Nuprl Lemma : nh-comp-nc-m-eq2
∀[I,K:fset(ℕ)]. ∀[i,j:ℕ]. ∀[f:K ⟶ I+i+j]. (i0) ⋅ s ⋅ f = m(i;j) ⋅ f ∈ K ⟶ I+i supposing (f i) = 0 ∈ Point(dM(K))
Proof
Definitions occuring in Statement :
nc-m: m(i;j),
nc-0: (i0),
nc-s: s,
add-name: I+i,
nh-comp: g ⋅ f,
names-hom: I ⟶ J,
dM0: 0,
dM: dM(I),
lattice-point: Point(l),
fset: fset(T),
nat: ℕ,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
apply: f a,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
prop: ℙ,
squash: ↓T,
true: True,
subtype_rel: A ⊆r B,
DeMorgan-algebra: DeMorganAlgebra,
so_lambda: λ2x.t[x],
and: P ∧ Q,
guard: {T},
so_apply: x[s],
names-hom: I ⟶ J,
all: ∀x:A. B[x],
names: names(I),
nat: ℕ,
implies: P ⇒ Q,
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q
Lemmas referenced :
nh-comp-nc-m-eq,
equal_wf,
squash_wf,
true_wf,
names-hom_wf,
add-name_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,
trivial-member-add-name2,
fset-member_wf,
nat_wf,
int-deq_wf,
strong-subtype-deq-subtype,
strong-subtype-set3,
le_wf,
strong-subtype-self,
dM0_wf,
fset_wf,
f-subset-add-name1,
f-subset-add-name,
nh-comp-assoc,
nc-s_wf,
nc-0_wf,
iff_weakening_equal,
nh-comp_wf,
s-comp-s
Rules used in proof :
cut,
introduction,
extract_by_obid,
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
hypothesis,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
independent_isectElimination,
hyp_replacement,
equalitySymmetry,
sqequalRule,
applyEquality,
lambdaEquality,
imageElimination,
equalityTransitivity,
universeEquality,
natural_numberEquality,
imageMemberEquality,
baseClosed,
instantiate,
productEquality,
cumulativity,
because_Cache,
dependent_functionElimination,
dependent_set_memberEquality,
intEquality,
independent_functionElimination,
productElimination
Latex:
\mforall{}[I,K:fset(\mBbbN{})]. \mforall{}[i,j:\mBbbN{}]. \mforall{}[f:K {}\mrightarrow{} I+i+j]. (i0) \mcdot{} s \mcdot{} f = m(i;j) \mcdot{} f supposing (f i) = 0
Date html generated:
2017_10_05-AM-01_03_26
Last ObjectModification:
2017_07_28-AM-09_26_40
Theory : cubical!type!theory
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