Nuprl Lemma : case-term-equal-left'
∀[Gamma:j⊢]. ∀[phi:{Gamma ⊢ _:𝔽}]. ∀[A:{Gamma, phi ⊢ _}]. ∀[u:{Gamma, phi ⊢ _:A}]. ∀[v:Top]. ∀[x:{Gamma, phi ⊢ _:A}].
Gamma, phi ⊢ (u ∨ v)=x:A supposing x = u ∈ {Gamma, phi ⊢ _:A}
Proof
Definitions occuring in Statement :
case-term: (u ∨ v),
same-cubical-term: X ⊢ u=v:A,
context-subset: Gamma, phi,
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-equal-left,
istype-top,
cubical-term_wf,
context-subset_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,
equalityTransitivity,
equalitySymmetry,
equalityIstype,
inhabitedIsType,
universeIsType,
instantiate,
applyEquality,
sqequalRule
Latex:
\mforall{}[Gamma:j\mvdash{}]. \mforall{}[phi:\{Gamma \mvdash{} \_:\mBbbF{}\}]. \mforall{}[A:\{Gamma, phi \mvdash{} \_\}]. \mforall{}[u:\{Gamma, phi \mvdash{} \_:A\}]. \mforall{}[v:Top].
\mforall{}[x:\{Gamma, phi \mvdash{} \_:A\}].
Gamma, phi \mvdash{} (u \mvee{} v)=x:A supposing x = u
Date html generated:
2020_05_20-PM-03_11_18
Last ObjectModification:
2020_04_07-PM-00_58_42
Theory : cubical!type!theory
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