Nuprl Lemma : fl_all-1
∀I,J,i:Top. ((∀i.1) ~ 1)
Proof
Definitions occuring in Statement :
fl_all: (∀i.phi),
face_lattice: face_lattice(I),
lattice-1: 1,
top: Top,
all: ∀x:A. B[x],
sqequal: s ~ t
Definitions unfolded in proof :
all: ∀x:A. B[x],
fl_all: (∀i.phi),
fl-all-hom: fl-all-hom(I;i),
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-1: 1,
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,
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,
bfalse: ff,
lattice-join: a ∨ b,
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),
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,
member: t ∈ T
Lemmas referenced :
face-lattice-property,
free-dist-lattice-with-constraints-property,
decidable__f-subset,
decidable__all_fset,
decidable_functionality,
iff_preserves_decidability,
decidable__assert,
decidable__equal_fset,
decidable__and2,
decidable__and,
top_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
cut,
sqequalRule,
hypothesis,
lemma_by_obid
Latex:
\mforall{}I,J,i:Top. ((\mforall{}i.1) \msim{} 1)
Date html generated:
2016_05_18-PM-00_17_49
Last ObjectModification:
2016_03_25-AM-11_34_36
Theory : cubical!type!theory
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