benchmark_name stringclasses 3
values | index stringlengths 1 3 | method_filepath stringlengths 21 58 | method_without_assertion_filename stringlengths 17 78 | method_name stringlengths 6 66 | method_content stringlengths 183 6.2k | method_without_assertion_content stringlengths 133 6.16k |
|---|---|---|---|---|---|---|
libraries | 30 | ./src/JSON/ZeroCopy/Serializer.dfy | MembersImpl_fix_30.dfy | MembersImpl | method MembersImpl(obj: jobject, writer: Writer) returns (wr: Writer)
decreases obj, 1
ensures wr == MembersSpec(obj, obj.data, writer)
{
wr := writer;
var members := obj.data;
assert wr == MembersSpec(obj, members[..0], writer);
for i := 0 to |members| // FIXME uint32
invariant wr == ... | method MembersImpl(obj: jobject, writer: Writer) returns (wr: Writer)
decreases obj, 1
ensures wr == MembersSpec(obj, obj.data, writer)
{
wr := writer;
var members := obj.data;
for i := 0 to |members| // FIXME uint32
invariant wr == MembersSpec(obj, members[..i], writer)
{
as... |
libraries | 31 | ./src/JSON/ZeroCopy/Serializer.dfy | MembersImpl_fix_31.dfy | MembersImpl | method MembersImpl(obj: jobject, writer: Writer) returns (wr: Writer)
decreases obj, 1
ensures wr == MembersSpec(obj, obj.data, writer)
{
wr := writer;
var members := obj.data;
assert wr == MembersSpec(obj, members[..0], writer);
for i := 0 to |members| // FIXME uint32
invariant wr == ... | method MembersImpl(obj: jobject, writer: Writer) returns (wr: Writer)
decreases obj, 1
ensures wr == MembersSpec(obj, obj.data, writer)
{
wr := writer;
var members := obj.data;
assert wr == MembersSpec(obj, members[..0], writer);
for i := 0 to |members| // FIXME uint32
invariant wr == ... |
libraries | 32 | ./src/JSON/ZeroCopy/Serializer.dfy | MembersImpl_fix_32.dfy | MembersImpl | method MembersImpl(obj: jobject, writer: Writer) returns (wr: Writer)
decreases obj, 1
ensures wr == MembersSpec(obj, obj.data, writer)
{
wr := writer;
var members := obj.data;
assert wr == MembersSpec(obj, members[..0], writer);
for i := 0 to |members| // FIXME uint32
invariant wr == ... | method MembersImpl(obj: jobject, writer: Writer) returns (wr: Writer)
decreases obj, 1
ensures wr == MembersSpec(obj, obj.data, writer)
{
wr := writer;
var members := obj.data;
assert wr == MembersSpec(obj, members[..0], writer);
for i := 0 to |members| // FIXME uint32
invariant wr == ... |
libraries | 39 | ./src/Collections/Sets/Sets.dfy | LemmaIsSingleton_fix_39.dfy | LemmaIsSingleton | lemma LemmaIsSingleton<T>(s: set<T>)
ensures |s| == 1 <==> IsSingleton(s)
{
if |s| == 1 {
forall x, y | x in s && y in s ensures x == y {
LemmaSingletonEquality(s, x, y);
}
}
if IsSingleton(s) {
var x :| x in s;
assert s == {x};
assert |s| == 1;
}
}
| lemma LemmaIsSingleton<T>(s: set<T>)
ensures |s| == 1 <==> IsSingleton(s)
{
if |s| == 1 {
forall x, y | x in s && y in s ensures x == y {
LemmaSingletonEquality(s, x, y);
}
}
if IsSingleton(s) {
var x :| x in s;
assert |s| == 1;
}
}
|
libraries | 42 | ./src/Collections/Sets/Sets.dfy | LemmaUnionSize_fix_42.dfy | LemmaUnionSize | lemma LemmaUnionSize<X>(xs: set<X>, ys: set<X>)
ensures |xs + ys| >= |xs|
ensures |xs + ys| >= |ys|
{
if ys == {} {
} else {
var y :| y in ys;
if y in xs {
var xr := xs - {y};
var yr := ys - {y};
assert xr + yr == xs + ys - {y};
LemmaUnionSize(xr, yr);
... | lemma LemmaUnionSize<X>(xs: set<X>, ys: set<X>)
ensures |xs + ys| >= |xs|
ensures |xs + ys| >= |ys|
{
if ys == {} {
} else {
var y :| y in ys;
if y in xs {
var xr := xs - {y};
var yr := ys - {y};
LemmaUnionSize(xr, yr);
} else {
var yr := ys ... |
libraries | 43 | ./src/Collections/Sets/Sets.dfy | LemmaUnionSize_fix_43.dfy | LemmaUnionSize | lemma LemmaUnionSize<X>(xs: set<X>, ys: set<X>)
ensures |xs + ys| >= |xs|
ensures |xs + ys| >= |ys|
{
if ys == {} {
} else {
var y :| y in ys;
if y in xs {
var xr := xs - {y};
var yr := ys - {y};
assert xr + yr == xs + ys - {y};
LemmaUnionSize(xr, yr);
... | lemma LemmaUnionSize<X>(xs: set<X>, ys: set<X>)
ensures |xs + ys| >= |xs|
ensures |xs + ys| >= |ys|
{
if ys == {} {
} else {
var y :| y in ys;
if y in xs {
var xr := xs - {y};
var yr := ys - {y};
assert xr + yr == xs + ys - {y};
LemmaUnionSize(xr, yr);
... |
libraries | 45 | ./src/Collections/Sequences/LittleEndianNat.dfy | LemmaSeqNeq_fix_45.dfy | LemmaSeqNeq | lemma LemmaSeqNeq(xs: seq<uint>, ys: seq<uint>)
requires |xs| == |ys|
requires xs != ys
ensures ToNatRight(xs) != ToNatRight(ys)
{
ghost var i: nat, n: nat := 0, |xs|;
while i < n
invariant 0 <= i < n
invariant xs[..i] == ys[..i]
{
if xs[i] != ys[i] {
break;
... | lemma LemmaSeqNeq(xs: seq<uint>, ys: seq<uint>)
requires |xs| == |ys|
requires xs != ys
ensures ToNatRight(xs) != ToNatRight(ys)
{
ghost var i: nat, n: nat := 0, |xs|;
while i < n
invariant 0 <= i < n
invariant xs[..i] == ys[..i]
{
if xs[i] != ys[i] {
break;
... |
libraries | 46 | ./src/Collections/Sequences/LittleEndianNat.dfy | LemmaSeqNeq_fix_46.dfy | LemmaSeqNeq | lemma LemmaSeqNeq(xs: seq<uint>, ys: seq<uint>)
requires |xs| == |ys|
requires xs != ys
ensures ToNatRight(xs) != ToNatRight(ys)
{
ghost var i: nat, n: nat := 0, |xs|;
while i < n
invariant 0 <= i < n
invariant xs[..i] == ys[..i]
{
if xs[i] != ys[i] {
break;
... | lemma LemmaSeqNeq(xs: seq<uint>, ys: seq<uint>)
requires |xs| == |ys|
requires xs != ys
ensures ToNatRight(xs) != ToNatRight(ys)
{
ghost var i: nat, n: nat := 0, |xs|;
while i < n
invariant 0 <= i < n
invariant xs[..i] == ys[..i]
{
if xs[i] != ys[i] {
break;
... |
libraries | 49 | ./src/Collections/Sequences/LittleEndianNat.dfy | LemmaSeqPrefixNeq_fix_49.dfy | LemmaSeqPrefixNeq | lemma LemmaSeqPrefixNeq(xs: seq<uint>, ys: seq<uint>, i: nat)
requires 0 <= i <= |xs| == |ys|
requires ToNatRight(xs[..i]) != ToNatRight(ys[..i])
ensures ToNatRight(xs) != ToNatRight(ys)
decreases |xs| - i
{
if i == |xs| {
assert xs[..i] == xs;
assert ys[..i] == ys;
} else {
... | lemma LemmaSeqPrefixNeq(xs: seq<uint>, ys: seq<uint>, i: nat)
requires 0 <= i <= |xs| == |ys|
requires ToNatRight(xs[..i]) != ToNatRight(ys[..i])
ensures ToNatRight(xs) != ToNatRight(ys)
decreases |xs| - i
{
if i == |xs| {
assert ys[..i] == ys;
} else {
if xs[i] == ys[i] {
... |
libraries | 50 | ./src/Collections/Sequences/LittleEndianNat.dfy | LemmaSeqPrefixNeq_fix_50.dfy | LemmaSeqPrefixNeq | lemma LemmaSeqPrefixNeq(xs: seq<uint>, ys: seq<uint>, i: nat)
requires 0 <= i <= |xs| == |ys|
requires ToNatRight(xs[..i]) != ToNatRight(ys[..i])
ensures ToNatRight(xs) != ToNatRight(ys)
decreases |xs| - i
{
if i == |xs| {
assert xs[..i] == xs;
assert ys[..i] == ys;
} else {
... | lemma LemmaSeqPrefixNeq(xs: seq<uint>, ys: seq<uint>, i: nat)
requires 0 <= i <= |xs| == |ys|
requires ToNatRight(xs[..i]) != ToNatRight(ys[..i])
ensures ToNatRight(xs) != ToNatRight(ys)
decreases |xs| - i
{
if i == |xs| {
assert xs[..i] == xs;
} else {
if xs[i] == ys[i] {
... |
libraries | 51 | ./src/Collections/Sequences/LittleEndianNat.dfy | LemmaSeqPrefixNeq_fix_51.dfy | LemmaSeqPrefixNeq | lemma LemmaSeqPrefixNeq(xs: seq<uint>, ys: seq<uint>, i: nat)
requires 0 <= i <= |xs| == |ys|
requires ToNatRight(xs[..i]) != ToNatRight(ys[..i])
ensures ToNatRight(xs) != ToNatRight(ys)
decreases |xs| - i
{
if i == |xs| {
assert xs[..i] == xs;
assert ys[..i] == ys;
} else {
... | lemma LemmaSeqPrefixNeq(xs: seq<uint>, ys: seq<uint>, i: nat)
requires 0 <= i <= |xs| == |ys|
requires ToNatRight(xs[..i]) != ToNatRight(ys[..i])
ensures ToNatRight(xs) != ToNatRight(ys)
decreases |xs| - i
{
if i == |xs| {
assert xs[..i] == xs;
assert ys[..i] == ys;
} else {
... |
libraries | 52 | ./src/Collections/Sequences/LittleEndianNat.dfy | LemmaSeqPrefixNeq_fix_52.dfy | LemmaSeqPrefixNeq | lemma LemmaSeqPrefixNeq(xs: seq<uint>, ys: seq<uint>, i: nat)
requires 0 <= i <= |xs| == |ys|
requires ToNatRight(xs[..i]) != ToNatRight(ys[..i])
ensures ToNatRight(xs) != ToNatRight(ys)
decreases |xs| - i
{
if i == |xs| {
assert xs[..i] == xs;
assert ys[..i] == ys;
} else {
... | lemma LemmaSeqPrefixNeq(xs: seq<uint>, ys: seq<uint>, i: nat)
requires 0 <= i <= |xs| == |ys|
requires ToNatRight(xs[..i]) != ToNatRight(ys[..i])
ensures ToNatRight(xs) != ToNatRight(ys)
decreases |xs| - i
{
if i == |xs| {
assert xs[..i] == xs;
assert ys[..i] == ys;
} else {
... |
