Nuprl Lemma : dM-0-not-1
∀[I:fset(ℕ)]. (¬(0 = 1 ∈ Point(dM(I))))
Proof
Definitions occuring in Statement :
dM1: 1,
dM0: 0,
dM: dM(I),
lattice-point: Point(l),
fset: fset(T),
nat: ℕ,
uall: ∀[x:A]. B[x],
not: ¬A,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
not: ¬A,
implies: P ⇒ Q,
false: False,
dM1: 1,
dM0: 0,
dM: dM(I),
prop: ℙ,
subtype_rel: A ⊆r B,
DeMorgan-algebra: DeMorganAlgebra,
so_lambda: λ2x.t[x],
and: P ∧ Q,
guard: {T},
uimplies: b supposing a,
so_apply: x[s],
top: Top,
lattice-0: 0,
record-select: r.x,
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,
empty-fset: {},
nil: [],
it: ⋅,
lattice-1: 1,
fset-singleton: {x},
cons: [a / b],
all: ∀x:A. B[x]
Lemmas referenced :
equal_wf,
lattice-point_wf,
dM_wf,
subtype_rel_set,
DeMorgan-algebra-structure_wf,
lattice-structure_wf,
lattice-axioms_wf,
bounded-lattice-structure-subtype,
DeMorgan-algebra-structure-subtype,
subtype_rel_transitivity,
bounded-lattice-structure_wf,
bounded-lattice-axioms_wf,
uall_wf,
lattice-meet_wf,
lattice-join_wf,
DeMorgan-algebra-axioms_wf,
dM0_wf,
dM1_wf,
fset_wf,
nat_wf,
free-dma-point,
free-dml-0-not-1,
names_wf,
names-deq_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
lambdaFormation,
thin,
hypothesis,
sqequalHypSubstitution,
independent_functionElimination,
voidElimination,
extract_by_obid,
isectElimination,
hypothesisEquality,
applyEquality,
sqequalRule,
instantiate,
lambdaEquality,
productEquality,
independent_isectElimination,
cumulativity,
universeEquality,
because_Cache,
dependent_functionElimination,
isect_memberEquality,
voidEquality
Latex:
\mforall{}[I:fset(\mBbbN{})]. (\mneg{}(0 = 1))
Date html generated:
2017_10_05-AM-00_59_21
Last ObjectModification:
2017_07_28-AM-09_25_18
Theory : cubical!type!theory
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