Nuprl Lemma : set-equal-permute
∀[T:Type]. ∀as,bs:T List. set-equal(T;as @ bs;bs @ as)
Proof
Definitions occuring in Statement :
set-equal: set-equal(T;x;y),
append: as @ bs,
list: T List,
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
set-equal: set-equal(T;x;y),
iff: P ⇐⇒ Q,
and: P ∧ Q,
implies: P ⇒ Q,
or: P ∨ Q,
member: t ∈ T,
prop: ℙ,
rev_implies: P ⇐ Q,
so_lambda: λ2x.t[x],
so_apply: x[s]
Lemmas referenced :
l_member_wf,
or_wf,
member_append,
append_wf,
all_wf,
iff_wf,
list_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
lambdaFormation,
cut,
independent_pairFormation,
sqequalHypSubstitution,
unionElimination,
thin,
inrFormation,
hypothesis,
lemma_by_obid,
isectElimination,
hypothesisEquality,
inlFormation,
because_Cache,
addLevel,
allFunctionality,
productElimination,
impliesFunctionality,
dependent_functionElimination,
independent_functionElimination,
sqequalRule,
lambdaEquality,
universeEquality
Latex:
\mforall{}[T:Type]. \mforall{}as,bs:T List. set-equal(T;as @ bs;bs @ as)
Date html generated:
2016_05_14-PM-01_37_31
Last ObjectModification:
2015_12_26-PM-05_27_52
Theory : list_1
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