Nuprl Lemma : compat_symmetry
∀[T:Type]. ∀as,bs:T List. (as || bs ⇐⇒ bs || as)
Proof
Definitions occuring in Statement :
compat: l1 || l2,
list: T List,
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
iff: P ⇐⇒ Q,
universe: Type
Definitions unfolded in proof :
compat: l1 || l2,
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
iff: P ⇐⇒ Q,
and: P ∧ Q,
implies: P ⇒ Q,
or: P ∨ Q,
guard: {T},
member: t ∈ T,
prop: ℙ,
rev_implies: P ⇐ Q
Lemmas referenced :
iseg_wf,
or_wf,
list_wf
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
isect_memberFormation,
lambdaFormation,
independent_pairFormation,
sqequalHypSubstitution,
unionElimination,
thin,
cut,
hypothesis,
inrFormation,
lemma_by_obid,
isectElimination,
hypothesisEquality,
inlFormation,
because_Cache,
universeEquality
Latex:
\mforall{}[T:Type]. \mforall{}as,bs:T List. (as || bs \mLeftarrow{}{}\mRightarrow{} bs || as)
Date html generated:
2016_05_15-PM-03_50_11
Last ObjectModification:
2015_12_27-PM-01_23_18
Theory : general
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