Nuprl Lemma : csm-rev-type-line
∀[G,K:j⊢]. ∀[A:{G.𝕀 ⊢ _}]. ∀[tau:K j⟶ G]. (((A)-)tau+ = ((A)tau+)- ∈ {K.𝕀 ⊢ _})
Proof
Definitions occuring in Statement :
rev-type-line: (A)-,
interval-type: 𝕀,
csm+: tau+,
cube-context-adjoin: X.A,
csm-ap-type: (AF)s,
cubical-type: {X ⊢ _},
cube_set_map: A ⟶ B,
cubical_set: CubicalSet,
uall: ∀[x:A]. B[x],
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
csm-ap-type: (AF)s,
rev-type-line: (A)-,
cubical-type: {X ⊢ _},
cc-snd: q,
interval-rev: 1-(r),
cc-fst: p,
csm-adjoin: (s;u),
csm-ap: (s)x,
interval-type: 𝕀,
csm+: tau+,
cubical-term-at: u(a),
constant-cubical-type: (X),
csm-comp: G o F,
pi1: fst(t),
pi2: snd(t),
compose: f o g,
subtype_rel: A ⊆r B,
cube_set_map: A ⟶ B,
psc_map: A ⟶ B,
nat-trans: nat-trans(C;D;F;G),
cat-ob: cat-ob(C),
op-cat: op-cat(C),
spreadn: spread4,
cube-cat: CubeCat,
fset: fset(T),
quotient: x,y:A//B[x; y],
cat-arrow: cat-arrow(C),
type-cat: TypeCat,
all: ∀x:A. B[x],
names-hom: I ⟶ J,
cat-comp: cat-comp(C),
uimplies: b supposing a,
cube-context-adjoin: X.A,
interval-presheaf: 𝕀,
and: P ∧ Q,
I_cube: A(I),
DeMorgan-algebra: DeMorganAlgebra,
so_lambda: λ2x.t[x],
prop: ℙ,
guard: {T},
so_apply: x[s],
cubical_set: CubicalSet,
ps_context: __⊢
Lemmas referenced :
cubical-type-equal,
cube-context-adjoin_wf,
interval-type_wf,
csm-ap-type_wf,
rev-type-line_wf,
csm+_wf_interval,
subtype_rel_self,
cube_set_map_wf,
cubical-type_wf,
cubical_set_cumulativity-i-j,
cubical_set_wf,
I_cube_pair_redex_lemma,
cube_set_restriction_pair_lemma,
cubical_type_at_pair_lemma,
cubical_type_ap_morph_pair_lemma,
interval-type-at,
cat-ob_wf,
op-cat_wf,
cube-cat_wf,
dma-neg_wf,
dM_wf,
lattice-point_wf,
I_cube_wf,
subtype_rel_set,
DeMorgan-algebra-structure_wf,
lattice-structure_wf,
lattice-axioms_wf,
bounded-lattice-structure-subtype,
DeMorgan-algebra-structure-subtype,
subtype_rel_transitivity,
bounded-lattice-structure_wf,
bounded-lattice-axioms_wf,
equal_wf,
lattice-meet_wf,
lattice-join_wf,
DeMorgan-algebra-axioms_wf,
fset_wf,
nat_wf,
names-hom_wf,
cube-set-restriction_wf,
pi1_wf_top,
dM-lift_wf2,
pi2_wf,
csm-ap-restriction,
interval-type-ap-morph,
dM-lift-neg,
functor-ob_wf,
type-cat_wf,
small-category-cumulativity-2
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation_alt,
introduction,
cut,
sqequalHypSubstitution,
setElimination,
thin,
rename,
productElimination,
sqequalRule,
hypothesis,
instantiate,
extract_by_obid,
isectElimination,
hypothesisEquality,
applyEquality,
because_Cache,
equalityTransitivity,
equalitySymmetry,
independent_isectElimination,
universeIsType,
isect_memberEquality_alt,
axiomEquality,
isectIsTypeImplies,
inhabitedIsType,
dependent_functionElimination,
Error :memTop,
dependent_pairEquality_alt,
functionExtensionality,
lambdaEquality_alt,
productEquality,
cumulativity,
isectEquality,
functionIsType,
productIsType,
independent_pairEquality,
hyp_replacement,
functionEquality,
universeEquality
Latex:
\mforall{}[G,K:j\mvdash{}]. \mforall{}[A:\{G.\mBbbI{} \mvdash{} \_\}]. \mforall{}[tau:K j{}\mrightarrow{} G]. (((A)-)tau+ = ((A)tau+)-)
Date html generated:
2020_05_20-PM-04_16_49
Last ObjectModification:
2020_04_10-AM-04_48_34
Theory : cubical!type!theory
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