Nuprl Lemma : seteqweaken1_ext
∀s1,s2:coSet{i:l}. ((s1 = s2 ∈ coSet{i:l}) ⇒ seteq(s1;s2))
Proof
Definitions occuring in Statement :
seteq: seteq(s1;s2),
coSet: coSet{i:l},
all: ∀x:A. B[x],
implies: P ⇒ Q,
equal: s = t ∈ T
Definitions unfolded in proof :
uimplies: b supposing a,
so_apply: x[s],
so_lambda: λ2x.t[x],
so_apply: x[s1;s2;s3;s4],
so_lambda: so_lambda(x,y,z,w.t[x; y; z; w]),
any: any x,
bool_cases_sqequal,
implies-sg-win2,
iff_weakening_equal,
coW-equiv_weakening,
coW-equiv-equiv_rel,
seteq-equiv,
seteqweaken1,
top: Top,
uall: ∀[x:A]. B[x],
ifthenelse: if b then t else f fi ,
bfalse: ff,
it: ⋅,
btrue: tt,
lt_int: i <z j,
subtract: n - m,
member: t ∈ T
Lemmas referenced :
strict4-decide,
lifting-strict-less,
less-as-ifthenelse,
seteqweaken1,
bool_cases_sqequal,
implies-sg-win2,
iff_weakening_equal,
coW-equiv_weakening,
coW-equiv-equiv_rel,
seteq-equiv
Rules used in proof :
independent_isectElimination,
baseClosed,
voidEquality,
voidElimination,
isect_memberEquality,
isectElimination,
equalitySymmetry,
equalityTransitivity,
sqequalHypSubstitution,
thin,
sqequalRule,
hypothesis,
extract_by_obid,
instantiate,
cut,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution,
introduction
Latex:
\mforall{}s1,s2:coSet\{i:l\}. ((s1 = s2) {}\mRightarrow{} seteq(s1;s2))
Date html generated:
2018_07_29-AM-09_50_54
Last ObjectModification:
2018_07_11-AM-11_59_33
Theory : constructive!set!theory
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