Nuprl Lemma : quotient-top-union-top-not-subtype
¬(⇃(Top + Top) ⊆r (Top + Top))
Proof
Definitions occuring in Statement :
quotient: x,y:A//B[x; y],
subtype_rel: A ⊆r B,
top: Top,
not: ¬A,
true: True,
union: left + right
Definitions unfolded in proof :
not: ¬A,
implies: P ⇒ Q,
uall: ∀[x:A]. B[x],
member: t ∈ T,
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
uimplies: b supposing a,
all: ∀x:A. B[x],
top: Top,
true: True,
subtype_rel: A ⊆r B,
prop: ℙ,
sq_type: SQType(T),
guard: {T},
false: False
Lemmas referenced :
quotient-member-eq,
top_wf,
true_wf,
equiv_rel_true,
subtype_rel_wf,
quotient_wf,
equal_wf,
subtype_base_sq,
int_subtype_base
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
unionEquality,
hypothesis,
sqequalRule,
lambdaEquality,
independent_isectElimination,
dependent_functionElimination,
inlEquality,
isect_memberEquality,
voidElimination,
voidEquality,
inrEquality,
independent_functionElimination,
natural_numberEquality,
applyEquality,
because_Cache,
applyLambdaEquality,
hypothesisEquality,
equalityTransitivity,
equalitySymmetry,
unionElimination,
instantiate,
cumulativity,
intEquality,
promote_hyp
Latex:
\mneg{}(\00D9(Top + Top) \msubseteq{}r (Top + Top))
Date html generated:
2019_06_20-PM-00_33_04
Last ObjectModification:
2018_08_21-PM-01_53_14
Theory : quot_1
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