libraries | 54 | ./src/Collections/Sequences/Seq.dfy | LemmaCardinalityOfEmptySetIs0_fix_54.dfy | LemmaCardinalityOfEmptySetIs0 | lemma LemmaCardinalityOfEmptySetIs0<T>(xs: seq<T>)
ensures |ToSet(xs)| == 0 <==> |xs| == 0
{
reveal ToSet();
if |xs| != 0 {
assert xs[0] in ToSet(xs);
}
}
| lemma LemmaCardinalityOfEmptySetIs0<T>(xs: seq<T>)
ensures |ToSet(xs)| == 0 <==> |xs| == 0
{
reveal ToSet();
if |xs| != 0 {
}
}
|
libraries | 56 | ./src/Collections/Sequences/Seq.dfy | LemmaFlattenReverseConcat_fix_56.dfy | LemmaFlattenReverseConcat | lemma LemmaFlattenReverseConcat<T>(xs: seq<seq<T>>, ys: seq<seq<T>>)
ensures FlattenReverse(xs + ys) == FlattenReverse(xs) + FlattenReverse(ys)
{
if |ys| == 0 {
assert FlattenReverse(ys) == [];
assert xs + ys == xs;
} else {
calc == {
FlattenReverse(xs + ys);
{ assert L... | lemma LemmaFlattenReverseConcat<T>(xs: seq<seq<T>>, ys: seq<seq<T>>)
ensures FlattenReverse(xs + ys) == FlattenReverse(xs) + FlattenReverse(ys)
{
if |ys| == 0 {
assert FlattenReverse(ys) == [];
} else {
calc == {
FlattenReverse(xs + ys);
{ assert Last(xs + ys) == Last(y... |
libraries | 57 | ./src/Collections/Sequences/Seq.dfy | LemmaInvFoldRight_fix_57.dfy | LemmaInvFoldRight | lemma LemmaInvFoldRight<A,B>(inv: (seq<A>, B) -> bool,
stp: (A, B, B) -> bool,
f: (A, B) -> B,
b: B,
xs: seq<A>)
requires InvFoldRight(inv, stp)
requires forall a, b :: stp(a, b, f(a, b)... | lemma LemmaInvFoldRight<A,B>(inv: (seq<A>, B) -> bool,
stp: (A, B, B) -> bool,
f: (A, B) -> B,
b: B,
xs: seq<A>)
requires InvFoldRight(inv, stp)
requires forall a, b :: stp(a, b, f(a, b)... |
libraries | 58 | ./src/Collections/Sequences/Seq.dfy | LemmaInvFoldLeft_fix_58.dfy | LemmaInvFoldLeft | lemma LemmaInvFoldLeft<A,B>(inv: (B, seq<A>) -> bool,
stp: (B, A, B) -> bool,
f: (B, A) -> B,
b: B,
xs: seq<A>)
requires InvFoldLeft(inv, stp)
requires forall b, a :: stp(b, a, f(b, a))
... | lemma LemmaInvFoldLeft<A,B>(inv: (B, seq<A>) -> bool,
stp: (B, A, B) -> bool,
f: (B, A) -> B,
b: B,
xs: seq<A>)
requires InvFoldLeft(inv, stp)
requires forall b, a :: stp(b, a, f(b, a))
... |
libraries | 59 | ./src/Collections/Sequences/Seq.dfy | LemmaSubseqMin_fix_59.dfy | LemmaSubseqMin | lemma LemmaSubseqMin(xs: seq<int>, from: nat, to: nat)
requires from < to <= |xs|
ensures Min(xs[from..to]) >= Min(xs)
{
var subseq := xs[from..to];
if Min(subseq) < Min(xs) {
var k :| 0 <= k < |subseq| && subseq[k] == Min(subseq);
assert xs[seq(|subseq|, i requires 0 <= i < |subseq| => ... | lemma LemmaSubseqMin(xs: seq<int>, from: nat, to: nat)
requires from < to <= |xs|
ensures Min(xs[from..to]) >= Min(xs)
{
var subseq := xs[from..to];
if Min(subseq) < Min(xs) {
var k :| 0 <= k < |subseq| && subseq[k] == Min(subseq);
}
}
|
libraries | 60 | ./src/Collections/Sequences/Seq.dfy | LemmaFlattenConcat_fix_60.dfy | LemmaFlattenConcat | lemma LemmaFlattenConcat<T>(xs: seq<seq<T>>, ys: seq<seq<T>>)
ensures Flatten(xs + ys) == Flatten(xs) + Flatten(ys)
{
if |xs| == 0 {
assert xs + ys == ys;
} else {
calc == {
Flatten(xs + ys);
{ assert (xs + ys)[0] == xs[0]; assert (xs + ys)[1..] == xs[1..] + ys; }
xs... | lemma LemmaFlattenConcat<T>(xs: seq<seq<T>>, ys: seq<seq<T>>)
ensures Flatten(xs + ys) == Flatten(xs) + Flatten(ys)
{
if |xs| == 0 {
} else {
calc == {
Flatten(xs + ys);
{ assert (xs + ys)[0] == xs[0]; assert (xs + ys)[1..] == xs[1..] + ys; }
xs[0] + Flatten(xs[1..] ... |
libraries | 61 | ./src/Collections/Sequences/Seq.dfy | LemmaSubseqMax_fix_61.dfy | LemmaSubseqMax | lemma LemmaSubseqMax(xs: seq<int>, from: nat, to: nat)
requires from < to <= |xs|
ensures Max(xs[from..to]) <= Max(xs)
{
var subseq := xs[from..to];
if Max(subseq) > Max(xs) {
var k :| 0 <= k < |subseq| && subseq[k] == Max(subseq);
assert xs[seq(|subseq|, i requires 0 <= i < |subseq| => ... | lemma LemmaSubseqMax(xs: seq<int>, from: nat, to: nat)
requires from < to <= |xs|
ensures Max(xs[from..to]) <= Max(xs)
{
var subseq := xs[from..to];
if Max(subseq) > Max(xs) {
var k :| 0 <= k < |subseq| && subseq[k] == Max(subseq);
assert false;
}
}
|
libraries | 63 | ./src/Collections/Sequences/Seq.dfy | LemmaFlattenLengthLeMul_fix_63.dfy | LemmaFlattenLengthLeMul | lemma LemmaFlattenLengthLeMul<T>(xs: seq<seq<T>>, j: int)
requires forall i | 0 <= i < |xs| :: |xs[i]| <= j
ensures |FlattenReverse(xs)| <= |xs| * j
{
if |xs| == 0 {
} else {
LemmaFlattenLengthLeMul(xs[..|xs|-1], j);
assert |FlattenReverse(xs[..|xs|-1])| <= (|xs|-1) * j;
}
}
| lemma LemmaFlattenLengthLeMul<T>(xs: seq<seq<T>>, j: int)
requires forall i | 0 <= i < |xs| :: |xs[i]| <= j
ensures |FlattenReverse(xs)| <= |xs| * j
{
if |xs| == 0 {
} else {
LemmaFlattenLengthLeMul(xs[..|xs|-1], j);
}
}
|
libraries | 64 | ./src/Collections/Sequences/Seq.dfy | LemmaCardinalityOfSet_fix_64.dfy | LemmaCardinalityOfSet | lemma LemmaCardinalityOfSet<T>(xs: seq<T>)
ensures |ToSet(xs)| <= |xs|
{
reveal ToSet();
if |xs| == 0 {
} else {
assert ToSet(xs) == ToSet(DropLast(xs)) + {Last(xs)};
LemmaCardinalityOfSet(DropLast(xs));
}
}
| lemma LemmaCardinalityOfSet<T>(xs: seq<T>)
ensures |ToSet(xs)| <= |xs|
{
reveal ToSet();
if |xs| == 0 {
} else {
LemmaCardinalityOfSet(DropLast(xs));
}
}
|
libraries | 65 | ./src/Collections/Sequences/Seq.dfy | LemmaCardinalityOfSetNoDuplicates_fix_65.dfy | LemmaCardinalityOfSetNoDuplicates | lemma LemmaCardinalityOfSetNoDuplicates<T>(xs: seq<T>)
requires HasNoDuplicates(xs)
ensures |ToSet(xs)| == |xs|
{
reveal HasNoDuplicates();
reveal ToSet();
if |xs| == 0 {
} else {
LemmaCardinalityOfSetNoDuplicates(DropLast(xs));
assert ToSet(xs) == ToSet(DropLast(xs)) + {Last(xs)... | lemma LemmaCardinalityOfSetNoDuplicates<T>(xs: seq<T>)
requires HasNoDuplicates(xs)
ensures |ToSet(xs)| == |xs|
{
reveal HasNoDuplicates();
reveal ToSet();
if |xs| == 0 {
} else {
LemmaCardinalityOfSetNoDuplicates(DropLast(xs));
}
}
|
libraries | 67 | ./src/Collections/Sequences/Seq.dfy | LemmaNoDuplicatesCardinalityOfSet_fix_67.dfy | LemmaNoDuplicatesCardinalityOfSet | lemma LemmaNoDuplicatesCardinalityOfSet<T>(xs: seq<T>)
requires |ToSet(xs)| == |xs|
ensures HasNoDuplicates(xs)
{
reveal HasNoDuplicates();
reveal ToSet();
if |xs| == 0 {
} else {
assert xs == [First(xs)] + DropFirst(xs);
assert ToSet(xs) == {First(xs)} + ToSet(DropFirst(xs));
... | lemma LemmaNoDuplicatesCardinalityOfSet<T>(xs: seq<T>)
requires |ToSet(xs)| == |xs|
ensures HasNoDuplicates(xs)
{
reveal HasNoDuplicates();
reveal ToSet();
if |xs| == 0 {
} else {
assert xs == [First(xs)] + DropFirst(xs);
if First(xs) in DropFirst(xs) {
// If there ... |
libraries | 71 | ./src/Collections/Sequences/Seq.dfy | LemmaMultisetHasNoDuplicates_fix_71.dfy | LemmaMultisetHasNoDuplicates | lemma LemmaMultisetHasNoDuplicates<T>(xs: seq<T>)
requires HasNoDuplicates(xs)
ensures forall x | x in multiset(xs) :: multiset(xs)[x] == 1
{
if |xs| == 0 {
} else {
assert xs == DropLast(xs) + [Last(xs)];
assert Last(xs) !in DropLast(xs) by {
reveal HasNoDuplicates();
}
... | lemma LemmaMultisetHasNoDuplicates<T>(xs: seq<T>)
requires HasNoDuplicates(xs)
ensures forall x | x in multiset(xs) :: multiset(xs)[x] == 1
{
if |xs| == 0 {
} else {
assert Last(xs) !in DropLast(xs) by {
reveal HasNoDuplicates();
}
assert HasNoDuplicates(DropLast(xs))... |
libraries | 73 | ./src/Collections/Sequences/Seq.dfy | LemmaMinOfConcat_fix_73.dfy | LemmaMinOfConcat | lemma LemmaMinOfConcat(xs: seq<int>, ys: seq<int>)
requires 0 < |xs| && 0 < |ys|
ensures Min(xs+ys) <= Min(xs)
ensures Min(xs+ys) <= Min(ys)
ensures forall i :: i in xs + ys ==> Min(xs + ys) <= i
{
reveal Min();
if |xs| == 1 {
} else {
assert xs[1..] + ys == (xs + ys)[1..];
L... | lemma LemmaMinOfConcat(xs: seq<int>, ys: seq<int>)
requires 0 < |xs| && 0 < |ys|
ensures Min(xs+ys) <= Min(xs)
ensures Min(xs+ys) <= Min(ys)
ensures forall i :: i in xs + ys ==> Min(xs + ys) <= i
{
reveal Min();
if |xs| == 1 {
} else {
LemmaMinOfConcat(xs[1..], ys);
}
}... |
libraries | 74 | ./src/Collections/Sequences/Seq.dfy | LemmaMaxOfConcat_fix_74.dfy | LemmaMaxOfConcat | lemma LemmaMaxOfConcat(xs: seq<int>, ys: seq<int>)
requires 0 < |xs| && 0 < |ys|
ensures Max(xs+ys) >= Max(xs)
ensures Max(xs+ys) >= Max(ys)
ensures forall i {:trigger i in [Max(xs + ys)]} :: i in xs + ys ==> Max(xs + ys) >= i
{
reveal Max();
if |xs| == 1 {
} else {
