Nuprl Lemma : face-lattice-0-not-1
∀[J:fset(ℕ)]. (¬(0 = 1 ∈ Point(face_lattice(J))))
Proof
Definitions occuring in Statement :
face_lattice: face_lattice(I),
lattice-0: 0,
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,
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,
lattice-0: 0,
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,
empty-fset: {},
nil: [],
it: ⋅,
lattice-1: 1,
fset-singleton: {x},
cons: [a / b],
guard: {T},
all: ∀x:A. B[x],
squash: ↓T,
uiff: uiff(P;Q),
top: Top
Lemmas referenced :
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,
lattice-0_wf,
bdd-distributive-lattice_wf,
lattice-1_wf,
fset_wf,
nat_wf,
fl-point,
names_wf,
names-deq_wf,
subtype_rel_weakening,
face-lattice_wf,
assert_wf,
fset-antichain_wf,
union-deq_wf,
all_wf,
fset-member_wf,
deq-fset_wf,
not_wf,
member-fset-singleton,
empty-fset_wf,
mem_empty_lemma
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
lambdaFormation,
thin,
because_Cache,
hypothesis,
sqequalHypSubstitution,
independent_functionElimination,
voidElimination,
extract_by_obid,
isectElimination,
hypothesisEquality,
applyEquality,
sqequalRule,
instantiate,
lambdaEquality,
productEquality,
cumulativity,
universeEquality,
independent_isectElimination,
setElimination,
rename,
dependent_functionElimination,
setEquality,
unionEquality,
functionEquality,
inlEquality,
inrEquality,
applyLambdaEquality,
imageMemberEquality,
baseClosed,
imageElimination,
productElimination,
equalitySymmetry,
hyp_replacement,
isect_memberEquality,
voidEquality
Latex:
\mforall{}[J:fset(\mBbbN{})]. (\mneg{}(0 = 1))
Date html generated:
2017_10_05-AM-01_10_00
Last ObjectModification:
2017_07_28-AM-09_29_37
Theory : cubical!type!theory
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