Nuprl Lemma : glue-term_wf2
∀[Gamma:j⊢]. ∀[A:{Gamma ⊢ _}]. ∀[phi:{Gamma ⊢ _:𝔽}]. ∀[T:{Gamma, phi ⊢ _}]. ∀[w:{Gamma, phi ⊢ _:(T ⟶ A)}].
∀[t:{Gamma, phi ⊢ _:T}]. ∀[a:{Gamma ⊢ _:A[phi |⟶ app(w; t)]}].
  (glue [phi ⊢→ t] a ∈ {Gamma ⊢ _:Glue [phi ⊢→ (T;w)] A[phi |⟶ t]})
Proof
Definitions occuring in Statement : 
glue-term: glue [phi ⊢→ t] a
, 
glue-type: Glue [phi ⊢→ (T;w)] A
, 
constrained-cubical-term: {Gamma ⊢ _:A[phi |⟶ t]}
, 
context-subset: Gamma, phi
, 
face-type: 𝔽
, 
cubical-app: app(w; u)
, 
cubical-fun: (A ⟶ B)
, 
cubical-term: {X ⊢ _:A}
, 
cubical-type: {X ⊢ _}
, 
cubical_set: CubicalSet
, 
uall: ∀[x:A]. B[x]
, 
member: t ∈ T
Definitions unfolded in proof : 
uall: ∀[x:A]. B[x]
, 
member: t ∈ T
, 
constrained-cubical-term: {Gamma ⊢ _:A[phi |⟶ t]}
, 
same-cubical-type: Gamma ⊢ A = B
, 
subtype_rel: A ⊆r B
, 
same-cubical-term: X ⊢ u=v:A
, 
uimplies: b supposing a
Lemmas referenced : 
glue-term_wf, 
glue-type-constraint, 
constrained-cubical-term_wf, 
cubical-type-cumulativity2, 
cubical_set_cumulativity-i-j, 
cubical-app_wf_fun, 
context-subset_wf, 
thin-context-subset, 
istype-cubical-term, 
cubical-fun_wf, 
cubical-type_wf, 
face-type_wf, 
cubical_set_wf, 
glue-term-constraint, 
cubical-term-eqcd, 
context-subset-term-subtype, 
glue-type_wf
Rules used in proof : 
cut, 
introduction, 
extract_by_obid, 
sqequalSubstitution, 
sqequalTransitivity, 
computationStep, 
sqequalReflexivity, 
isect_memberFormation_alt, 
hypothesis, 
sqequalHypSubstitution, 
isectElimination, 
thin, 
hypothesisEquality, 
dependent_set_memberEquality_alt, 
equalityTransitivity, 
equalitySymmetry, 
because_Cache, 
universeIsType, 
instantiate, 
applyEquality, 
sqequalRule, 
Error :memTop, 
independent_isectElimination, 
lambdaEquality_alt, 
cumulativity, 
universeEquality, 
hyp_replacement, 
equalityIstype
Latex:
\mforall{}[Gamma:j\mvdash{}].  \mforall{}[A:\{Gamma  \mvdash{}  \_\}].  \mforall{}[phi:\{Gamma  \mvdash{}  \_:\mBbbF{}\}].  \mforall{}[T:\{Gamma,  phi  \mvdash{}  \_\}].
\mforall{}[w:\{Gamma,  phi  \mvdash{}  \_:(T  {}\mrightarrow{}  A)\}].  \mforall{}[t:\{Gamma,  phi  \mvdash{}  \_:T\}].  \mforall{}[a:\{Gamma  \mvdash{}  \_:A[phi  |{}\mrightarrow{}  app(w;  t)]\}].
    (glue  [phi  \mvdash{}\mrightarrow{}  t]  a  \mmember{}  \{Gamma  \mvdash{}  \_:Glue  [phi  \mvdash{}\mrightarrow{}  (T;w)]  A[phi  |{}\mrightarrow{}  t]\})
Date html generated:
2020_05_20-PM-05_44_49
Last ObjectModification:
2020_04_21-PM-07_03_55
Theory : cubical!type!theory
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