Nuprl Lemma : rev-type-line-0
∀[Gamma:j⊢]. ∀[A:{Gamma.𝕀 ⊢ _}]. (((A)-)[0(𝕀)] ~ (A)[1(𝕀)])
Proof
Definitions occuring in Statement :
rev-type-line: (A)-,
interval-1: 1(𝕀),
interval-0: 0(𝕀),
interval-type: 𝕀,
csm-id-adjoin: [u],
cube-context-adjoin: X.A,
csm-ap-type: (AF)s,
cubical-type: {X ⊢ _},
cubical_set: CubicalSet,
uall: ∀[x:A]. B[x],
sqequal: s ~ t
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
rev-type-line: (A)-,
interval-rev: 1-(r),
cubical-type: {X ⊢ _},
interval-1: 1(𝕀),
csm-id-adjoin: [u],
csm-ap-type: (AF)s,
cc-snd: q,
cubical-term-at: u(a),
cc-fst: p,
csm-adjoin: (s;u),
interval-0: 0(𝕀),
csm-id: 1(X),
csm-ap: (s)x,
pi1: fst(t),
pi2: snd(t),
subtype_rel: A ⊆r B
Lemmas referenced :
dma-neg-dM0,
cubical-type_wf,
cube-context-adjoin_wf,
cubical_set_cumulativity-i-j,
interval-type_wf,
cubical_set_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation_alt,
introduction,
axiomSqEquality,
sqequalHypSubstitution,
setElimination,
thin,
rename,
cut,
productElimination,
sqequalRule,
extract_by_obid,
isectElimination,
Error :memTop,
hypothesis,
because_Cache,
universeIsType,
instantiate,
hypothesisEquality,
applyEquality
Latex:
\mforall{}[Gamma:j\mvdash{}]. \mforall{}[A:\{Gamma.\mBbbI{} \mvdash{} \_\}]. (((A)-)[0(\mBbbI{})] \msim{} (A)[1(\mBbbI{})])
Date html generated:
2020_05_20-PM-04_17_03
Last ObjectModification:
2020_04_10-AM-04_49_00
Theory : cubical!type!theory
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