Nuprl Lemma : dM-lift-1-sq
∀[I,J,f:Top]. (dM-lift(I;J;f) 1 ~ 1)
Proof
Definitions occuring in Statement :
dM-lift: dM-lift(I;J;f),
dM1: 1,
uall: ∀[x:A]. B[x],
top: Top,
apply: f a,
sqequal: s ~ t
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
dM-lift: dM-lift(I;J;f),
free-dma-lift: free-dma-lift(T;eq;dm;eq2;f),
free-DeMorgan-algebra-property,
free-dist-lattice-property,
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,
dM1: 1,
lattice-1: 1,
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-singleton: {x},
cons: [a / b],
nil: [],
it: ⋅,
fset-union: x ⋃ y,
l-union: as ⋃ bs,
insert: insert(a;L),
eval_list: eval_list(t),
deq-member: x ∈b L,
lattice-join: a ∨ b,
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),
lattice-0: 0,
empty-fset: {},
lattice-fset-meet: /\(s),
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,
bnot: ¬bb,
deq-fset: deq-fset(eq),
decidable__equal_fset,
decidable__and2,
decidable__and
Lemmas referenced :
top_wf,
free-DeMorgan-algebra-property,
free-dist-lattice-property,
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,
introduction,
cut,
sqequalRule,
hypothesis,
sqequalAxiom,
extract_by_obid,
sqequalHypSubstitution,
isect_memberEquality,
isectElimination,
thin,
hypothesisEquality,
because_Cache
Latex:
\mforall{}[I,J,f:Top]. (dM-lift(I;J;f) 1 \msim{} 1)
Date html generated:
2018_05_23-AM-08_27_47
Last ObjectModification:
2018_05_20-PM-05_35_53
Theory : cubical!type!theory
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