Nuprl Lemma : case-term-1'
∀[Gamma:j⊢]. ∀[phi:{Gamma ⊢ _:𝔽}]. ∀[A:{Gamma ⊢ _}]. ∀[u,x:{Gamma ⊢ _:A}]. ∀[v:Top].
(Gamma ⊢ (u ∨ v)=x:A) supposing ((x = u ∈ {Gamma ⊢ _:A}) and (phi = 1(𝔽) ∈ {Gamma ⊢ _:𝔽}))
Proof
Definitions occuring in Statement :
case-term: (u ∨ v),
same-cubical-term: X ⊢ u=v:A,
face-1: 1(𝔽),
face-type: 𝔽,
cubical-term: {X ⊢ _:A},
cubical-type: {X ⊢ _},
cubical_set: CubicalSet,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
top: Top,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
same-cubical-term: X ⊢ u=v:A,
subtype_rel: A ⊆r B
Lemmas referenced :
case-term-1,
face-1_wf,
istype-top,
cubical-term_wf,
cubical-type-cumulativity2,
cubical_set_cumulativity-i-j,
cubical-type_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,
independent_isectElimination,
equalityTransitivity,
equalitySymmetry,
equalityIstype,
inhabitedIsType,
universeIsType,
instantiate,
applyEquality,
sqequalRule
Latex:
\mforall{}[Gamma:j\mvdash{}]. \mforall{}[phi:\{Gamma \mvdash{} \_:\mBbbF{}\}]. \mforall{}[A:\{Gamma \mvdash{} \_\}]. \mforall{}[u,x:\{Gamma \mvdash{} \_:A\}]. \mforall{}[v:Top].
(Gamma \mvdash{} (u \mvee{} v)=x:A) supposing ((x = u) and (phi = 1(\mBbbF{})))
Date html generated:
2020_05_20-PM-03_11_41
Last ObjectModification:
2020_04_07-PM-00_58_51
Theory : cubical!type!theory
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