Nuprl Lemma : fl-eq-0-1-false
∀I:Top. ((0==1) ~ ff)
Proof
Definitions occuring in Statement :
fl-eq: (x==y),
face_lattice: face_lattice(I),
lattice-0: 0,
lattice-1: 1,
bfalse: ff,
top: Top,
all: ∀x:A. B[x],
sqequal: s ~ t
Definitions unfolded in proof :
all: ∀x:A. B[x],
fl-eq: (x==y),
free-dml-deq: free-dml-deq(T;eq),
deq-fset: deq-fset(eq),
isl: isl(x),
decidable__equal_fset,
decidable_functionality,
iff_preserves_decidability,
decidable__and2,
decidable__f-subset,
decidable__all_fset,
decidable__assert,
fset-null: fset-null(s),
null: null(as),
fset-filter: {x ∈ s | P[x]},
filter: filter(P;l),
reduce: reduce(f;k;as),
list_ind: list_ind,
lattice-0: 0,
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,
empty-fset: {},
nil: [],
it: ⋅,
decidable__and,
lattice-1: 1,
fset-singleton: {x},
cons: [a / b],
bnot: ¬bb,
decidable__fset-member,
deq-fset-member: a ∈b s,
deq-member: x ∈b L,
member: t ∈ T
Lemmas referenced :
top_wf,
decidable__equal_fset,
decidable_functionality,
iff_preserves_decidability,
decidable__and2,
decidable__f-subset,
decidable__all_fset,
decidable__assert,
decidable__and,
decidable__fset-member
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
cut,
sqequalRule,
hypothesis,
introduction,
extract_by_obid
Latex:
\mforall{}I:Top. ((0==1) \msim{} ff)
Date html generated:
2018_05_23-AM-08_38_36
Last ObjectModification:
2017_11_24-PM-02_45_44
Theory : cubical!type!theory
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