Nuprl Lemma : fl-morph-0
∀[A,B:fset(ℕ)]. ∀[g:A ⟶ B]. ((0)<g> = 0 ∈ Point(face_lattice(A)))
Proof
Definitions occuring in Statement :
fl-morph: <f>,
face_lattice: face_lattice(I),
names-hom: I ⟶ J,
lattice-0: 0,
lattice-point: Point(l),
fset: fset(T),
nat: ℕ,
uall: ∀[x:A]. B[x],
apply: f a,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
fl-morph: <f>,
fl-lift: fl-lift(T;eq;L;eqL;f0;f1),
face-lattice-property,
free-dist-lattice-with-constraints-property,
lattice-extend-wc: lattice-extend-wc(L;eq;eqL;f;ac),
lattice-extend: lattice-extend(L;eq;eqL;f;ac),
lattice-fset-join: \/(s),
reduce: reduce(f;k;as),
list_ind: list_ind,
fset-image: f"(s),
f-union: f-union(domeq;rngeq;s;x.g[x]),
list_accum: list_accum,
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: ⋅,
subtype_rel: A ⊆r B,
bdd-distributive-lattice: BoundedDistributiveLattice
Lemmas referenced :
face-lattice-property,
free-dist-lattice-with-constraints-property,
lattice-0_wf,
face_lattice_wf,
bdd-distributive-lattice_wf,
names-hom_wf,
fset_wf,
nat_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
hypothesis,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
applyEquality,
lambdaEquality,
setElimination,
rename,
isect_memberEquality,
axiomEquality,
because_Cache
Latex:
\mforall{}[A,B:fset(\mBbbN{})]. \mforall{}[g:A {}\mrightarrow{} B]. ((0)<g> = 0)
Date html generated:
2016_05_18-PM-00_15_59
Last ObjectModification:
2015_12_28-PM-03_00_16
Theory : cubical!type!theory
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