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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