Nuprl Lemma : case-term-0
∀[Gamma:j⊢]. ∀[phi:{Gamma ⊢ _:𝔽}]. ∀[A:{Gamma ⊢ _}]. ∀[u:Top]. ∀[v:{Gamma ⊢ _:A}].
Gamma ⊢ (u ∨ v)=v:A supposing phi = 0(𝔽) ∈ {Gamma ⊢ _:𝔽}
Proof
Definitions occuring in Statement :
case-term: (u ∨ v),
same-cubical-term: X ⊢ u=v:A,
face-0: 0(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,
subtype_rel: A ⊆r B,
same-cubical-term: X ⊢ u=v:A,
guard: {T},
and: P ∧ Q,
squash: ↓T,
true: True,
prop: ℙ,
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
implies: P ⇒ Q
Lemmas referenced :
case-term-equal-right,
face-1_wf,
thin-context-subset,
face-or_wf,
context-subset-term-subtype,
face-0_wf,
cubical-term_wf,
cubical-type-cumulativity2,
cubical_set_cumulativity-i-j,
istype-top,
cubical-type_wf,
face-type_wf,
cubical_set_wf,
empty-context-subset-lemma3,
subtype_rel-equal,
context-subset_wf,
subset-cubical-term,
face-and_wf,
face-term-implies-subset,
face-term-and-implies1,
sub_cubical_set_wf,
squash_wf,
true_wf,
iff_weakening_equal,
context-1-subset
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation_alt,
introduction,
cut,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
because_Cache,
equalityTransitivity,
equalitySymmetry,
applyEquality,
sqequalRule,
independent_isectElimination,
axiomEquality,
equalityIstype,
inhabitedIsType,
isect_memberEquality_alt,
isectIsTypeImplies,
universeIsType,
instantiate,
Error :memTop,
dependent_set_memberEquality_alt,
independent_pairFormation,
productIsType,
applyLambdaEquality,
setElimination,
rename,
productElimination,
lambdaEquality_alt,
imageElimination,
natural_numberEquality,
imageMemberEquality,
baseClosed,
independent_functionElimination
Latex:
\mforall{}[Gamma:j\mvdash{}]. \mforall{}[phi:\{Gamma \mvdash{} \_:\mBbbF{}\}]. \mforall{}[A:\{Gamma \mvdash{} \_\}]. \mforall{}[u:Top]. \mforall{}[v:\{Gamma \mvdash{} \_:A\}].
Gamma \mvdash{} (u \mvee{} v)=v:A supposing phi = 0(\mBbbF{})
Date html generated:
2020_05_20-PM-04_14_50
Last ObjectModification:
2020_04_10-AM-04_44_16
Theory : cubical!type!theory
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