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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