Nuprl Lemma : face-term-0-and-1
∀G:j⊢. G.𝕀 ⊢ (((q=0) ∧ (q=1)) ⇒ 0(𝔽))
Proof
Definitions occuring in Statement :
face-term-implies: Gamma ⊢ (phi ⇒ psi),
face-zero: (i=0),
face-one: (i=1),
face-and: (a ∧ b),
face-0: 0(𝔽),
interval-type: 𝕀,
cc-snd: q,
cube-context-adjoin: X.A,
cubical_set: CubicalSet,
all: ∀x:A. B[x]
Definitions unfolded in proof :
all: ∀x:A. B[x],
face-term-implies: Gamma ⊢ (phi ⇒ psi),
implies: P ⇒ Q,
member: t ∈ T,
uall: ∀[x:A]. B[x],
subtype_rel: A ⊆r B,
bdd-distributive-lattice: BoundedDistributiveLattice,
so_lambda: λ2x.t[x],
prop: ℙ,
and: P ∧ Q,
so_apply: x[s],
uimplies: b supposing a,
cc-snd: q,
interval-type: 𝕀,
cc-fst: p,
csm-ap-type: (AF)s,
constant-cubical-type: (X),
iff: P ⇐⇒ Q,
interval-presheaf: 𝕀,
not: ¬A,
false: False,
cubical-type-at: A(a),
pi1: fst(t),
face-type: 𝔽,
I_cube: A(I),
functor-ob: ob(F),
face-presheaf: 𝔽,
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
Lemmas referenced :
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,
lattice-1_wf,
I_cube_wf,
cube-context-adjoin_wf,
interval-type_wf,
fset_wf,
nat_wf,
cubical_set_wf,
face-and-eq-1,
face-zero_wf,
cc-snd_wf,
face-one_wf,
face-zero-eq-1,
face-one-eq-1,
interval-type-at,
I_cube_pair_redex_lemma,
dM-0-not-1,
face-and_wf,
cubical-term-at_wf,
face-type_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation_alt,
cut,
hypothesis,
equalityIstype,
universeIsType,
introduction,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
applyEquality,
sqequalRule,
instantiate,
lambdaEquality_alt,
productEquality,
cumulativity,
isectEquality,
because_Cache,
independent_isectElimination,
setElimination,
rename,
inhabitedIsType,
equalityTransitivity,
equalitySymmetry,
dependent_functionElimination,
productElimination,
independent_functionElimination,
Error :memTop,
voidElimination,
hyp_replacement
Latex:
\mforall{}G:j\mvdash{}. G.\mBbbI{} \mvdash{} (((q=0) \mwedge{} (q=1)) {}\mRightarrow{} 0(\mBbbF{}))
Date html generated:
2020_05_20-PM-07_27_41
Last ObjectModification:
2020_04_25-PM-10_15_10
Theory : cubical!type!theory
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