Nuprl Lemma : csm-m_wf
∀[Gamma:j⊢]. (m ∈ Gamma.𝕀.𝕀 j⟶ Gamma.𝕀)
Proof
Definitions occuring in Statement :
csm-m: m,
interval-type: 𝕀,
cube-context-adjoin: X.A,
cube_set_map: A ⟶ B,
cubical_set: CubicalSet,
uall: ∀[x:A]. B[x],
member: t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
cube_set_map: A ⟶ B,
psc_map: A ⟶ B,
nat-trans: nat-trans(C;D;F;G),
type-cat: TypeCat,
cat-arrow: cat-arrow(C),
op-cat: op-cat(C),
cat-ob: cat-ob(C),
cube-cat: CubeCat,
spreadn: spread4,
pi2: snd(t),
pi1: fst(t),
csm-m: m,
cube-context-adjoin: X.A,
functor-ob: ob(F),
all: ∀x:A. B[x],
cat-comp: cat-comp(C),
functor-arrow: arrow(F),
compose: f o g,
cc-adjoin-cube: (v;u),
interval-presheaf: 𝕀,
subtype_rel: A ⊆r B,
DeMorgan-algebra: DeMorganAlgebra,
so_lambda: λ2x.t[x],
prop: ℙ,
and: P ∧ Q,
guard: {T},
uimplies: b supposing a,
so_apply: x[s],
interval-type: 𝕀,
cubical-type-ap-morph: (u a f),
constant-cubical-type: (X),
squash: ↓T,
true: True,
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
implies: P ⇒ Q
Lemmas referenced :
I_cube_pair_redex_lemma,
cube_set_restriction_pair_lemma,
cubical_set_wf,
lattice-meet_wf,
dM_wf,
I_cube_wf,
lattice-point_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-join_wf,
DeMorgan-algebra-axioms_wf,
fset_wf,
nat_wf,
cube-set-restriction_wf,
squash_wf,
true_wf,
istype-universe,
dM-lift-meet,
dM-lift_wf2,
subtype_rel_self,
iff_weakening_equal,
names-hom_wf,
pi1_wf_top,
top_wf,
pi2_wf,
interval-type-at
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation_alt,
dependent_set_memberEquality_alt,
sqequalRule,
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
dependent_functionElimination,
thin,
Error :memTop,
hypothesis,
hypothesisEquality,
universeIsType,
instantiate,
because_Cache,
functionExtensionality,
productElimination,
dependent_pairEquality_alt,
isectElimination,
applyEquality,
inhabitedIsType,
productEquality,
cumulativity,
lambdaEquality_alt,
independent_isectElimination,
isectEquality,
lambdaFormation_alt,
imageElimination,
equalityTransitivity,
equalitySymmetry,
universeEquality,
natural_numberEquality,
imageMemberEquality,
baseClosed,
independent_functionElimination,
functionIsType,
equalityIstype,
productIsType,
independent_pairEquality
Latex:
\mforall{}[Gamma:j\mvdash{}]. (m \mmember{} Gamma.\mBbbI{}.\mBbbI{} j{}\mrightarrow{} Gamma.\mBbbI{})
Date html generated:
2020_05_20-PM-04_41_53
Last ObjectModification:
2020_04_13-PM-01_25_51
Theory : cubical!type!theory
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