Nuprl Lemma : dma-neg-dM0
∀[I:Top]. (¬(0) ~ 1)
Proof
Definitions occuring in Statement :
dM1: 1,
dM0: 0,
dM: dM(I),
dma-neg: ¬(x),
uall: ∀[x:A]. B[x],
top: Top,
sqequal: s ~ t
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
dma-neg: ¬(x),
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,
btrue: tt,
dm-neg: ¬(x),
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,
dM0: 0,
lattice-0: 0,
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),
empty-fset: {},
nil: [],
it: ⋅,
opposite-lattice: opposite-lattice(L),
lattice-1: 1,
fset-singleton: {x},
cons: [a / b],
dM1: 1,
member: t ∈ T
Lemmas referenced :
top_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
sqequalRule,
cut,
introduction,
extract_by_obid,
hypothesis
Latex:
\mforall{}[I:Top]. (\mneg{}(0) \msim{} 1)
Date html generated:
2018_05_23-AM-08_27_26
Last ObjectModification:
2018_05_20-PM-05_35_20
Theory : cubical!type!theory
Home
Index