Nuprl Lemma : fl0-not-1
∀[I:fset(ℕ)]. ∀[x:names(I)]. (¬((x=0) = 1 ∈ Point(face_lattice(I))))
Proof
Definitions occuring in Statement :
fl0: (x=0),
face_lattice: face_lattice(I),
names: names(I),
lattice-1: 1,
lattice-point: Point(l),
fset: fset(T),
nat: ℕ,
uall: ∀[x:A]. B[x],
not: ¬A,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
not: ¬A,
implies: P ⇒ Q,
false: False,
face_lattice: face_lattice(I),
lattice-1: 1,
fl0: (x=0),
face-lattice: face-lattice(T;eq),
face-lattice0: (x=0),
free-dist-lattice-with-constraints: free-dist-lattice-with-constraints(T;eq;x.Cs[x]),
lattice-point: Point(l),
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),
all: ∀x:A. B[x],
top: Top,
eq_atom: x =a y,
ifthenelse: if b then t else f fi ,
bfalse: ff,
btrue: tt,
squash: ↓T,
prop: ℙ,
subtype_rel: A ⊆r B,
bdd-distributive-lattice: BoundedDistributiveLattice,
so_lambda: λ2x.t[x],
and: P ∧ Q,
so_apply: x[s],
uimplies: b supposing a,
uiff: uiff(P;Q)
Lemmas referenced :
rec_select_update_lemma,
equal_wf,
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,
uall_wf,
lattice-meet_wf,
lattice-join_wf,
fl0_wf,
lattice-1_wf,
bdd-distributive-lattice_wf,
names_wf,
fset_wf,
nat_wf,
fset-singletons-equal,
deq-fset_wf,
union-deq_wf,
names-deq_wf,
fset-singleton_wf,
empty-fset_wf,
member-fset-singleton,
fset-member_wf,
mem_empty_lemma
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
lambdaFormation,
thin,
sqequalHypSubstitution,
sqequalRule,
extract_by_obid,
dependent_functionElimination,
isect_memberEquality,
voidElimination,
voidEquality,
hypothesis,
applyLambdaEquality,
setElimination,
rename,
imageMemberEquality,
hypothesisEquality,
baseClosed,
imageElimination,
because_Cache,
independent_functionElimination,
isectElimination,
applyEquality,
instantiate,
lambdaEquality,
productEquality,
cumulativity,
universeEquality,
independent_isectElimination,
unionEquality,
inlEquality,
productElimination,
equalitySymmetry,
hyp_replacement
Latex:
\mforall{}[I:fset(\mBbbN{})]. \mforall{}[x:names(I)]. (\mneg{}((x=0) = 1))
Date html generated:
2017_10_05-AM-01_10_50
Last ObjectModification:
2017_07_28-AM-09_29_52
Theory : cubical!type!theory
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