Nuprl Lemma : dM-dM-homs-equal
∀[I,J:fset(ℕ)]. ∀[h1,h2:dma-hom(dM(I);dM(J))].
h1 = h2 ∈ (Point(dM(I)) ⟶ Point(dM(J))) supposing ∀i:names(I). ((h1 <i>) = (h2 <i>) ∈ Point(dM(J)))
Proof
Definitions occuring in Statement :
dM_inc: <x>,
dM: dM(I),
names: names(I),
dma-hom: dma-hom(dma1;dma2),
lattice-point: Point(l),
fset: fset(T),
nat: ℕ,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
apply: f a,
function: x:A ⟶ B[x],
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
subtype_rel: A ⊆r B,
guard: {T},
all: ∀x:A. B[x],
dma-hom: dma-hom(dma1;dma2),
and: P ∧ Q,
cand: A c∧ B,
squash: ↓T,
prop: ℙ,
bounded-lattice-hom: Hom(l1;l2),
lattice-hom: Hom(l1;l2),
true: True,
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
implies: P ⇒ Q,
so_lambda: λ2x.t[x],
DeMorgan-algebra: DeMorganAlgebra,
so_apply: x[s]
Lemmas referenced :
dM-homs-equal,
dM_wf,
bdd-distributive-lattice-subtype-bdd-lattice,
DeMorgan-algebra-subtype,
subtype_rel_transitivity,
DeMorgan-algebra_wf,
bdd-distributive-lattice_wf,
bdd-lattice_wf,
dM-deq_wf,
equal_wf,
squash_wf,
true_wf,
lattice-point_wf,
dM_inc_wf,
iff_weakening_equal,
names_wf,
all_wf,
subtype_rel_set,
DeMorgan-algebra-structure_wf,
lattice-structure_wf,
lattice-axioms_wf,
bounded-lattice-structure-subtype,
DeMorgan-algebra-structure-subtype,
bounded-lattice-structure_wf,
bounded-lattice-axioms_wf,
uall_wf,
lattice-meet_wf,
lattice-join_wf,
DeMorgan-algebra-axioms_wf,
dma-hom_wf,
fset_wf,
nat_wf,
dM_opp_wf,
dma-neg-dM_inc,
dma-neg_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
applyEquality,
instantiate,
independent_isectElimination,
sqequalRule,
dependent_functionElimination,
setElimination,
rename,
lambdaFormation,
lambdaEquality,
imageElimination,
equalityTransitivity,
equalitySymmetry,
universeEquality,
because_Cache,
natural_numberEquality,
imageMemberEquality,
baseClosed,
productElimination,
independent_functionElimination,
independent_pairFormation,
productEquality,
cumulativity,
isect_memberEquality,
axiomEquality,
hyp_replacement
Latex:
\mforall{}[I,J:fset(\mBbbN{})]. \mforall{}[h1,h2:dma-hom(dM(I);dM(J))]. h1 = h2 supposing \mforall{}i:names(I). ((h1 <i>) = (h2 <i>))
Date html generated:
2017_10_05-AM-01_00_26
Last ObjectModification:
2017_07_28-AM-09_25_46
Theory : cubical!type!theory
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