Nuprl Lemma : quicksort-int-length
∀[L:ℤ List]. (||L|| = ||quicksort-int(L)|| ∈ ℤ)
Proof
Definitions occuring in Statement :
quicksort-int: quicksort-int(L),
length: ||as||,
list: T List,
uall: ∀[x:A]. B[x],
int: ℤ,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
member: t ∈ T,
squash: ↓T,
prop: ℙ,
and: P ∧ Q,
uimplies: b supposing a
Lemmas referenced :
permutation-length,
permutation_wf,
l_member_wf,
le_wf,
sorted-by_wf,
and_wf,
list_wf,
quicksort-int_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
cut,
lemma_by_obid,
sqequalHypSubstitution,
dependent_functionElimination,
thin,
hypothesisEquality,
applyEquality,
lambdaEquality,
setElimination,
rename,
hypothesis,
sqequalRule,
imageMemberEquality,
baseClosed,
setEquality,
isectElimination,
intEquality,
introduction,
because_Cache,
imageElimination,
productElimination,
equalityTransitivity,
equalitySymmetry,
independent_isectElimination
Latex:
\mforall{}[L:\mBbbZ{} List]. (||L|| = ||quicksort-int(L)||)
Date html generated:
2016_05_15-PM-04_29_53
Last ObjectModification:
2016_01_16-AM-11_14_09
Theory : general
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