assert xs[1..] ... | lemma LemmaMaxOfConcat(xs: seq<int>, ys: seq<int>)
requires 0 < |xs| && 0 < |ys|
ensures Max(xs+ys) >= Max(xs)
ensures Max(xs+ys) >= Max(ys)
ensures forall i {:trigger i in [Max(xs + ys)]} :: i in xs + ys ==> Max(xs + ys) >= i
{
reveal Max();
if |xs| == 1 {
} else {
LemmaMaxO... |
libraries | 76 | ./src/Collections/Sequences/Seq.dfy | SortedUnique_fix_76.dfy | SortedUnique | lemma SortedUnique<T>(xs: seq<T>, ys: seq<T>, R: (T, T) -> bool)
requires SortedBy(xs, R)
requires SortedBy(ys, R)
requires TotalOrdering(R)
requires multiset(xs) == multiset(ys)
ensures xs == ys
{
assert |xs| == |multiset(xs)| == |multiset(ys)| == |ys|;
if xs == [] || ys == [] {
} e... | lemma SortedUnique<T>(xs: seq<T>, ys: seq<T>, R: (T, T) -> bool)
requires SortedBy(xs, R)
requires SortedBy(ys, R)
requires TotalOrdering(R)
requires multiset(xs) == multiset(ys)
ensures xs == ys
{
assert |xs| == |multiset(xs)| == |multiset(ys)| == |ys|;
if xs == [] || ys == [] {
} e... |
libraries | 77 | ./src/Collections/Sequences/Seq.dfy | SortedUnique_fix_77.dfy | SortedUnique | lemma SortedUnique<T>(xs: seq<T>, ys: seq<T>, R: (T, T) -> bool)
requires SortedBy(xs, R)
requires SortedBy(ys, R)
requires TotalOrdering(R)
requires multiset(xs) == multiset(ys)
ensures xs == ys
{
assert |xs| == |multiset(xs)| == |multiset(ys)| == |ys|;
if xs == [] || ys == [] {
} e... | lemma SortedUnique<T>(xs: seq<T>, ys: seq<T>, R: (T, T) -> bool)
requires SortedBy(xs, R)
requires SortedBy(ys, R)
requires TotalOrdering(R)
requires multiset(xs) == multiset(ys)
ensures xs == ys
{
assert |xs| == |multiset(xs)| == |multiset(ys)| == |ys|;
if xs == [] || ys == [] {
} e... |
libraries | 99 | ./src/NonlinearArithmetic/Power2.dfy | LemmaPow2MaskDiv2_fix_99.dfy | LemmaPow2MaskDiv2 | lemma LemmaPow2MaskDiv2(e: nat)
requires 0 < e
ensures (Pow2(e) - 1) / 2 == Pow2(e - 1) - 1
{
LemmaPow2Auto();
LemmaPowAuto();
var f := e => 0 < e ==> (Pow2(e) - 1) / 2 == Pow2(e - 1) - 1;
assert forall i {:trigger IsLe(0, i)} :: IsLe(0, i) && f(i) ==> f(i + 1);
assert forall i {:trigger... | lemma LemmaPow2MaskDiv2(e: nat)
requires 0 < e
ensures (Pow2(e) - 1) / 2 == Pow2(e - 1) - 1
{
LemmaPow2Auto();
LemmaPowAuto();
var f := e => 0 < e ==> (Pow2(e) - 1) / 2 == Pow2(e - 1) - 1;
assert forall i {:trigger IsLe(i, 0)} :: IsLe(i, 0) && f(i) ==> f(i - 1);
LemmaMulInductionAuto... |
libraries | 151 | ./src/NonlinearArithmetic/Internals/GeneralInternals.dfy | LemmaInductionHelper_fix_151.dfy | LemmaInductionHelper | lemma LemmaInductionHelper(n: int, f: int -> bool, x: int)
requires n > 0
requires forall i :: 0 <= i < n ==> f(i)
requires forall i {:trigger f(i), f(i + n)} :: i >= 0 && f(i) ==> f(i + n)
requires forall i {:trigger f(i), f(i - n)} :: i < n && f(i) ==> f(i - n)
ensures f(x)
decreases if x ... | lemma LemmaInductionHelper(n: int, f: int -> bool, x: int)
requires n > 0
requires forall i :: 0 <= i < n ==> f(i)
requires forall i {:trigger f(i), f(i + n)} :: i >= 0 && f(i) ==> f(i + n)
requires forall i {:trigger f(i), f(i - n)} :: i < n && f(i) ==> f(i - n)
ensures f(x)
decreases if x ... |
libraries | 152 | ./src/NonlinearArithmetic/Internals/GeneralInternals.dfy | LemmaInductionHelper_fix_152.dfy | LemmaInductionHelper | lemma LemmaInductionHelper(n: int, f: int -> bool, x: int)
requires n > 0
requires forall i :: 0 <= i < n ==> f(i)
requires forall i {:trigger f(i), f(i + n)} :: i >= 0 && f(i) ==> f(i + n)
requires forall i {:trigger f(i), f(i - n)} :: i < n && f(i) ==> f(i - n)
ensures f(x)
decreases if x ... | lemma LemmaInductionHelper(n: int, f: int -> bool, x: int)
requires n > 0
requires forall i :: 0 <= i < n ==> f(i)
requires forall i {:trigger f(i), f(i + n)} :: i >= 0 && f(i) ==> f(i + n)
requires forall i {:trigger f(i), f(i - n)} :: i < n && f(i) ==> f(i - n)
ensures f(x)
decreases if x ... |
libraries | 153 | ./src/NonlinearArithmetic/Internals/DivInternals.dfy | LemmaDivInductionAutoForall_fix_153.dfy | LemmaDivInductionAutoForall | lemma LemmaDivInductionAutoForall(n:int, f:int->bool)
requires n > 0
requires DivAuto(n) ==> && (forall i {:trigger IsLe(0, i)} :: IsLe(0, i) && i < n ==> f(i))
&& (forall i {:trigger IsLe(0, i)} :: IsLe(0, i) && f(i) ==> f(i + n))
&& (forall i {:trigger... | lemma LemmaDivInductionAutoForall(n:int, f:int->bool)
requires n > 0
requires DivAuto(n) ==> && (forall i {:trigger IsLe(0, i)} :: IsLe(0, i) && i < n ==> f(i))
&& (forall i {:trigger IsLe(0, i)} :: IsLe(0, i) && f(i) ==> f(i + n))
&& (forall i {:trigger... |
libraries | 154 | ./src/NonlinearArithmetic/Internals/DivInternals.dfy | LemmaDivInductionAutoForall_fix_154.dfy | LemmaDivInductionAutoForall | lemma LemmaDivInductionAutoForall(n:int, f:int->bool)
requires n > 0
requires DivAuto(n) ==> && (forall i {:trigger IsLe(0, i)} :: IsLe(0, i) && i < n ==> f(i))
&& (forall i {:trigger IsLe(0, i)} :: IsLe(0, i) && f(i) ==> f(i + n))
&& (forall i {:trigger... | lemma LemmaDivInductionAutoForall(n:int, f:int->bool)
requires n > 0
requires DivAuto(n) ==> && (forall i {:trigger IsLe(0, i)} :: IsLe(0, i) && i < n ==> f(i))
&& (forall i {:trigger IsLe(0, i)} :: IsLe(0, i) && f(i) ==> f(i + n))
&& (forall i {:trigger... |
libraries | 155 | ./src/NonlinearArithmetic/Internals/DivInternals.dfy | LemmaDivInductionAutoForall_fix_155.dfy | LemmaDivInductionAutoForall | lemma LemmaDivInductionAutoForall(n:int, f:int->bool)
requires n > 0
requires DivAuto(n) ==> && (forall i {:trigger IsLe(0, i)} :: IsLe(0, i) && i < n ==> f(i))
&& (forall i {:trigger IsLe(0, i)} :: IsLe(0, i) && f(i) ==> f(i + n))
&& (forall i {:trigger... | lemma LemmaDivInductionAutoForall(n:int, f:int->bool)
requires n > 0
requires DivAuto(n) ==> && (forall i {:trigger IsLe(0, i)} :: IsLe(0, i) && i < n ==> f(i))
&& (forall i {:trigger IsLe(0, i)} :: IsLe(0, i) && f(i) ==> f(i + n))
&& (forall i {:trigger... |
libraries | 156 | ./src/NonlinearArithmetic/Internals/DivInternals.dfy | LemmaDivInductionAuto_fix_156.dfy | LemmaDivInductionAuto | lemma LemmaDivInductionAuto(n: int, x: int, f: int->bool)
requires n > 0
requires DivAuto(n) ==> && (forall i {:trigger IsLe(0, i)} :: IsLe(0, i) && i < n ==> f(i))
&& (forall i {:trigger IsLe(0, i)} :: IsLe(0, i) && f(i) ==> f(i + n))
&& (forall i {:tri... | lemma LemmaDivInductionAuto(n: int, x: int, f: int->bool)
requires n > 0
requires DivAuto(n) ==> && (forall i {:trigger IsLe(0, i)} :: IsLe(0, i) && i < n ==> f(i))
&& (forall i {:trigger IsLe(0, i)} :: IsLe(0, i) && f(i) ==> f(i + n))
&& (forall i {:tri... |
libraries | 157 | ./src/NonlinearArithmetic/Internals/DivInternals.dfy | LemmaDivInductionAuto_fix_157.dfy | LemmaDivInductionAuto | lemma LemmaDivInductionAuto(n: int, x: int, f: int->bool)
requires n > 0
requires DivAuto(n) ==> && (forall i {:trigger IsLe(0, i)} :: IsLe(0, i) && i < n ==> f(i))
&& (forall i {:trigger IsLe(0, i)} :: IsLe(0, i) && f(i) ==> f(i + n))
&& (forall i {:tri... | lemma LemmaDivInductionAuto(n: int, x: int, f: int->bool)
requires n > 0
requires DivAuto(n) ==> && (forall i {:trigger IsLe(0, i)} :: IsLe(0, i) && i < n ==> f(i))
&& (forall i {:trigger IsLe(0, i)} :: IsLe(0, i) && f(i) ==> f(i + n))
&& (forall i {:tri... |
libraries | 158 | ./src/NonlinearArithmetic/Internals/DivInternals.dfy | LemmaDivInductionAuto_fix_158.dfy | LemmaDivInductionAuto | lemma LemmaDivInductionAuto(n: int, x: int, f: int->bool)
requires n > 0
requires DivAuto(n) ==> && (forall i {:trigger IsLe(0, i)} :: IsLe(0, i) && i < n ==> f(i))
&& (forall i {:trigger IsLe(0, i)} :: IsLe(0, i) && f(i) ==> f(i + n))
&& (forall i {:tri... | lemma LemmaDivInductionAuto(n: int, x: int, f: int->bool)
requires n > 0
requires DivAuto(n) ==> && (forall i {:trigger IsLe(0, i)} :: IsLe(0, i) && i < n ==> f(i))
&& (forall i {:trigger IsLe(0, i)} :: IsLe(0, i) && f(i) ==> f(i + n))
&& (forall i {:tri... |
libraries | 170 | ./src/NonlinearArithmetic/Internals/DivInternals.dfy | LemmaDivAuto_fix_170.dfy | LemmaDivAuto | lemma LemmaDivAuto(n: int)
requires n > 0
ensures DivAuto(n)
{
LemmaModAuto(n);
LemmaDivBasics(n);
assert (0 + n) / n == 1;
assert (0 - n) / n == -1;
forall x:int, y:int {:trigger (x + y) / n}
ensures var z := (x % n) + (y % n);
(|| (0 <= z < n && (x + y) / n == x ... | lemma LemmaDivAuto(n: int)
