Nuprl Lemma : dM1-meet-dM1
∀[I:Top]. (1 ∧ 1 ~ 1)
Proof
Definitions occuring in Statement :
dM1: 1,
dM: dM(I),
lattice-meet: a ∧ b,
uall: ∀[x:A]. B[x],
top: Top,
sqequal: s ~ t
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
lattice-meet: a ∧ b,
record-select: r.x,
dM: dM(I),
free-DeMorgan-algebra: free-DeMorgan-algebra(T;eq),
mk-DeMorgan-algebra: mk-DeMorgan-algebra(L;n),
record-update: r[x := v],
ifthenelse: if b then t else f fi ,
eq_atom: x =a y,
bfalse: ff,
free-DeMorgan-lattice: free-DeMorgan-lattice(T;eq),
free-dist-lattice: free-dist-lattice(T; eq),
mk-bounded-distributive-lattice: mk-bounded-distributive-lattice,
mk-bounded-lattice: mk-bounded-lattice(T;m;j;z;o),
btrue: tt,
fset-ac-glb: fset-ac-glb(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,
f-union: f-union(domeq;rngeq;s;x.g[x]),
list_accum: list_accum,
dM1: 1,
lattice-1: 1,
fset-singleton: {x},
cons: [a / b],
nil: [],
it: ⋅,
fset-union: x ⋃ y,
l-union: as ⋃ bs,
fset-image: f"(s),
insert: insert(a;L),
eval_list: eval_list(t),
deq-member: x ∈b L,
fset-minimal: fset-minimal(x,y.less[x; y];s;a),
fset-null: fset-null(s),
null: null(as),
f-proper-subset-dec: f-proper-subset-dec(eq;xs;ys),
band: p ∧b q,
deq-f-subset: deq-f-subset(eq),
isl: isl(x),
decidable__f-subset,
decidable__all_fset,
decidable_functionality,
iff_preserves_decidability,
decidable__assert,
empty-fset: {},
bnot: ¬bb,
deq-fset: deq-fset(eq),
decidable__equal_fset,
decidable__and2,
decidable__and,
member: t ∈ T
Lemmas referenced :
top_wf,
decidable__f-subset,
decidable__all_fset,
decidable_functionality,
iff_preserves_decidability,
decidable__assert,
decidable__equal_fset,
decidable__and2,
decidable__and
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
sqequalRule,
cut,
introduction,
extract_by_obid,
hypothesis
Latex:
\mforall{}[I:Top]. (1 \mwedge{} 1 \msim{} 1)
Date html generated:
2018_05_23-AM-08_27_22
Last ObjectModification:
2017_11_26-PM-01_51_57
Theory : cubical!type!theory
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