Nuprl Lemma : face_lattice-join-invariant
∀[v,y,I,J:Top]. (v ∨ y ~ v ∨ y)
Proof
Definitions occuring in Statement :
face_lattice: face_lattice(I),
lattice-join: a ∨ b,
uall: ∀[x:A]. B[x],
top: Top,
sqequal: s ~ t
Definitions unfolded in proof :
lattice-join: a ∨ b,
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,
fset-constrained-ac-lub: lub(P;ac1;ac2),
fset-ac-lub: fset-ac-lub(eq;ac1;ac2),
fset-minimals: fset-minimals(x,y.less[x; y]; s),
fset-filter: {x ∈ s | P[x]},
filter: filter(P;l),
reduce: reduce(f;k;as),
list_ind: list_ind,
fset-union: x ⋃ y,
l-union: as ⋃ bs,
union-deq: union-deq(A;B;a;b),
member: t ∈ T,
uall: ∀[x:A]. B[x]
Lemmas referenced :
top_wf
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
cut,
introduction,
extract_by_obid,
hypothesis,
because_Cache,
isect_memberFormation,
sqequalAxiom,
sqequalHypSubstitution,
isect_memberEquality,
isectElimination,
thin,
hypothesisEquality
Latex:
\mforall{}[v,y,I,J:Top]. (v \mvee{} y \msim{} v \mvee{} y)
Date html generated:
2017_02_21-AM-10_32_21
Last ObjectModification:
2017_02_03-PM-08_41_35
Theory : cubical!type!theory
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