Nuprl Lemma : face-forall-q=0-or-q=1
∀[Gamma:j⊢]. ((Gamma ⊢ ∀ ((q=0) ∨ (q=1))) = 0(𝔽) ∈ {Gamma ⊢ _:𝔽})
Proof
Definitions occuring in Statement :
face-forall: (∀ phi),
face-zero: (i=0),
face-one: (i=1),
face-or: (a ∨ b),
face-0: 0(𝔽),
face-type: 𝔽,
cc-snd: q,
cubical-term: {X ⊢ _:A},
cubical_set: CubicalSet,
uall: ∀[x:A]. B[x],
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
subtype_rel: A ⊆r B,
cc-snd: q,
interval-type: 𝕀,
cc-fst: p,
csm-ap-type: (AF)s,
constant-cubical-type: (X),
true: True,
squash: ↓T,
prop: ℙ,
uimplies: b supposing a,
guard: {T},
iff: P ⇐⇒ Q,
and: P ∧ Q,
rev_implies: P ⇐ Q,
implies: P ⇒ Q
Lemmas referenced :
cubical_set_wf,
face-zero_wf,
cube-context-adjoin_wf,
cubical_set_cumulativity-i-j,
interval-type_wf,
cc-snd_wf,
face-one_wf,
face-0_wf,
face-or-0,
equal_wf,
squash_wf,
true_wf,
istype-universe,
face-forall-or,
face-or_wf,
cubical-term_wf,
face-type_wf,
face-forall-q=0,
face-forall-q=1,
subtype_rel_self,
iff_weakening_equal
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation_alt,
cut,
hypothesis,
universeIsType,
instantiate,
introduction,
extract_by_obid,
because_Cache,
hypothesisEquality,
thin,
sqequalHypSubstitution,
isectElimination,
applyEquality,
sqequalRule,
equalityTransitivity,
equalitySymmetry,
natural_numberEquality,
lambdaEquality_alt,
imageElimination,
universeEquality,
inhabitedIsType,
imageMemberEquality,
baseClosed,
independent_isectElimination,
productElimination,
independent_functionElimination
Latex:
\mforall{}[Gamma:j\mvdash{}]. ((Gamma \mvdash{} \mforall{} ((q=0) \mvee{} (q=1))) = 0(\mBbbF{}))
Date html generated:
2020_05_20-PM-02_50_59
Last ObjectModification:
2020_04_06-AM-10_23_41
Theory : cubical!type!theory
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