Nuprl Lemma : same-cubical-term-by-cases2
∀[Gamma:j⊢]. ∀[phi,psi:{Gamma ⊢ _:𝔽}]. ∀[A:{Gamma ⊢ _}]. ∀[a,b:{Gamma, (phi ∨ psi) ⊢ _:A}].
  (Gamma, (phi ∨ psi) ⊢ a=b:A) supposing (Gamma, phi ⊢ a=b:A and Gamma, psi ⊢ a=b:A)
Proof
Definitions occuring in Statement : 
same-cubical-term: X ⊢ u=v:A
, 
context-subset: Gamma, phi
, 
face-or: (a ∨ b)
, 
face-type: 𝔽
, 
cubical-term: {X ⊢ _:A}
, 
cubical-type: {X ⊢ _}
, 
cubical_set: CubicalSet
, 
uimplies: b supposing a
, 
uall: ∀[x:A]. B[x]
Definitions unfolded in proof : 
uall: ∀[x:A]. B[x]
, 
member: t ∈ T
Lemmas referenced : 
same-cubical-term-by-cases, 
thin-context-subset, 
face-or_wf, 
cubical-type_wf, 
cubical-term_wf, 
face-type_wf, 
cubical_set_wf
Rules used in proof : 
cut, 
introduction, 
extract_by_obid, 
sqequalSubstitution, 
sqequalTransitivity, 
computationStep, 
sqequalReflexivity, 
isect_memberFormation_alt, 
hypothesis, 
sqequalHypSubstitution, 
isectElimination, 
thin, 
hypothesisEquality, 
because_Cache, 
universeIsType, 
inhabitedIsType, 
instantiate
Latex:
\mforall{}[Gamma:j\mvdash{}].  \mforall{}[phi,psi:\{Gamma  \mvdash{}  \_:\mBbbF{}\}].  \mforall{}[A:\{Gamma  \mvdash{}  \_\}].  \mforall{}[a,b:\{Gamma,  (phi  \mvee{}  psi)  \mvdash{}  \_:A\}].
    (Gamma,  (phi  \mvee{}  psi)  \mvdash{}  a=b:A)  supposing  (Gamma,  phi  \mvdash{}  a=b:A  and  Gamma,  psi  \mvdash{}  a=b:A)
Date html generated:
2020_05_20-PM-03_01_56
Last ObjectModification:
2020_04_06-AM-10_32_30
Theory : cubical!type!theory
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