requires n > 0
ensures DivAuto(n)
{
LemmaModAuto(n);
LemmaDivBasics(n);
assert (0 + n) / n == 1;
assert (0 - n) / n == -1;
forall x:int, y:int {:trigger (x + y) / n}
ensures var z := (x % n) + (y % n);
(|| (0 <= z < n && (x + y) / n == x ... |
libraries | 180 | ./src/NonlinearArithmetic/Internals/MulInternals.dfy | LemmaMulInductionAutoForall_fix_180.dfy | LemmaMulInductionAutoForall | lemma LemmaMulInductionAutoForall(f: int -> bool)
requires MulAuto() ==> f(0)
&& (forall i {:trigger IsLe(0, i)} :: IsLe(0, i) && f(i) ==> f(i + 1))
&& (forall i {:trigger IsLe(i, 0)} :: IsLe(i, 0) && f(i) ==> f(i - 1))
ensures MulAuto()
ensures fora... | lemma LemmaMulInductionAutoForall(f: int -> bool)
requires MulAuto() ==> f(0)
&& (forall i {:trigger IsLe(0, i)} :: IsLe(0, i) && f(i) ==> f(i + 1))
&& (forall i {:trigger IsLe(i, 0)} :: IsLe(i, 0) && f(i) ==> f(i - 1))
ensures MulAuto()
ensures fora... |
libraries | 181 | ./src/NonlinearArithmetic/Internals/MulInternals.dfy | LemmaMulInductionAutoForall_fix_181.dfy | LemmaMulInductionAutoForall | lemma LemmaMulInductionAutoForall(f: int -> bool)
requires MulAuto() ==> f(0)
&& (forall i {:trigger IsLe(0, i)} :: IsLe(0, i) && f(i) ==> f(i + 1))
&& (forall i {:trigger IsLe(i, 0)} :: IsLe(i, 0) && f(i) ==> f(i - 1))
ensures MulAuto()
ensures fora... | lemma LemmaMulInductionAutoForall(f: int -> bool)
requires MulAuto() ==> f(0)
&& (forall i {:trigger IsLe(0, i)} :: IsLe(0, i) && f(i) ==> f(i + 1))
&& (forall i {:trigger IsLe(i, 0)} :: IsLe(i, 0) && f(i) ==> f(i - 1))
ensures MulAuto()
ensures fora... |
libraries | 182 | ./src/NonlinearArithmetic/Internals/MulInternals.dfy | LemmaMulInductionAuto_fix_182.dfy | LemmaMulInductionAuto | lemma LemmaMulInductionAuto(x: int, f: int -> bool)
requires MulAuto() ==> f(0)
&& (forall i {:trigger IsLe(0, i)} :: IsLe(0, i) && f(i) ==> f(i + 1))
&& (forall i {:trigger IsLe(i, 0)} :: IsLe(i, 0) && f(i) ==> f(i - 1))
ensures MulAuto()
ensures f(... | lemma LemmaMulInductionAuto(x: int, f: int -> bool)
requires MulAuto() ==> f(0)
&& (forall i {:trigger IsLe(0, i)} :: IsLe(0, i) && f(i) ==> f(i + 1))
&& (forall i {:trigger IsLe(i, 0)} :: IsLe(i, 0) && f(i) ==> f(i - 1))
ensures MulAuto()
ensures f(... |
libraries | 183 | ./src/NonlinearArithmetic/Internals/MulInternals.dfy | LemmaMulInductionAuto_fix_183.dfy | LemmaMulInductionAuto | lemma LemmaMulInductionAuto(x: int, f: int -> bool)
requires MulAuto() ==> f(0)
&& (forall i {:trigger IsLe(0, i)} :: IsLe(0, i) && f(i) ==> f(i + 1))
&& (forall i {:trigger IsLe(i, 0)} :: IsLe(i, 0) && f(i) ==> f(i - 1))
ensures MulAuto()
ensures f(... | lemma LemmaMulInductionAuto(x: int, f: int -> bool)
requires MulAuto() ==> f(0)
&& (forall i {:trigger IsLe(0, i)} :: IsLe(0, i) && f(i) ==> f(i + 1))
&& (forall i {:trigger IsLe(i, 0)} :: IsLe(i, 0) && f(i) ==> f(i - 1))
ensures MulAuto()
ensures f(... |
libraries | 185 | ./src/NonlinearArithmetic/Internals/MulInternals.dfy | LemmaMulDistributes_fix_185.dfy | LemmaMulDistributes | lemma LemmaMulDistributes()
ensures forall x:int, y:int, z:int {:trigger (x + y) * z} :: (x + y) * z == x * z + y * z
ensures forall x:int, y:int, z:int {:trigger (x - y) * z} :: (x - y) * z == x * z - y * z
{
LemmaMulSuccessor();
forall x:int, y:int, z:int
ensures (x + y) * z == x * z + y * z... | lemma LemmaMulDistributes()
ensures forall x:int, y:int, z:int {:trigger (x + y) * z} :: (x + y) * z == x * z + y * z
ensures forall x:int, y:int, z:int {:trigger (x - y) * z} :: (x - y) * z == x * z - y * z
{
LemmaMulSuccessor();
forall x:int, y:int, z:int
ensures (x + y) * z == x * z + y * z... |
libraries | 186 | ./src/NonlinearArithmetic/Internals/MulInternals.dfy | LemmaMulDistributes_fix_186.dfy | LemmaMulDistributes | lemma LemmaMulDistributes()
ensures forall x:int, y:int, z:int {:trigger (x + y) * z} :: (x + y) * z == x * z + y * z
ensures forall x:int, y:int, z:int {:trigger (x - y) * z} :: (x - y) * z == x * z - y * z
{
LemmaMulSuccessor();
forall x:int, y:int, z:int
ensures (x + y) * z == x * z + y * z... | lemma LemmaMulDistributes()
ensures forall x:int, y:int, z:int {:trigger (x + y) * z} :: (x + y) * z == x * z + y * z
ensures forall x:int, y:int, z:int {:trigger (x - y) * z} :: (x - y) * z == x * z - y * z
{
LemmaMulSuccessor();
forall x:int, y:int, z:int
ensures (x + y) * z == x * z + y * z... |
libraries | 187 | ./src/NonlinearArithmetic/Internals/MulInternals.dfy | LemmaMulDistributes_fix_187.dfy | LemmaMulDistributes | lemma LemmaMulDistributes()
ensures forall x:int, y:int, z:int {:trigger (x + y) * z} :: (x + y) * z == x * z + y * z
ensures forall x:int, y:int, z:int {:trigger (x - y) * z} :: (x - y) * z == x * z - y * z
{
LemmaMulSuccessor();
forall x:int, y:int, z:int
ensures (x + y) * z == x * z + y * z... | lemma LemmaMulDistributes()
ensures forall x:int, y:int, z:int {:trigger (x + y) * z} :: (x + y) * z == x * z + y * z
ensures forall x:int, y:int, z:int {:trigger (x - y) * z} :: (x - y) * z == x * z - y * z
{
LemmaMulSuccessor();
forall x:int, y:int, z:int
ensures (x + y) * z == x * z + y * z... |
libraries | 188 | ./src/NonlinearArithmetic/Internals/MulInternals.dfy | LemmaMulDistributes_fix_188.dfy | LemmaMulDistributes | lemma LemmaMulDistributes()
ensures forall x:int, y:int, z:int {:trigger (x + y) * z} :: (x + y) * z == x * z + y * z
ensures forall x:int, y:int, z:int {:trigger (x - y) * z} :: (x - y) * z == x * z - y * z
{
LemmaMulSuccessor();
forall x:int, y:int, z:int
ensures (x + y) * z == x * z + y * z... | lemma LemmaMulDistributes()
ensures forall x:int, y:int, z:int {:trigger (x + y) * z} :: (x + y) * z == x * z + y * z
ensures forall x:int, y:int, z:int {:trigger (x - y) * z} :: (x - y) * z == x * z - y * z
{
LemmaMulSuccessor();
forall x:int, y:int, z:int
ensures (x + y) * z == x * z + y * z... |
libraries | 189 | ./src/NonlinearArithmetic/Internals/MulInternals.dfy | LemmaMulDistributes_fix_189.dfy | LemmaMulDistributes | lemma LemmaMulDistributes()
ensures forall x:int, y:int, z:int {:trigger (x + y) * z} :: (x + y) * z == x * z + y * z
ensures forall x:int, y:int, z:int {:trigger (x - y) * z} :: (x - y) * z == x * z - y * z
{
LemmaMulSuccessor();
forall x:int, y:int, z:int
ensures (x + y) * z == x * z + y * z... | lemma LemmaMulDistributes()
ensures forall x:int, y:int, z:int {:trigger (x + y) * z} :: (x + y) * z == x * z + y * z
ensures forall x:int, y:int, z:int {:trigger (x - y) * z} :: (x - y) * z == x * z - y * z
{
LemmaMulSuccessor();
forall x:int, y:int, z:int
ensures (x + y) * z == x * z + y * z... |
libraries | 190 | ./src/NonlinearArithmetic/Internals/MulInternals.dfy | LemmaMulDistributes_fix_190.dfy | LemmaMulDistributes | lemma LemmaMulDistributes()
ensures forall x:int, y:int, z:int {:trigger (x + y) * z} :: (x + y) * z == x * z + y * z
ensures forall x:int, y:int, z:int {:trigger (x - y) * z} :: (x - y) * z == x * z - y * z
{
LemmaMulSuccessor();
forall x:int, y:int, z:int
ensures (x + y) * z == x * z + y * z... | lemma LemmaMulDistributes()
ensures forall x:int, y:int, z:int {:trigger (x + y) * z} :: (x + y) * z == x * z + y * z
ensures forall x:int, y:int, z:int {:trigger (x - y) * z} :: (x - y) * z == x * z - y * z
{
LemmaMulSuccessor();
forall x:int, y:int, z:int
ensures (x + y) * z == x * z + y * z... |
libraries | 197 | ./src/NonlinearArithmetic/Internals/ModInternals.dfy | LemmaModInductionAuto_fix_197.dfy | LemmaModInductionAuto | lemma LemmaModInductionAuto(n: int, x: int, f: int -> bool)
requires n > 0
requires ModAuto(n) ==> && (forall i {:trigger IsLe(0, i)} :: IsLe(0, i) && i < n ==> f(i))
&& (forall i {:trigger IsLe(0, i)} :: IsLe(0, i) && f(i) ==> f(i + n))
&& (forall i {:t... | lemma LemmaModInductionAuto(n: int, x: int, f: int -> bool)
requires n > 0
requires ModAuto(n) ==> && (forall i {:trigger IsLe(0, i)} :: IsLe(0, i) && i < n ==> f(i))
&& (forall i {:trigger IsLe(0, i)} :: IsLe(0, i) && f(i) ==> f(i + n))
&& (forall i {:t... |
libraries | 199 | ./src/NonlinearArithmetic/Internals/ModInternals.dfy | LemmaModInductionForall2_fix_199.dfy | LemmaModInductionForall2 | lemma LemmaModInductionForall2(n: int, f:(int, int)->bool)
requires n > 0
requires forall i, j :: 0 <= i < n && 0 <= j < n ==> f(i, j)
