Nuprl Lemma : set-subtype-coSet
Set{i:l} ⊆r coSet{i:l}
Proof
Definitions occuring in Statement :
Set: Set{i:l},
coSet: coSet{i:l},
subtype_rel: A ⊆r B
Definitions unfolded in proof :
all: ∀x:A. B[x],
exists: ∃x:A. B[x],
not: ¬A,
false: False,
less_than': less_than'(a;b),
and: P ∧ Q,
le: A ≤ B,
nat: ℕ,
pcw-path: Path,
prop: ℙ,
implies: P ⇒ Q,
so_apply: x[s1;s2;s3],
top: Top,
so_lambda: so_lambda(x,y,z.t[x; y; z]),
so_apply: x[s1;s2],
so_lambda: λ2x y.t[x; y],
so_apply: x[s],
so_lambda: λ2x.t[x],
uall: ∀[x:A]. B[x],
member: t ∈ T,
subtype_rel: A ⊆r B,
param-W: pW,
W: W(A;a.B[a]),
coW: coW(A;a.B[a]),
Set: Set{i:l},
coSet: coSet{i:l}
Lemmas referenced :
pcw-partial_wf,
pcw-pp-barred_wf,
nat_wf,
exists_wf,
squash_wf,
le_wf,
false_wf,
pcw-step-agree_wf,
it_wf,
unit_wf2,
pcw-path_wf,
all_wf,
top_wf,
param-co-W_wf
Rules used in proof :
lambdaFormation,
independent_pairFormation,
natural_numberEquality,
dependent_set_memberEquality,
functionEquality,
voidEquality,
voidElimination,
isect_memberEquality,
because_Cache,
universeEquality,
cumulativity,
isectElimination,
extract_by_obid,
introduction,
instantiate,
applyEquality,
setEquality,
hypothesis,
sqequalHypSubstitution,
hypothesisEquality,
cut,
rename,
thin,
setElimination,
lambdaEquality,
sqequalRule,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution
Latex:
Set\{i:l\} \msubseteq{}r coSet\{i:l\}
Date html generated:
2018_07_29-AM-09_50_29
Last ObjectModification:
2018_07_10-PM-05_40_11
Theory : constructive!set!theory
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