Nuprl Lemma : dM1-sq-singleton-empty
∀[I:Top]. (1 ~ {{}})
Proof
Definitions occuring in Statement :
dM1: 1,
empty-fset: {},
fset-singleton: {x},
uall: ∀[x:A]. B[x],
top: Top,
sqequal: s ~ t
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
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],
empty-fset: {},
nil: [],
it: ⋅
Lemmas referenced :
top_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
hypothesis,
sqequalAxiom,
lemma_by_obid
Latex:
\mforall{}[I:Top]. (1 \msim{} \{\{\}\})
Date html generated:
2016_05_18-AM-11_56_52
Last ObjectModification:
2016_02_04-PM-00_37_54
Theory : cubical!type!theory
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