Nuprl Lemma : quicksort-int-null
∀[L:ℤ List]. uiff(↑null(quicksort-int(L));↑null(L))
Proof
Definitions occuring in Statement :
quicksort-int: quicksort-int(L),
null: null(as),
list: T List,
assert: ↑b,
uiff: uiff(P;Q),
uall: ∀[x:A]. B[x],
int: ℤ
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uiff: uiff(P;Q),
and: P ∧ Q,
uimplies: b supposing a,
rev_uimplies: rev_uimplies(P;Q),
all: ∀x:A. B[x],
subtype_rel: A ⊆r B,
prop: ℙ,
squash: ↓T,
true: True,
guard: {T},
iff: P ⇐⇒ Q,
implies: P ⇒ Q,
top: Top,
so_lambda: λ2x.t[x],
so_apply: x[s],
rev_implies: P ⇐ Q
Lemmas referenced :
assert_of_null,
quicksort-int_wf,
list_wf,
sorted-by_wf,
le_wf,
l_member_wf,
permutation_wf,
length_of_null_list,
equal_wf,
squash_wf,
true_wf,
quicksort-int-length,
iff_weakening_equal,
length_zero,
assert_witness,
null_wf3,
subtype_rel_list,
top_wf,
assert_wf,
subtype_rel_set,
quicksort-int-nil
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
independent_pairFormation,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
intEquality,
hypothesisEquality,
hypothesis,
productElimination,
independent_isectElimination,
dependent_functionElimination,
applyEquality,
lambdaEquality,
setElimination,
rename,
setEquality,
productEquality,
sqequalRule,
equalityTransitivity,
equalitySymmetry,
imageElimination,
universeEquality,
because_Cache,
natural_numberEquality,
imageMemberEquality,
baseClosed,
independent_functionElimination,
isect_memberEquality,
voidElimination,
voidEquality,
independent_pairEquality,
lambdaFormation
Latex:
\mforall{}[L:\mBbbZ{} List]. uiff(\muparrow{}null(quicksort-int(L));\muparrow{}null(L))
Date html generated:
2018_05_21-PM-07_35_14
Last ObjectModification:
2017_07_26-PM-05_09_29
Theory : general
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