requires forall i, j {:trigger f(i, j), f(i + n, j)} :: i >= 0 && f(i, j) ==> f(i + n, j)
requires forall i, j {:trigger f(i, j), f(i, j + n)} :: j >= 0 && f(i, j) ==>... | lemma LemmaModInductionForall2(n: int, f:(int, int)->bool)
requires n > 0
requires forall i, j :: 0 <= i < n && 0 <= j < n ==> f(i, j)
requires forall i, j {:trigger f(i, j), f(i + n, j)} :: i >= 0 && f(i, j) ==> f(i + n, j)
requires forall i, j {:trigger f(i, j), f(i, j + n)} :: j >= 0 && f(i, j) ==>... |
libraries | 200 | ./src/NonlinearArithmetic/Internals/ModInternals.dfy | LemmaModInductionForall2_fix_200.dfy | LemmaModInductionForall2 | lemma LemmaModInductionForall2(n: int, f:(int, int)->bool)
requires n > 0
requires forall i, j :: 0 <= i < n && 0 <= j < n ==> f(i, j)
requires forall i, j {:trigger f(i, j), f(i + n, j)} :: i >= 0 && f(i, j) ==> f(i + n, j)
requires forall i, j {:trigger f(i, j), f(i, j + n)} :: j >= 0 && f(i, j) ==>... | lemma LemmaModInductionForall2(n: int, f:(int, int)->bool)
requires n > 0
requires forall i, j :: 0 <= i < n && 0 <= j < n ==> f(i, j)
requires forall i, j {:trigger f(i, j), f(i + n, j)} :: i >= 0 && f(i, j) ==> f(i + n, j)
requires forall i, j {:trigger f(i, j), f(i, j + n)} :: j >= 0 && f(i, j) ==>... |
libraries | 201 | ./src/NonlinearArithmetic/Internals/ModInternals.dfy | LemmaModInductionAutoForall_fix_201.dfy | LemmaModInductionAutoForall | lemma LemmaModInductionAutoForall(n: int, f: int -> bool)
requires n > 0
requires ModAuto(n) ==> && (forall i {:trigger IsLe(0, i)} :: IsLe(0, i) && i < n ==> f(i))
&& (forall i {:trigger IsLe(0, i)} :: IsLe(0, i) && f(i) ==> f(i + n))
&& (forall i {:tri... | lemma LemmaModInductionAutoForall(n: int, f: int -> bool)
requires n > 0
requires ModAuto(n) ==> && (forall i {:trigger IsLe(0, i)} :: IsLe(0, i) && i < n ==> f(i))
&& (forall i {:trigger IsLe(0, i)} :: IsLe(0, i) && f(i) ==> f(i + n))
&& (forall i {:tri... |
libraries | 202 | ./src/NonlinearArithmetic/Internals/ModInternals.dfy | LemmaModInductionAutoForall_fix_202.dfy | LemmaModInductionAutoForall | lemma LemmaModInductionAutoForall(n: int, f: int -> bool)
requires n > 0
requires ModAuto(n) ==> && (forall i {:trigger IsLe(0, i)} :: IsLe(0, i) && i < n ==> f(i))
&& (forall i {:trigger IsLe(0, i)} :: IsLe(0, i) && f(i) ==> f(i + n))
&& (forall i {:tri... | lemma LemmaModInductionAutoForall(n: int, f: int -> bool)
requires n > 0
requires ModAuto(n) ==> && (forall i {:trigger IsLe(0, i)} :: IsLe(0, i) && i < n ==> f(i))
&& (forall i {:trigger IsLe(0, i)} :: IsLe(0, i) && f(i) ==> f(i + n))
&& (forall i {:tri... |
libraries | 203 | ./src/NonlinearArithmetic/Internals/ModInternals.dfy | LemmaModInductionAutoForall_fix_203.dfy | LemmaModInductionAutoForall | lemma LemmaModInductionAutoForall(n: int, f: int -> bool)
requires n > 0
requires ModAuto(n) ==> && (forall i {:trigger IsLe(0, i)} :: IsLe(0, i) && i < n ==> f(i))
&& (forall i {:trigger IsLe(0, i)} :: IsLe(0, i) && f(i) ==> f(i + n))
&& (forall i {:tri... | lemma LemmaModInductionAutoForall(n: int, f: int -> bool)
requires n > 0
requires ModAuto(n) ==> && (forall i {:trigger IsLe(0, i)} :: IsLe(0, i) && i < n ==> f(i))
&& (forall i {:trigger IsLe(0, i)} :: IsLe(0, i) && f(i) ==> f(i + n))
&& (forall i {:tri... |
libraries | 204 | ./src/Unicode/UnicodeEncodingForm.dfy | LemmaSplitPrefixMinimalWellFormedCodeUnitSubsequenceInvertsPrepend_fix_204.dfy | LemmaSplitPrefixMinimalWellFormedCodeUnitSubsequenceInvertsPrepend | lemma LemmaSplitPrefixMinimalWellFormedCodeUnitSubsequenceInvertsPrepend(m: MinimalWellFormedCodeUnitSeq, s: CodeUnitSeq)
ensures SplitPrefixMinimalWellFormedCodeUnitSubsequence(m + s) == Some(m)
{
var ms := m + s;
assert IsMinimalWellFormedCodeUnitSubsequence(ms[..|m|]);
var prefix := SplitPrefixMi... | lemma LemmaSplitPrefixMinimalWellFormedCodeUnitSubsequenceInvertsPrepend(m: MinimalWellFormedCodeUnitSeq, s: CodeUnitSeq)
ensures SplitPrefixMinimalWellFormedCodeUnitSubsequence(m + s) == Some(m)
{
var ms := m + s;
var prefix := SplitPrefixMinimalWellFormedCodeUnitSubsequence(ms).Extract();
calc... |
libraries | 211 | ./src/dafny/BinaryOperations.dfy | MonoidInverseIsUnique_fix_211.dfy | MonoidInverseIsUnique | lemma MonoidInverseIsUnique<T(!new)>(m: Monoid<T>, inverse1: T -> T, inverse2: T -> T)
requires IsInverse(m.bop, inverse1, m.unit)
requires IsInverse(m.bop, inverse2, m.unit)
ensures forall x :: inverse1(x) == inverse2(x)
{
assert IsMonoid(m.bop, m.unit);
forall x ensures inverse1(x) == inverse2... | lemma MonoidInverseIsUnique<T(!new)>(m: Monoid<T>, inverse1: T -> T, inverse2: T -> T)
requires IsInverse(m.bop, inverse1, m.unit)
requires IsInverse(m.bop, inverse2, m.unit)
ensures forall x :: inverse1(x) == inverse2(x)
{
forall x ensures inverse1(x) == inverse2(x) {
calc {
inver... |
libraries | 378 | ./src/dafny/NonlinearArithmetic/Internals/ModInternals.dfy | LemmaModInductionAuto_fix_378.dfy | LemmaModInductionAuto | lemma LemmaModInductionAuto(n: int, x: int, f: int -> bool)
requires n > 0
requires ModAuto(n) ==> && (forall i {:trigger IsLe(0, i)} :: IsLe(0, i) && i < n ==> f(i))
&& (forall i {:trigger IsLe(0, i)} :: IsLe(0, i) && f(i) ==> f(i + n))
&& (forall i {:t... | lemma LemmaModInductionAuto(n: int, x: int, f: int -> bool)
requires n > 0
requires ModAuto(n) ==> && (forall i {:trigger IsLe(0, i)} :: IsLe(0, i) && i < n ==> f(i))
&& (forall i {:trigger IsLe(0, i)} :: IsLe(0, i) && f(i) ==> f(i + n))
&& (forall i {:t... |
libraries | 379 | ./src/dafny/NonlinearArithmetic/Internals/ModInternals.dfy | LemmaModInductionAuto_fix_379.dfy | LemmaModInductionAuto | lemma LemmaModInductionAuto(n: int, x: int, f: int -> bool)
requires n > 0
requires ModAuto(n) ==> && (forall i {:trigger IsLe(0, i)} :: IsLe(0, i) && i < n ==> f(i))
&& (forall i {:trigger IsLe(0, i)} :: IsLe(0, i) && f(i) ==> f(i + n))
&& (forall i {:t... | lemma LemmaModInductionAuto(n: int, x: int, f: int -> bool)
requires n > 0
requires ModAuto(n) ==> && (forall i {:trigger IsLe(0, i)} :: IsLe(0, i) && i < n ==> f(i))
&& (forall i {:trigger IsLe(0, i)} :: IsLe(0, i) && f(i) ==> f(i + n))
&& (forall i {:t... |
cedar | 891 | ./cedar-dafny/def/ext/ipaddr.dfy | CountDCComp_fix_891.dfy | CountDCComp | lemma CountDCComp(l: seq<SegV6>, r: seq<SegV6>)
ensures countDC(l+r) == countDC(l)+countDC(r)
{
if |l| == 0 {
assert l + r == r;
} else {
assert l + r == [l[0]] + (l[1..] + r);
}
}
| lemma CountDCComp(l: seq<SegV6>, r: seq<SegV6>)
ensures countDC(l+r) == countDC(l)+countDC(r)
{
if |l| == 0 {
} else {
assert l + r == [l[0]] + (l[1..] + r);
}
}
|
cedar | 443 | ./cedar-dafny/validation/thm/soundness.dfy | SoundEqAuxDiffUids_fix_443.dfy | SoundEqAuxDiffUids | lemma SoundEqAuxDiffUids(u1: EntityUID, u2: EntityUID, t: Type, effs: Effects)
requires Typesafe(BinaryApp(BinaryOp.Eq,PrimitiveLit(Primitive.EntityUID(u1)),PrimitiveLit(Primitive.EntityUID(u2))),effs,t)
requires u1 != u2
ensures IsSafe(r,s,BinaryApp(BinaryOp.Eq,PrimitiveLit(Primitive.EntityUID(u1... | lemma SoundEqAuxDiffUids(u1: EntityUID, u2: EntityUID, t: Type, effs: Effects)
requires Typesafe(BinaryApp(BinaryOp.Eq,PrimitiveLit(Primitive.EntityUID(u1)),PrimitiveLit(Primitive.EntityUID(u2))),effs,t)
requires u1 != u2
ensures IsSafe(r,s,BinaryApp(BinaryOp.Eq,PrimitiveLit(Primitive.EntityUID(u1... |
cedar | 104 | ./cedar-dafny/validation/thm/model.dfy | OrRShortSafe_fix_104.dfy | OrRShortSafe | lemma OrRShortSafe(r: Request, s: EntityStore, e: Expr, e': Expr)
requires IsSafe(r,s,e,Type.Bool(AnyBool))
requires IsTrue(r,s,e')
ensures IsTrue(r,s,Or(e,e'))
{
reveal IsSafe();
if Evaluate(e,r,s).Ok? && Evaluate(e',r,s).Ok? {
assert Evaluate(e',r,s) == base.Ok(Value.Primitive(Primitive.... | lemma OrRShortSafe(r: Request, s: EntityStore, e: Expr, e': Expr)
requires IsSafe(r,s,e,Type.Bool(AnyBool))
requires IsTrue(r,s,e')
ensures IsTrue(r,s,Or(e,e'))
{
reveal IsSafe();
if Evaluate(e,r,s).Ok? && Evaluate(e',r,s).Ok? {
assert Evaluate(e',r,s) == base.Ok(Value.Primitive(Primitive.... |
cedar | 854 | ./cedar-dafny/validation/thm/strict_soundness.dfy | StrictGetLubRecordType_fix_854.dfy | StrictGetLubRecordType | lemma StrictGetLubRecordType(lub: EntityLUB)
requires ets.getLubRecordType(lub, ValidationMode.Strict).Ok?
