Nuprl Lemma : dM-to-FL-dM0
∀[I:fset(ℕ)]. (dM-to-FL(I;0) = 0 ∈ Point(face_lattice(I)))
Proof
Definitions occuring in Statement :
dM-to-FL: dM-to-FL(I;z),
face_lattice: face_lattice(I),
dM0: 0,
lattice-0: 0,
lattice-point: Point(l),
fset: fset(T),
nat: ℕ,
uall: ∀[x:A]. B[x],
equal: s = t ∈ T
Definitions unfolded in proof :
bdd-distributive-lattice: BoundedDistributiveLattice,
subtype_rel: A ⊆r B,
member: t ∈ T,
constrained-antichain-lattice: constrained-antichain-lattice(T;eq;P),
free-dist-lattice-with-constraints: free-dist-lattice-with-constraints(T;eq;x.Cs[x]),
face-lattice: face-lattice(T;eq),
face_lattice: face_lattice(I),
it: ⋅,
nil: [],
empty-fset: {},
btrue: tt,
mk-bounded-lattice: mk-bounded-lattice(T;m;j;z;o),
mk-bounded-distributive-lattice: mk-bounded-distributive-lattice,
free-dist-lattice: free-dist-lattice(T; eq),
free-DeMorgan-lattice: free-DeMorgan-lattice(T;eq),
bfalse: ff,
eq_atom: x =a y,
ifthenelse: if b then t else f fi ,
record-update: r[x := v],
mk-DeMorgan-algebra: mk-DeMorgan-algebra(L;n),
free-DeMorgan-algebra: free-DeMorgan-algebra(T;eq),
dM: dM(I),
record-select: r.x,
lattice-0: 0,
list_accum: list_accum,
f-union: f-union(domeq;rngeq;s;x.g[x]),
fset-image: f"(s),
list_ind: list_ind,
reduce: reduce(f;k;as),
lattice-fset-join: \/(s),
lattice-extend: lattice-extend(L;eq;eqL;f;ac),
dM-to-FL: dM-to-FL(I;z),
uall: ∀[x:A]. B[x],
dM0: 0
Lemmas referenced :
lattice-0_wf,
face_lattice_wf,
bdd-distributive-lattice_wf,
fset_wf,
nat_wf
Rules used in proof :
rename,
setElimination,
lambdaEquality,
applyEquality,
hypothesisEquality,
thin,
isectElimination,
sqequalHypSubstitution,
lemma_by_obid,
hypothesis,
cut,
isect_memberFormation,
computationStep,
sqequalTransitivity,
sqequalReflexivity,
sqequalRule,
sqequalSubstitution
Latex:
\mforall{}[I:fset(\mBbbN{})]. (dM-to-FL(I;0) = 0)
Date html generated:
2016_05_18-PM-00_12_56
Last ObjectModification:
2016_04_18-PM-08_49_38
Theory : cubical!type!theory
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