Nuprl Lemma : decidable__equal-poset-cat-ob
∀I:Cname List. ∀c1,c2:cat-ob(poset-cat(I)). Dec(c1 = c2 ∈ cat-ob(poset-cat(I)))
Proof
Definitions occuring in Statement :
poset-cat: poset-cat(J),
coordinate_name: Cname,
cat-ob: cat-ob(C),
list: T List,
decidable: Dec(P),
all: ∀x:A. B[x],
equal: s = t ∈ T
Definitions unfolded in proof :
all: ∀x:A. B[x],
member: t ∈ T,
decidable: Dec(P),
or: P ∨ Q,
prop: ℙ,
uall: ∀[x:A]. B[x],
guard: {T},
not: ¬A,
implies: P ⇒ Q,
exists: ∃x:A. B[x],
nequal: a ≠ b ∈ T ,
false: False,
poset-cat: poset-cat(J),
cat-ob: cat-ob(C),
pi1: fst(t),
name-morph: name-morph(I;J),
squash: ↓T,
subtype_rel: A ⊆r B
Lemmas referenced :
nil_wf,
extd-nameset_subtype_int,
coordinate_name_wf,
list_wf,
poset-cat_wf,
cat-ob_wf,
equal_wf,
not_wf,
poset-cat-ob-cases
Rules used in proof :
cut,
lemma_by_obid,
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
hypothesis,
sqequalHypSubstitution,
dependent_functionElimination,
thin,
hypothesisEquality,
unionElimination,
inlFormation,
isectElimination,
sqequalRule,
inrFormation,
productElimination,
independent_functionElimination,
voidElimination,
applyEquality,
lambdaEquality,
setElimination,
rename,
imageMemberEquality,
baseClosed,
equalityUniverse,
levelHypothesis,
introduction,
because_Cache,
imageElimination
Latex:
\mforall{}I:Cname List. \mforall{}c1,c2:cat-ob(poset-cat(I)). Dec(c1 = c2)
Date html generated:
2016_06_16-PM-06_53_10
Last ObjectModification:
2016_01_18-PM-04_51_04
Theory : cubical!sets
Home
Index