Nuprl Lemma : cubical-term-1-q1
∀[Gamma:j⊢]. ∀[B:{Gamma ⊢ _}]. ∀[z:{Gamma.𝕀 ⊢ _:(B)p}]. (((z)[1(𝕀)])p = z ∈ {Gamma.𝕀, (q=1) ⊢ _:(B)p})
Proof
Definitions occuring in Statement :
context-subset: Gamma, phi,
face-one: (i=1),
interval-1: 1(𝕀),
interval-type: 𝕀,
csm-id-adjoin: [u],
cc-snd: q,
cc-fst: p,
cube-context-adjoin: X.A,
csm-ap-term: (t)s,
cubical-term: {X ⊢ _:A},
csm-ap-type: (AF)s,
cubical-type: {X ⊢ _},
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),
uimplies: b supposing a,
context-subset: Gamma, phi,
all: ∀x:A. B[x],
cube-context-adjoin: X.A,
cubical-type: {X ⊢ _},
interval-1: 1(𝕀),
csm-id-adjoin: [u],
csm-ap-term: (t)s,
csm-ap: (s)x,
csm-id: 1(X),
csm-adjoin: (s;u),
pi1: fst(t),
cubical-term: {X ⊢ _:A},
cubical-term-at: u(a),
pi2: snd(t)
Lemmas referenced :
csm-ap-type_wf,
cube-context-adjoin_wf,
interval-type_wf,
cc-fst_wf,
subset-cubical-type,
context-subset_wf,
face-one_wf,
cc-snd_wf,
context-subset-is-subset,
I_cube_wf,
cubical_set_cumulativity-i-j,
fset_wf,
nat_wf,
cubical-term-equal,
context-subset-term-subtype,
cubical-term_wf,
cubical-type-cumulativity2,
cubical-type_wf,
cubical_set_wf,
I_cube_pair_redex_lemma,
face-one-eq-1,
cubical_type_at_pair_lemma,
interval-type-at,
istype-cubical-type-at,
subtype_rel_self
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation_alt,
equalitySymmetry,
cut,
thin,
instantiate,
introduction,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
hypothesisEquality,
applyEquality,
because_Cache,
hypothesis,
sqequalRule,
equalityTransitivity,
independent_isectElimination,
functionExtensionality,
universeIsType,
dependent_functionElimination,
Error :memTop,
setElimination,
rename,
productElimination,
dependent_pairEquality_alt
Latex:
\mforall{}[Gamma:j\mvdash{}]. \mforall{}[B:\{Gamma \mvdash{} \_\}]. \mforall{}[z:\{Gamma.\mBbbI{} \mvdash{} \_:(B)p\}]. (((z)[1(\mBbbI{})])p = z)
Date html generated:
2020_05_20-PM-04_16_03
Last ObjectModification:
2020_04_10-PM-03_46_52
Theory : cubical!type!theory
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