Nuprl Lemma : fset-pair-symmetry
∀[T:Type]. ∀[a,b:T]. ({a,b} = {b,a} ∈ fset(T))
Proof
Definitions occuring in Statement :
fset-pair: {a,b},
fset: fset(T),
uall: ∀[x:A]. B[x],
universe: Type,
equal: s = t ∈ T
Definitions unfolded in proof :
rev_implies: P ⇐ Q,
false: False,
prop: ℙ,
guard: {T},
or: P ∨ Q,
and: P ∧ Q,
iff: P ⇐⇒ Q,
set-equal: set-equal(T;x;y),
implies: P ⇒ Q,
all: ∀x:A. B[x],
uimplies: b supposing a,
so_apply: x[s1;s2],
so_lambda: λ2x y.t[x; y],
fset: fset(T),
member: t ∈ T,
uall: ∀[x:A]. B[x],
fset-pair: {a,b}
Lemmas referenced :
iff_wf,
l_member_wf,
nil_member,
cons_member,
or_wf,
equal_wf,
false_wf,
nil_wf,
cons_wf,
set-equal-equiv,
list_wf,
set-equal_wf,
quotient-member-eq
Rules used in proof :
orFunctionality,
productElimination,
addLevel,
voidElimination,
inlFormation,
inrFormation,
unionElimination,
independent_pairFormation,
lambdaFormation,
axiomEquality,
isect_memberEquality,
independent_functionElimination,
dependent_functionElimination,
independent_isectElimination,
hypothesis,
hypothesisEquality,
cumulativity,
lambdaEquality,
because_Cache,
thin,
isectElimination,
sqequalHypSubstitution,
extract_by_obid,
cut,
introduction,
isect_memberFormation,
computationStep,
sqequalTransitivity,
sqequalReflexivity,
sqequalRule,
sqequalSubstitution
Latex:
\mforall{}[T:Type]. \mforall{}[a,b:T]. (\{a,b\} = \{b,a\})
Date html generated:
2017_02_20-AM-10_48_42
Last ObjectModification:
2017_02_10-PM-02_29_32
Theory : finite!sets
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