Nuprl Lemma : csm+-id
∀[G:j⊢]. ∀[A:{G ⊢ _}]. (1(G)+ = 1(G.A) ∈ G.A ij⟶ G.A)
Proof
Definitions occuring in Statement :
csm+: tau+,
cube-context-adjoin: X.A,
cubical-type: {X ⊢ _},
csm-id: 1(X),
cube_set_map: A ⟶ B,
cubical_set: CubicalSet,
uall: ∀[x:A]. B[x],
equal: s = t ∈ T
Definitions unfolded in proof :
member: t ∈ T,
uall: ∀[x:A]. B[x],
subtype_rel: A ⊆r B,
uimplies: b supposing a,
squash: ↓T,
prop: ℙ,
true: True,
guard: {T},
iff: P ⇐⇒ Q,
and: P ∧ Q,
rev_implies: P ⇐ Q,
implies: P ⇒ Q,
all: ∀x:A. B[x],
cube-context-adjoin: X.A,
cubical-type: {X ⊢ _},
csm-id: 1(X),
csm+: tau+,
cc-snd: q,
cc-fst: p,
csm-ap-type: (AF)s,
csm-comp: G o F,
csm-adjoin: (s;u),
pi2: snd(t),
compose: f o g,
csm-ap: (s)x,
pi1: fst(t)
Lemmas referenced :
cube-context-adjoin_wf,
cubical_set_cumulativity-i-j,
cubical-type-cumulativity2,
csm+_wf,
csm-id_wf,
subtype_rel-equal,
cube_set_map_wf,
csm-ap-type_wf,
equal_wf,
squash_wf,
true_wf,
istype-universe,
cubical_set_wf,
csm-ap-id-type,
subtype_rel_self,
iff_weakening_equal,
I_cube_pair_redex_lemma,
cubical_type_at_pair_lemma,
I_cube_wf,
fset_wf,
nat_wf,
csm-equal2,
cubical-type_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
cut,
thin,
instantiate,
introduction,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
hypothesisEquality,
applyEquality,
hypothesis,
sqequalRule,
because_Cache,
independent_isectElimination,
lambdaEquality_alt,
imageElimination,
equalityTransitivity,
equalitySymmetry,
universeIsType,
universeEquality,
natural_numberEquality,
imageMemberEquality,
baseClosed,
productElimination,
independent_functionElimination,
lambdaFormation_alt,
dependent_functionElimination,
Error :memTop,
setElimination,
rename,
dependent_pairEquality_alt,
isect_memberFormation_alt,
isect_memberEquality_alt,
axiomEquality,
isectIsTypeImplies,
inhabitedIsType
Latex:
\mforall{}[G:j\mvdash{}]. \mforall{}[A:\{G \mvdash{} \_\}]. (1(G)+ = 1(G.A))
Date html generated:
2020_05_20-PM-01_58_21
Last ObjectModification:
2020_04_21-PM-00_16_28
Theory : cubical!type!theory
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