Nuprl Lemma : dm-neg-sq
∀[I,J,v:Top]. (dm-neg(names(I);NamesDeq;v) ~ dm-neg(names(J);NamesDeq;v))
Proof
Definitions occuring in Statement :
names-deq: NamesDeq,
names: names(I),
dm-neg: ¬(x),
uall: ∀[x:A]. B[x],
top: Top,
sqequal: s ~ t
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
dm-neg: ¬(x),
union-deq: union-deq(A;B;a;b),
lattice-extend: lattice-extend(L;eq;eqL;f;ac),
lattice-fset-meet: /\(s),
lattice-fset-join: \/(s),
lattice-1: 1,
lattice-meet: a ∧ b,
lattice-0: 0,
lattice-join: a ∨ b,
record-select: r.x,
opposite-lattice: opposite-lattice(L),
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,
so_lambda: λ2x y.t[x; y],
free-DeMorgan-lattice: free-DeMorgan-lattice(T;eq),
free-dist-lattice: free-dist-lattice(T; eq),
all: ∀x:A. B[x],
top: Top,
fset-singleton: {x},
cons: [a / b],
empty-fset: {},
nil: [],
it: ⋅
Lemmas referenced :
rec_select_update_lemma,
top_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
hypothesis,
sqequalAxiom,
lemma_by_obid,
sqequalHypSubstitution,
isect_memberEquality,
isectElimination,
thin,
hypothesisEquality,
because_Cache,
dependent_functionElimination,
voidElimination,
voidEquality
Latex:
\mforall{}[I,J,v:Top]. (dm-neg(names(I);NamesDeq;v) \msim{} dm-neg(names(J);NamesDeq;v))
Date html generated:
2016_05_18-PM-00_12_00
Last ObjectModification:
2016_03_26-PM-08_50_11
Theory : cubical!type!theory
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