ensures ets.getLubRecordType(lub, ValidationMode.Permissive) == ets.getLubRecordType(lub, ValidationMode.Strict)
{
if lub.AnyEntity? || exists et <- lub.tys :: isAction(et) {
asse... | lemma StrictGetLubRecordType(lub: EntityLUB)
requires ets.getLubRecordType(lub, ValidationMode.Strict).Ok?
ensures ets.getLubRecordType(lub, ValidationMode.Permissive) == ets.getLubRecordType(lub, ValidationMode.Strict)
{
if lub.AnyEntity? || exists et <- lub.tys :: isAction(et) {
... |
cedar | 94 | ./cedar-dafny/validation/thm/model.dfy | OrRRetSafe_fix_94.dfy | OrRRetSafe | lemma OrRRetSafe(r: Request, s: EntityStore, e: Expr, e': Expr, t: Type)
requires IsFalse(r,s,e)
requires IsSafe(r,s,e',t)
requires SemanticSubty(t,Type.Bool(AnyBool))
ensures IsSafe(r,s,Or(e,e'),t)
{
reveal IsSafe();
if Evaluate(e,r,s).Ok? && Evaluate(e',r,s).Ok? {
assert Evaluate(e,r... | lemma OrRRetSafe(r: Request, s: EntityStore, e: Expr, e': Expr, t: Type)
requires IsFalse(r,s,e)
requires IsSafe(r,s,e',t)
requires SemanticSubty(t,Type.Bool(AnyBool))
ensures IsSafe(r,s,Or(e,e'),t)
{
reveal IsSafe();
if Evaluate(e,r,s).Ok? && Evaluate(e',r,s).Ok? {
assert Evaluate(e,r... |
cedar | 109 | ./cedar-dafny/validation/thm/model.dfy | OrRShortSafe_fix_109.dfy | OrRShortSafe | lemma OrRShortSafe(r: Request, s: EntityStore, e: Expr, e': Expr)
requires IsSafe(r,s,e,Type.Bool(AnyBool))
requires IsTrue(r,s,e')
ensures IsTrue(r,s,Or(e,e'))
{
reveal IsSafe();
if Evaluate(e,r,s).Ok? && Evaluate(e',r,s).Ok? {
assert Evaluate(e',r,s) == base.Ok(Value.Primitive(Primitive.... | lemma OrRShortSafe(r: Request, s: EntityStore, e: Expr, e': Expr)
requires IsSafe(r,s,e,Type.Bool(AnyBool))
requires IsTrue(r,s,e')
ensures IsTrue(r,s,Or(e,e'))
{
reveal IsSafe();
if Evaluate(e,r,s).Ok? && Evaluate(e',r,s).Ok? {
assert Evaluate(e',r,s) == base.Ok(Value.Primitive(Primitive.... |
cedar | 82 | ./cedar-dafny/validation/thm/model.dfy | AndRShortSafe_fix_82.dfy | AndRShortSafe | lemma AndRShortSafe(r: Request, s: EntityStore, e: Expr, e': Expr)
requires IsSafe(r,s,e,Type.Bool(AnyBool))
requires IsFalse(r,s,e')
ensures IsFalse(r,s,And(e,e'))
{
reveal IsSafe();
if Evaluate(e,r,s).Ok? && Evaluate(e',r,s).Ok? {
assert Evaluate(e',r,s) == base.Ok(Value.Primitive(Primit... | lemma AndRShortSafe(r: Request, s: EntityStore, e: Expr, e': Expr)
requires IsSafe(r,s,e,Type.Bool(AnyBool))
requires IsFalse(r,s,e')
ensures IsFalse(r,s,And(e,e'))
{
reveal IsSafe();
if Evaluate(e,r,s).Ok? && Evaluate(e',r,s).Ok? {
assert Evaluate(e',r,s) == base.Ok(Value.Primitive(Primit... |
cedar | 788 | ./cedar-dafny/validation/thm/soundness.dfy | SoundArith_fix_788.dfy | SoundArith | lemma SoundArith(op: BinaryOp, e1: Expr, e2: Expr, t: Type, effs: Effects)
decreases BinaryApp(op,e1,e2) , 0
requires op == Add || op == Sub
requires WellFormedRequestAndStore()
requires EffectsInvariant(effs)
requires Typesafe(BinaryApp(op,e1,e2),effs,t)
ensures IsSafe(r,s,Binar... | lemma SoundArith(op: BinaryOp, e1: Expr, e2: Expr, t: Type, effs: Effects)
decreases BinaryApp(op,e1,e2) , 0
requires op == Add || op == Sub
requires WellFormedRequestAndStore()
requires EffectsInvariant(effs)
requires Typesafe(BinaryApp(op,e1,e2),effs,t)
ensures IsSafe(r,s,Binar... |
cedar | 816 | ./cedar-dafny/validation/thm/soundness.dfy | SoundInSetMemberFalse_fix_816.dfy | SoundInSetMemberFalse | lemma SoundInSetMemberFalse(e1: Expr, ei2s: seq<Expr>, i: nat, effs: Effects)
decreases BinaryApp(BinaryOp.In,e1,Expr.Set(ei2s)) , 0 , Expr.Set(ei2s) , 0
requires WellFormedRequestAndStore()
requires EffectsInvariant(effs)
requires WellTyped(BinaryApp(BinaryOp.In,e1,Expr.Set(ei2s)),effs)
... | lemma SoundInSetMemberFalse(e1: Expr, ei2s: seq<Expr>, i: nat, effs: Effects)
decreases BinaryApp(BinaryOp.In,e1,Expr.Set(ei2s)) , 0 , Expr.Set(ei2s) , 0
requires WellFormedRequestAndStore()
requires EffectsInvariant(effs)
requires WellTyped(BinaryApp(BinaryOp.In,e1,Expr.Set(ei2s)),effs)
... |
cedar | 797 | ./cedar-dafny/validation/thm/soundness.dfy | SoundIneq_fix_797.dfy | SoundIneq | lemma SoundIneq(op: BinaryOp, e1: Expr, e2: Expr, t: Type, effs: Effects)
decreases BinaryApp(op,e1,e2) , 0
requires op == Less || op == BinaryOp.LessEq
requires WellFormedRequestAndStore()
requires EffectsInvariant(effs)
requires Typesafe(BinaryApp(op,e1,e2),effs,t)
ensures IsSa... | lemma SoundIneq(op: BinaryOp, e1: Expr, e2: Expr, t: Type, effs: Effects)
decreases BinaryApp(op,e1,e2) , 0
requires op == Less || op == BinaryOp.LessEq
requires WellFormedRequestAndStore()
requires EffectsInvariant(effs)
requires Typesafe(BinaryApp(op,e1,e2),effs,t)
ensures IsSa... |
cedar | 857 | ./cedar-dafny/validation/thm/strict_soundness.dfy | StrictGetLubRecordType_fix_857.dfy | StrictGetLubRecordType | lemma StrictGetLubRecordType(lub: EntityLUB)
requires ets.getLubRecordType(lub, ValidationMode.Strict).Ok?
ensures ets.getLubRecordType(lub, ValidationMode.Permissive) == ets.getLubRecordType(lub, ValidationMode.Strict)
{
if lub.AnyEntity? || exists et <- lub.tys :: isAction(et) {
asse... | lemma StrictGetLubRecordType(lub: EntityLUB)
requires ets.getLubRecordType(lub, ValidationMode.Strict).Ok?
ensures ets.getLubRecordType(lub, ValidationMode.Permissive) == ets.getLubRecordType(lub, ValidationMode.Strict)
{
if lub.AnyEntity? || exists et <- lub.tys :: isAction(et) {
asse... |
cedar | 2 | ./cedar-dafny/validation/subtyping.dfy | StrictSubtyIsStrict_fix_2.dfy | StrictSubtyIsStrict | lemma StrictSubtyIsStrict(t1: Type, t2: Type)
requires subty(t1, t2, ValidationMode.Strict)
ensures subty(t1, t2, ValidationMode.Permissive)
{
match (t1,t2) {
case (Record(rt1),Record(rt2)) => {
if(rt2.attrs.Keys <= rt1.attrs.Keys) {
if ! (forall k | k in rt2.attrs.Keys :: subty... | lemma StrictSubtyIsStrict(t1: Type, t2: Type)
requires subty(t1, t2, ValidationMode.Strict)
ensures subty(t1, t2, ValidationMode.Permissive)
{
match (t1,t2) {
case (Record(rt1),Record(rt2)) => {
if(rt2.attrs.Keys <= rt1.attrs.Keys) {
if ! (forall k | k in rt2.attrs.Keys :: subty... |
cedar | 856 | ./cedar-dafny/validation/thm/strict_soundness.dfy | StrictGetLubRecordType_fix_856.dfy | StrictGetLubRecordType | lemma StrictGetLubRecordType(lub: EntityLUB)
requires ets.getLubRecordType(lub, ValidationMode.Strict).Ok?
ensures ets.getLubRecordType(lub, ValidationMode.Permissive) == ets.getLubRecordType(lub, ValidationMode.Strict)
{
if lub.AnyEntity? || exists et <- lub.tys :: isAction(et) {
asse... | lemma StrictGetLubRecordType(lub: EntityLUB)
requires ets.getLubRecordType(lub, ValidationMode.Strict).Ok?
