gamma:j\mvdash{}. \mforall{}A:\{Gamma \mvdash{} \_\}. (Gamma \mvdash{} Compositon(A) {}\mRightarrow{} Gamma \mvdash{} Filling(A))
Date html generated:
2020_05_20-PM-04_47_46
Last ObjectModification:
2020_04_13-PM-11_36_20
Theory : cubical!type!theory
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