Nuprl Lemma : face-1-in-context-subset
ā[G:jā¢]. ā[phi:{G ā¢ _:š½}]. (phi = 1(š½) ā {G, phi ā¢ _:š½})
Proof
Definitions occuring in Statement :
context-subset: Gamma, phi
,
face-1: 1(š½)
,
face-type: š½
,
cubical-term: {X ā¢ _:A}
,
cubical_set: CubicalSet
,
uall: ā[x:A]. B[x]
,
equal: s = t ā T
Definitions unfolded in proof :
uall: ā[x:A]. B[x]
,
context-subset: Gamma, phi
,
all: āx:A. B[x]
,
member: t ā T
,
subtype_rel: A ār B
,
uimplies: b supposing a
,
face-1: 1(š½)
,
cubical-term-at: u(a)
,
lattice-point: Point(l)
,
record-select: r.x
,
face_lattice: face_lattice(I)
,
face-lattice: face-lattice(T;eq)
,
free-dist-lattice-with-constraints: free-dist-lattice-with-constraints(T;eq;x.Cs[x])
,
constrained-antichain-lattice: constrained-antichain-lattice(T;eq;P)
,
mk-bounded-distributive-lattice: mk-bounded-distributive-lattice,
mk-bounded-lattice: mk-bounded-lattice(T;m;j;z;o)
,
record-update: r[x := v]
,
ifthenelse: if b then t else f fi
,
eq_atom: x =a y
,
bfalse: ff
,
btrue: tt
,
cubical-type-at: A(a)
,
pi1: fst(t)
,
face-type: š½
,
constant-cubical-type: (X)
,
I_cube: A(I)
,
functor-ob: ob(F)
,
face-presheaf: š½
,
bdd-distributive-lattice: BoundedDistributiveLattice
,
so_lambda: Ī»2x.t[x]
,
prop: ā
,
and: P ā§ Q
,
so_apply: x[s]
,
guard: {T}
,
implies: P
ā Q
Lemmas referenced :
I_cube_pair_redex_lemma,
I_cube_wf,
context-subset_wf,
fset_wf,
nat_wf,
cubical-term-equal,
face-type_wf,
subset-cubical-term,
context-subset-is-subset,
cubical-term_wf,
cubical_set_wf,
subtype_rel_self,
cubical-type-at_wf_face-type,
equal_functionality_wrt_subtype_rel2,
lattice-point_wf,
face_lattice_wf,
subtype_rel_set,
bounded-lattice-structure_wf,
lattice-structure_wf,
lattice-axioms_wf,
bounded-lattice-structure-subtype,
bounded-lattice-axioms_wf,
equal_wf,
lattice-meet_wf,
lattice-join_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation_alt,
cut,
functionExtensionality,
sqequalHypSubstitution,
introduction,
extract_by_obid,
dependent_functionElimination,
thin,
Error :memTop,
hypothesis,
isectElimination,
hypothesisEquality,
applyEquality,
because_Cache,
independent_isectElimination,
sqequalRule,
equalityTransitivity,
equalitySymmetry,
universeIsType,
instantiate,
setElimination,
rename,
lambdaEquality_alt,
productEquality,
cumulativity,
isectEquality,
independent_functionElimination
Latex:
\mforall{}[G:j\mvdash{}]. \mforall{}[phi:\{G \mvdash{} \_:\mBbbF{}\}]. (phi = 1(\mBbbF{}))
Date html generated:
2020_05_20-PM-03_06_49
Last ObjectModification:
2020_04_04-PM-05_23_20
Theory : cubical!type!theory
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