ensures ets.getLubRecordType(lub, ValidationMode.Permissive) == ets.getLubRecordType(lub, ValidationMode.Strict)
{
if lub.AnyEntity? || exists et <- lub.tys :: isAction(et) {
asse... |
cedar | 895 | ./cedar-dafny/def/ext/ipaddr.dfy | CountDC1SepMeansNoDc_fix_895.dfy | CountDC1SepMeansNoDc | lemma CountDC1SepMeansNoDc(segs: seq<SegV6>)
requires countDC(segs) <= 1
ensures findDCIdx(segs).Some? ==> countDC(segs[0..findDCIdx(segs).value]) == 0 && countDC(segs[findDCIdx(segs).value+1..]) == 0
{
var idx := findDCIdx(segs);
if idx.None? {
} else {
assert segs == segs[0..idx.value+1... | lemma CountDC1SepMeansNoDc(segs: seq<SegV6>)
requires countDC(segs) <= 1
ensures findDCIdx(segs).Some? ==> countDC(segs[0..findDCIdx(segs).value]) == 0 && countDC(segs[findDCIdx(segs).value+1..]) == 0
{
var idx := findDCIdx(segs);
if idx.None? {
} else {
assert segs == segs[0..idx.value+1... |
cedar | 772 | ./cedar-dafny/validation/thm/soundness.dfy | SoundOr_fix_772.dfy | SoundOr | lemma SoundOr(e1: Expr, e2: Expr, t: Type, effs: Effects)
decreases Or(e1,e2) , 0
requires WellFormedRequestAndStore()
requires EffectsInvariant(effs)
requires Typesafe(Or(e1,e2),effs,t)
ensures IsSafe(r,s,Or(e1,e2),t)
ensures GuardedEffectsInvariant(Or(e1,e2),getEffects(Or(e1,e2... | lemma SoundOr(e1: Expr, e2: Expr, t: Type, effs: Effects)
decreases Or(e1,e2) , 0
requires WellFormedRequestAndStore()
requires EffectsInvariant(effs)
requires Typesafe(Or(e1,e2),effs,t)
ensures IsSafe(r,s,Or(e1,e2),t)
ensures GuardedEffectsInvariant(Or(e1,e2),getEffects(Or(e1,e2... |
cedar | 46 | ./cedar-dafny/validation/thm/model.dfy | OrTrueStrong_fix_46.dfy | OrTrueStrong | lemma OrTrueStrong(r: Request, s: EntityStore, e1: Expr, e2: Expr)
requires IsTrueStrong(r,s,Or(e1,e2))
ensures IsTrueStrong(r,s,e1) || IsTrueStrong(r,s,e2)
{
reveal IsSafeStrong();
reveal IsSafe();
assert Evaluator(r,s).interpretShortcircuit(Or(e1,e2),e1,e2,true) == base.Ok(Value.Bool(true));
... | lemma OrTrueStrong(r: Request, s: EntityStore, e1: Expr, e2: Expr)
requires IsTrueStrong(r,s,Or(e1,e2))
ensures IsTrueStrong(r,s,e1) || IsTrueStrong(r,s,e2)
{
reveal IsSafeStrong();
reveal IsSafe();
}
|
cedar | 67 | ./cedar-dafny/validation/thm/model.dfy | SubtyCompatMatchPointwise_fix_67.dfy | SubtyCompatMatchPointwise | lemma SubtyCompatMatchPointwise(t: Type, t': Type, v: Value)
requires subty(t,t',ValidationMode.Permissive)
requires InstanceOfType(v,t)
ensures InstanceOfType(v,t')
decreases t
{
match (t,t',v) {
case (Never,_,_) =>
case (String,String,_) =>
case (Int,Int,_) =>
case (Boo... | lemma SubtyCompatMatchPointwise(t: Type, t': Type, v: Value)
requires subty(t,t',ValidationMode.Permissive)
requires InstanceOfType(v,t)
ensures InstanceOfType(v,t')
decreases t
{
match (t,t',v) {
case (Never,_,_) =>
case (String,String,_) =>
case (Int,Int,_) =>
case (Boo... |
cedar | 888 | ./cedar-dafny/def/ext/decimal.dfy | ParseDigitsAndDot_fix_888.dfy | ParseDigitsAndDot | lemma ParseDigitsAndDot(s1: string, s2: string)
requires |s1| > 0
requires forall i | 0 <= i < |s1| :: '0' <= s1[i] <= '9'
ensures ParseDecStr(s1+"."+s2).Some? && ParseDecStr(s1+"."+s2).value.0 == s1 && ParseDecStr(s1+"."+s2).value.1 == "."+s2
{
if |s1| == 1 {
assert (s1+"."+s2)[1..] == "."+s2... | lemma ParseDigitsAndDot(s1: string, s2: string)
requires |s1| > 0
requires forall i | 0 <= i < |s1| :: '0' <= s1[i] <= '9'
ensures ParseDecStr(s1+"."+s2).Some? && ParseDecStr(s1+"."+s2).value.0 == s1 && ParseDecStr(s1+"."+s2).value.1 == "."+s2
{
if |s1| == 1 {
assert (s1+"."+s2)[1..] == "."+s2... |
cedar | 58 | ./cedar-dafny/validation/thm/model.dfy | AndSafe_fix_58.dfy | AndSafe | lemma AndSafe(r: Request, s: EntityStore, e: Expr, e': Expr)
requires IsSafe(r,s,e,Type.Bool(AnyBool))
requires IsSafe(r,s,e',Type.Bool(AnyBool))
ensures IsSafe(r,s,And(e,e'),Type.Bool(AnyBool))
{
reveal IsSafe();
if Evaluate(e,r,s).Ok? && Evaluate(e',r,s).Ok? {
assert Evaluator(r,s).inter... | lemma AndSafe(r: Request, s: EntityStore, e: Expr, e': Expr)
requires IsSafe(r,s,e,Type.Bool(AnyBool))
requires IsSafe(r,s,e',Type.Bool(AnyBool))
ensures IsSafe(r,s,And(e,e'),Type.Bool(AnyBool))
{
reveal IsSafe();
if Evaluate(e,r,s).Ok? && Evaluate(e',r,s).Ok? {
assert Evaluator(r,s).inter... |
cedar | 77 | ./cedar-dafny/validation/thm/model.dfy | AndLRetSafe_fix_77.dfy | AndLRetSafe | lemma AndLRetSafe(r: Request, s: EntityStore, e: Expr, e': Expr, t: Type)
requires IsSafe(r,s,e,t)
requires IsTrue(r,s,e')
requires SemanticSubty(t,Type.Bool(AnyBool))
ensures IsSafe(r,s,And(e,e'),t)
{
reveal IsSafe();
if Evaluate(e,r,s).Ok? && Evaluate(e',r,s).Ok? {
assert Evaluate(e'... | lemma AndLRetSafe(r: Request, s: EntityStore, e: Expr, e': Expr, t: Type)
requires IsSafe(r,s,e,t)
requires IsTrue(r,s,e')
requires SemanticSubty(t,Type.Bool(AnyBool))
ensures IsSafe(r,s,And(e,e'),t)
{
reveal IsSafe();
if Evaluate(e,r,s).Ok? && Evaluate(e',r,s).Ok? {
assert Evaluate(e'... |
cedar | 756 | ./cedar-dafny/validation/thm/soundness.dfy | SoundIf_fix_756.dfy | SoundIf | lemma SoundIf(e: Expr, e1: Expr, e2: Expr, t: Type, effs: Effects)
decreases If(e,e1,e2) , 0
requires WellFormedRequestAndStore()
requires EffectsInvariant(effs)
requires Typesafe(If(e,e1,e2),effs,t)
ensures IsSafe(r,s,If(e,e1,e2),t)
ensures GuardedEffectsInvariant(If(e,e1,e2),ge... | lemma SoundIf(e: Expr, e1: Expr, e2: Expr, t: Type, effs: Effects)
decreases If(e,e1,e2) , 0
requires WellFormedRequestAndStore()
requires EffectsInvariant(effs)
requires Typesafe(If(e,e1,e2),effs,t)
ensures IsSafe(r,s,If(e,e1,e2),t)
ensures GuardedEffectsInvariant(If(e,e1,e2),ge... |
cedar | 799 | ./cedar-dafny/validation/thm/soundness.dfy | SoundIneq_fix_799.dfy | SoundIneq | lemma SoundIneq(op: BinaryOp, e1: Expr, e2: Expr, t: Type, effs: Effects)
decreases BinaryApp(op,e1,e2) , 0
requires op == Less || op == BinaryOp.LessEq
requires WellFormedRequestAndStore()
requires EffectsInvariant(effs)
requires Typesafe(BinaryApp(op,e1,e2),effs,t)
ensures IsSa... | lemma SoundIneq(op: BinaryOp, e1: Expr, e2: Expr, t: Type, effs: Effects)
decreases BinaryApp(op,e1,e2) , 0
requires op == Less || op == BinaryOp.LessEq
requires WellFormedRequestAndStore()
requires EffectsInvariant(effs)
requires Typesafe(BinaryApp(op,e1,e2),effs,t)
ensures IsSa... |
cedar | 49 | ./cedar-dafny/validation/thm/model.dfy | OrSafe_fix_49.dfy | OrSafe | lemma OrSafe(r: Request, s: EntityStore, e: Expr, e': Expr)
requires IsSafe(r,s,e,Type.Bool(AnyBool))
requires IsSafe(r,s,e',Type.Bool(AnyBool))
ensures IsSafe(r,s,Or(e,e'),Type.Bool(AnyBool))
{
reveal IsSafe();
if Evaluate(e,r,s).Ok? && Evaluate(e',r,s).Ok? {
assert Evaluator(r,s).interpr... | lemma OrSafe(r: Request, s: EntityStore, e: Expr, e': Expr)
requires IsSafe(r,s,e,Type.Bool(AnyBool))
requires IsSafe(r,s,e',Type.Bool(AnyBool))
ensures IsSafe(r,s,Or(e,e'),Type.Bool(AnyBool))
{
reveal IsSafe();
if Evaluate(e,r,s).Ok? && Evaluate(e',r,s).Ok? {
assert Evaluator(r,s).interpr... |
cedar | 92 | ./cedar-dafny/validation/thm/model.dfy | OrRRetSafe_fix_92.dfy | OrRRetSafe | lemma OrRRetSafe(r: Request, s: EntityStore, e: Expr, e': Expr, t: Type)
requires IsFalse(r,s,e)
requires IsSafe(r,s,e',t)
requires SemanticSubty(t,Type.Bool(AnyBool))
ensures IsSafe(r,s,Or(e,e'),t)
{
reveal IsSafe();
if Evaluate(e,r,s).Ok? && Evaluate(e',r,s).Ok? {
assert Evaluate(e,r... | lemma OrRRetSafe(r: Request, s: EntityStore, e: Expr, e': Expr, t: Type)
requires IsFalse(r,s,e)
requires IsSafe(r,s,e',t)
requires SemanticSubty(t,Type.Bool(AnyBool))
ensures IsSafe(r,s,Or(e,e'),t)
{
reveal IsSafe();
if Evaluate(e,r,s).Ok? && Evaluate(e',r,s).Ok? {
assert Evaluate(e,r... |
cedar | 791 | ./cedar-dafny/validation/thm/soundness.dfy | SoundArith_fix_791.dfy | SoundArith | lemma SoundArith(op: BinaryOp, e1: Expr, e2: Expr, t: Type, effs: Effects)
decreases BinaryApp(op,e1,e2) , 0
requires op == Add || op == Sub
requires WellFormedRequestAndStore()
requires EffectsInvariant(effs)
requires Typesafe(BinaryApp(op,e1,e2),effs,t)
ensures IsSafe(r,s,Binar... | lemma SoundArith(op: BinaryOp, e1: Expr, e2: Expr, t: Type, effs: Effects)
decreases BinaryApp(op,e1,e2) , 0
requires op == Add || op == Sub
requires WellFormedRequestAndStore()
requires EffectsInvariant(effs)
requires Typesafe(BinaryApp(op,e1,e2),effs,t)
ensures IsSafe(r,s,Binar... |
cedar | 873 | ./cedar-dafny/thm/eval/basic.dfy | RecordSemanticsOkAttrs_fix_873.dfy | RecordSemanticsOkAttrs | lemma RecordSemanticsOkAttrs(es: seq<(Attr, Expr)>, E: Evaluator)
requires E.interpretRecord(es).Ok?
