Nuprl Lemma : set-equal-equiv
∀[T:Type]. EquivRel(T List;x,y.set-equal(T;x;y))
Proof
Definitions occuring in Statement :
set-equal: set-equal(T;x;y),
list: T List,
equiv_rel: EquivRel(T;x,y.E[x; y]),
uall: ∀[x:A]. B[x],
universe: Type
Definitions unfolded in proof :
set-equal: set-equal(T;x;y),
equiv_rel: EquivRel(T;x,y.E[x; y]),
trans: Trans(T;x,y.E[x; y]),
sym: Sym(T;x,y.E[x; y]),
refl: Refl(T;x,y.E[x; y]),
uall: ∀[x:A]. B[x],
and: P ∧ Q,
cand: A c∧ B,
all: ∀x:A. B[x],
iff: P ⇐⇒ Q,
implies: P ⇒ Q,
member: t ∈ T,
prop: ℙ,
rev_implies: P ⇐ Q,
so_lambda: λ2x.t[x],
so_apply: x[s],
guard: {T}
Lemmas referenced :
l_member_wf,
list_wf,
all_wf,
iff_wf
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
isect_memberFormation,
cut,
lambdaFormation,
independent_pairFormation,
hypothesis,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
because_Cache,
lambdaEquality,
universeEquality,
dependent_functionElimination,
productElimination,
independent_functionElimination
Latex:
\mforall{}[T:Type]. EquivRel(T List;x,y.set-equal(T;x;y))
Date html generated:
2016_05_14-PM-01_37_26
Last ObjectModification:
2015_12_26-PM-05_28_22
Theory : list_1
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