Nuprl Lemma : transform-comp-structure
∀Gamma,Delta:j⊢. ∀tau:Delta j⟶ Gamma. ∀A:{Gamma ⊢ _}. (Gamma ⊢ Compositon(A) ⇒ Delta ⊢ Compositon((A)tau))
Proof
Definitions occuring in Statement :
composition-structure: Gamma ⊢ Compositon(A),
csm-ap-type: (AF)s,
cubical-type: {X ⊢ _},
cube_set_map: A ⟶ B,
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],
csm-comp-structure: (cA)tau,
interval-type: 𝕀,
csm-comp: G o F,
compose: f o g
Lemmas referenced :
csm-comp-structure_wf,
composition-structure_wf,
cubical-type_wf,
cube_set_map_wf,
cubical_set_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation_alt,
rename,
introduction,
cut,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
sqequalRule,
hypothesis,
universeIsType,
inhabitedIsType,
instantiate
Latex:
\mforall{}Gamma,Delta:j\mvdash{}. \mforall{}tau:Delta j{}\mrightarrow{} Gamma. \mforall{}A:\{Gamma \mvdash{} \_\}.
(Gamma \mvdash{} Compositon(A) {}\mRightarrow{} Delta \mvdash{} Compositon((A)tau))
Date html generated:
2020_05_20-PM-05_12_52
Last ObjectModification:
2020_04_19-PM-01_52_58
Theory : cubical!type!theory
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