Nuprl Lemma : glue-term-subset
∀[Gamma:j⊢]. ∀[A,phi,T,t,a,xx:Top]. (Gamma, xx ⊢ glue [phi ⊢→ t] a ~ Gamma ⊢ glue [phi ⊢→ t] a)
Proof
Definitions occuring in Statement :
glue-term: glue [phi ⊢→ t] a,
context-subset: Gamma, phi,
cubical_set: CubicalSet,
uall: ∀[x:A]. B[x],
top: Top,
sqequal: s ~ t
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
glue-term: glue [phi ⊢→ t] a,
context-subset: Gamma, phi,
all: ∀x:A. B[x],
member: t ∈ T
Lemmas referenced :
cube_set_restriction_pair_lemma,
istype-top,
cubical_set_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation_alt,
sqequalRule,
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
dependent_functionElimination,
thin,
Error :memTop,
hypothesis,
because_Cache,
universeIsType,
instantiate
Latex:
\mforall{}[Gamma:j\mvdash{}]. \mforall{}[A,phi,T,t,a,xx:Top]. (Gamma, xx \mvdash{} glue [phi \mvdash{}\mrightarrow{} t] a \msim{} Gamma \mvdash{} glue [phi \mvdash{}\mrightarrow{} t] a)
Date html generated:
2020_05_20-PM-05_44_05
Last ObjectModification:
2020_04_21-PM-07_02_56
Theory : cubical!type!theory
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