Nuprl Lemma : rev-rev-type-line
∀[Gamma:j⊢]. ∀[A:{Gamma.𝕀 ⊢ _}]. (((A)-)- = A ∈ {Gamma.𝕀 ⊢ _})
Proof
Definitions occuring in Statement :
rev-type-line: (A)-,
interval-type: 𝕀,
cube-context-adjoin: X.A,
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,
uimplies: b supposing a,
cubical-type: {X ⊢ _},
rev-type-line: (A)-,
cc-snd: q,
interval-rev: 1-(r),
cc-fst: p,
csm-adjoin: (s;u),
csm-ap-type: (AF)s,
cubical-term-at: u(a),
csm-ap: (s)x,
pi1: fst(t),
pi2: snd(t),
cube-context-adjoin: X.A,
all: ∀x:A. B[x],
cc-adjoin-cube: (v;u),
squash: ↓T,
and: P ∧ Q,
subtype_rel: A ⊆r B,
cubical-type-at: A(a),
interval-type: 𝕀,
constant-cubical-type: (X),
I_cube: A(I),
functor-ob: ob(F),
interval-presheaf: 𝕀,
lattice-point: Point(l),
record-select: r.x,
dM: dM(I),
free-DeMorgan-algebra: free-DeMorgan-algebra(T;eq),
mk-DeMorgan-algebra: mk-DeMorgan-algebra(L;n),
record-update: r[x := v],
ifthenelse: if b then t else f fi ,
eq_atom: x =a y,
bfalse: ff,
free-DeMorgan-lattice: free-DeMorgan-lattice(T;eq),
free-dist-lattice: free-dist-lattice(T; eq),
mk-bounded-distributive-lattice: mk-bounded-distributive-lattice,
mk-bounded-lattice: mk-bounded-lattice(T;m;j;z;o),
btrue: tt,
DeMorgan-algebra: DeMorganAlgebra,
so_lambda: λ2x.t[x],
prop: ℙ,
guard: {T},
so_apply: x[s],
true: True,
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
implies: P ⇒ Q
Lemmas referenced :
cubical-type-equal2,
rev-type-line_wf,
cube-context-adjoin_wf,
interval-type_wf,
cubical-type_wf,
cubical_set_wf,
I_cube_wf,
fset_wf,
nat_wf,
names-hom_wf,
cube-set-restriction_wf,
I_cube_pair_redex_lemma,
cc-adjoin-cube_wf,
DeMorgan-algebra-laws,
dM_wf,
subtype_rel_self,
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-meet_wf,
lattice-join_wf,
DeMorgan-algebra-axioms_wf,
squash_wf,
true_wf,
istype-universe,
iff_weakening_equal,
subtype_rel-equal,
dma-neg_wf,
cubical-type-at_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation_alt,
introduction,
cut,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
because_Cache,
hypothesisEquality,
hypothesis,
independent_isectElimination,
instantiate,
universeIsType,
sqequalRule,
isect_memberEquality_alt,
axiomEquality,
isectIsTypeImplies,
inhabitedIsType,
setElimination,
rename,
productElimination,
dependent_pairEquality_alt,
functionExtensionality,
applyEquality,
functionIsType,
dependent_functionElimination,
Error :memTop,
lambdaEquality_alt,
imageElimination,
productEquality,
cumulativity,
isectEquality,
natural_numberEquality,
imageMemberEquality,
baseClosed,
dependent_set_memberEquality_alt,
independent_pairFormation,
equalityTransitivity,
equalitySymmetry,
productIsType,
equalityIstype,
applyLambdaEquality,
hyp_replacement,
universeEquality,
independent_functionElimination,
lambdaFormation_alt
Latex:
\mforall{}[Gamma:j\mvdash{}]. \mforall{}[A:\{Gamma.\mBbbI{} \mvdash{} \_\}]. (((A)-)- = A)
Date html generated:
2020_05_20-PM-04_17_33
Last ObjectModification:
2020_04_13-PM-00_54_00
Theory : cubical!type!theory
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