Nuprl Lemma : nc-e'-p2
∀[I,J:fset(ℕ)]. ∀[f:J ⟶ I]. ∀[r:Point(dM(I))]. ∀[i:ℕ]. ∀[j:{j:ℕ| ¬j ∈ J} ]. (f,i=j ⋅ (j/f(r)) = (i/r) ⋅ f ∈ J ⟶ I+i)
Proof
Definitions occuring in Statement :
interval-presheaf: 𝕀,
cube-set-restriction: f(s),
nc-e': g,i=j,
nc-p: (i/z),
add-name: I+i,
nh-comp: g ⋅ f,
names-hom: I ⟶ J,
dM: dM(I),
lattice-point: Point(l),
fset-member: a ∈ s,
fset: fset(T),
int-deq: IntDeq,
nat: ℕ,
uall: ∀[x:A]. B[x],
not: ¬A,
set: {x:A| B[x]} ,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
top: Top,
subtype_rel: A ⊆r B,
uimplies: b supposing a,
nat: ℕ,
so_lambda: λ2x.t[x],
so_apply: x[s],
prop: ℙ,
DeMorgan-algebra: DeMorganAlgebra,
and: P ∧ Q,
guard: {T}
Lemmas referenced :
fset_wf,
names-hom_wf,
DeMorgan-algebra-axioms_wf,
lattice-join_wf,
lattice-meet_wf,
equal_wf,
uall_wf,
bounded-lattice-axioms_wf,
bounded-lattice-structure_wf,
subtype_rel_transitivity,
DeMorgan-algebra-structure-subtype,
bounded-lattice-structure-subtype,
lattice-axioms_wf,
lattice-structure_wf,
DeMorgan-algebra-structure_wf,
subtype_rel_set,
dM_wf,
lattice-point_wf,
strong-subtype-self,
le_wf,
strong-subtype-set3,
strong-subtype-deq-subtype,
int-deq_wf,
fset-member_wf,
not_wf,
nat_wf,
interval-presheaf-restriction,
nc-e'-p
Rules used in proof :
cut,
lemma_by_obid,
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
hypothesis,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
equalitySymmetry,
sqequalRule,
isect_memberEquality,
voidElimination,
voidEquality,
setEquality,
applyEquality,
intEquality,
independent_isectElimination,
because_Cache,
lambdaEquality,
natural_numberEquality,
instantiate,
productEquality,
cumulativity,
universeEquality
Latex:
\mforall{}[I,J:fset(\mBbbN{})]. \mforall{}[f:J {}\mrightarrow{} I]. \mforall{}[r:Point(dM(I))]. \mforall{}[i:\mBbbN{}]. \mforall{}[j:\{j:\mBbbN{}| \mneg{}j \mmember{} J\} ].
(f,i=j \mcdot{} (j/f(r)) = (i/r) \mcdot{} f)
Date html generated:
2016_05_18-PM-00_06_47
Last ObjectModification:
2016_02_08-PM-05_39_49
Theory : cubical!type!theory
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