ensures E.interpretRecord(es).value.Keys == set e | e in es :: e.0
{
if es != [] {
RecordSemanticsOkAttrs(es[1..], E);
var rec' := E.interpretRecord(es[1..]).value;
if es[0].0 in rec'.K... | lemma RecordSemanticsOkAttrs(es: seq<(Attr, Expr)>, E: Evaluator)
requires E.interpretRecord(es).Ok?
ensures E.interpretRecord(es).value.Keys == set e | e in es :: e.0
{
if es != [] {
RecordSemanticsOkAttrs(es[1..], E);
var rec' := E.interpretRecord(es[1..]).value;
if es[0].0 in rec'.K... |
cedar | 45 | ./cedar-dafny/validation/thm/model.dfy | AndTrueStrong_fix_45.dfy | AndTrueStrong | lemma AndTrueStrong(r: Request, s: EntityStore, e1: Expr, e2: Expr)
requires IsTrue(r,s,e1)
requires IsTrueStrong(r,s,And(e1,e2))
ensures IsTrueStrong(r,s,e2)
{
reveal IsSafeStrong();
reveal IsSafe();
assert Evaluator(r,s).interpretShortcircuit(And(e1,e2),e1,e2,false) == base.Ok(Value.Bool(t... | lemma AndTrueStrong(r: Request, s: EntityStore, e1: Expr, e2: Expr)
requires IsTrue(r,s,e1)
requires IsTrueStrong(r,s,And(e1,e2))
ensures IsTrueStrong(r,s,e2)
{
reveal IsSafeStrong();
reveal IsSafe();
}
|
cedar | 750 | ./cedar-dafny/validation/thm/soundness.dfy | SoundLike_fix_750.dfy | SoundLike | lemma SoundLike(e: Expr, p: Pattern, t: Type, effs: Effects)
decreases UnaryApp(Like(p),e) , 0
requires WellFormedRequestAndStore()
requires EffectsInvariant(effs)
requires Typesafe(UnaryApp(Like(p),e),effs,t)
ensures IsSafe(r,s,UnaryApp(Like(p),e),t)
ensures getEffects(UnaryApp(... | lemma SoundLike(e: Expr, p: Pattern, t: Type, effs: Effects)
decreases UnaryApp(Like(p),e) , 0
requires WellFormedRequestAndStore()
requires EffectsInvariant(effs)
requires Typesafe(UnaryApp(Like(p),e),effs,t)
ensures IsSafe(r,s,UnaryApp(Like(p),e),t)
ensures getEffects(UnaryApp(... |
cedar | 820 | ./cedar-dafny/validation/thm/soundness.dfy | SoundInSetMemberFalse_fix_820.dfy | SoundInSetMemberFalse | lemma SoundInSetMemberFalse(e1: Expr, ei2s: seq<Expr>, i: nat, effs: Effects)
decreases BinaryApp(BinaryOp.In,e1,Expr.Set(ei2s)) , 0 , Expr.Set(ei2s) , 0
requires WellFormedRequestAndStore()
requires EffectsInvariant(effs)
requires WellTyped(BinaryApp(BinaryOp.In,e1,Expr.Set(ei2s)),effs)
... | lemma SoundInSetMemberFalse(e1: Expr, ei2s: seq<Expr>, i: nat, effs: Effects)
decreases BinaryApp(BinaryOp.In,e1,Expr.Set(ei2s)) , 0 , Expr.Set(ei2s) , 0
requires WellFormedRequestAndStore()
requires EffectsInvariant(effs)
requires WellTyped(BinaryApp(BinaryOp.In,e1,Expr.Set(ei2s)),effs)
... |
cedar | 862 | ./cedar-dafny/validation/thm/strict_soundness.dfy | StrictIn_fix_862.dfy | StrictIn | lemma StrictIn(e1: Expr, e2: Expr, effs: Effects)
decreases BinaryApp(BinaryOp.In, e1, e2), 0
requires S_TC.infer(BinaryApp(BinaryOp.In, e1, e2), effs).Ok?
ensures P_TC.infer(BinaryApp(BinaryOp.In, e1, e2), effs) == S_TC.infer(BinaryApp(BinaryOp.In, e1, e2), effs)
{
assert S_TC.ensureEnt... | lemma StrictIn(e1: Expr, e2: Expr, effs: Effects)
decreases BinaryApp(BinaryOp.In, e1, e2), 0
requires S_TC.infer(BinaryApp(BinaryOp.In, e1, e2), effs).Ok?
ensures P_TC.infer(BinaryApp(BinaryOp.In, e1, e2), effs) == S_TC.infer(BinaryApp(BinaryOp.In, e1, e2), effs)
{
assert P_TC.ens... |
cedar | 801 | ./cedar-dafny/validation/thm/soundness.dfy | SoundMulBy_fix_801.dfy | SoundMulBy | lemma SoundMulBy(i: int, e: Expr, t: Type, effs: Effects)
decreases UnaryApp(MulBy(i),e) , 0
requires WellFormedRequestAndStore()
requires EffectsInvariant(effs)
requires Typesafe(UnaryApp(MulBy(i),e),effs,t)
ensures IsSafe(r,s,UnaryApp(MulBy(i),e),t)
ensures getEffects(UnaryApp(... | lemma SoundMulBy(i: int, e: Expr, t: Type, effs: Effects)
decreases UnaryApp(MulBy(i),e) , 0
requires WellFormedRequestAndStore()
requires EffectsInvariant(effs)
requires Typesafe(UnaryApp(MulBy(i),e),effs,t)
ensures IsSafe(r,s,UnaryApp(MulBy(i),e),t)
ensures getEffects(UnaryApp(... |
cedar | 883 | ./cedar-dafny/def/util.dfy | SeqAddInequality_fix_883.dfy | SeqAddInequality | lemma SeqAddInequality<T>(s1: seq<T>, t1: T, s2: seq<T>, t2: T)
requires s1 != s2 || t1 != t2
ensures s1 + [t1] != s2 + [t2]
{
if s1 == s2 {
assert t1 != t2;
var len := |s1|;
assert (s1 + [t1])[len] != (s2 + [t2])[len];
} else if |s1| == |s2| {
var i :| 0 <= i < |s1| && s1[i]... | lemma SeqAddInequality<T>(s1: seq<T>, t1: T, s2: seq<T>, t2: T)
requires s1 != s2 || t1 != t2
ensures s1 + [t1] != s2 + [t2]
{
if s1 == s2 {
assert t1 != t2;
var len := |s1|;
assert (s1 + [t1])[len] != (s2 + [t2])[len];
} else if |s1| == |s2| {
var i :| 0 <= i < |s1| && s1[i]... |
cedar | 802 | ./cedar-dafny/validation/thm/soundness.dfy | SoundMulBy_fix_802.dfy | SoundMulBy | lemma SoundMulBy(i: int, e: Expr, t: Type, effs: Effects)
decreases UnaryApp(MulBy(i),e) , 0
requires WellFormedRequestAndStore()
requires EffectsInvariant(effs)
requires Typesafe(UnaryApp(MulBy(i),e),effs,t)
ensures IsSafe(r,s,UnaryApp(MulBy(i),e),t)
ensures getEffects(UnaryApp(... | lemma SoundMulBy(i: int, e: Expr, t: Type, effs: Effects)
decreases UnaryApp(MulBy(i),e) , 0
requires WellFormedRequestAndStore()
requires EffectsInvariant(effs)
requires Typesafe(UnaryApp(MulBy(i),e),effs,t)
ensures IsSafe(r,s,UnaryApp(MulBy(i),e),t)
ensures getEffects(UnaryApp(... |
cedar | 890 | ./cedar-dafny/def/ext/ipaddr.dfy | CountDCLast_fix_890.dfy | CountDCLast | lemma CountDCLast(s: seq<numV6>)
ensures countDC(wrapNumSegs(s)+[DC]) == 1
{
if |s| == 0 {
} else {
assert wrapNumSegs(s)+[DC] == wrapNumSegs([s[0]]) + (wrapNumSegs(s[1..]) + [DC]);
}
}
| lemma CountDCLast(s: seq<numV6>)
ensures countDC(wrapNumSegs(s)+[DC]) == 1
{
if |s| == 0 {
} else {
}
}
|
cedar | 99 | ./cedar-dafny/validation/thm/model.dfy | OrRRetSafe_fix_99.dfy | OrRRetSafe | lemma OrRRetSafe(r: Request, s: EntityStore, e: Expr, e': Expr, t: Type)
requires IsFalse(r,s,e)
requires IsSafe(r,s,e',t)
requires SemanticSubty(t,Type.Bool(AnyBool))
ensures IsSafe(r,s,Or(e,e'),t)
{
reveal IsSafe();
if Evaluate(e,r,s).Ok? && Evaluate(e',r,s).Ok? {
assert Evaluate(e,r... | lemma OrRRetSafe(r: Request, s: EntityStore, e: Expr, e': Expr, t: Type)
requires IsFalse(r,s,e)
requires IsSafe(r,s,e',t)
requires SemanticSubty(t,Type.Bool(AnyBool))
ensures IsSafe(r,s,Or(e,e'),t)
{
reveal IsSafe();
if Evaluate(e,r,s).Ok? && Evaluate(e',r,s).Ok? {
assert Evaluate(e,r... |
cedar | 852 | ./cedar-dafny/validation/thm/strict_inf_strict.dfy | StrictGetAttr_fix_852.dfy | StrictGetAttr | lemma StrictGetAttr(e: Expr, l: Attr, effs:Effects)
decreases GetAttr(e, l), 0
requires strictEnvironment()
requires S_TC.infer(GetAttr(e, l), effs).Ok?
ensures S_TC.infer(GetAttr(e, l), effs).value.0.isStrictType()
{
assert S_TC.inferRecordEntityType(e,effs).Ok?;
StrictTypeI... | lemma StrictGetAttr(e: Expr, l: Attr, effs:Effects)
decreases GetAttr(e, l), 0
requires strictEnvironment()
requires S_TC.infer(GetAttr(e, l), effs).Ok?
ensures S_TC.infer(GetAttr(e, l), effs).value.0.isStrictType()
{
StrictTypeInf(e, effs);
}
|
cedar | 37 | ./cedar-dafny/validation/thm/model.dfy | EqEntityDiffSafe_fix_37.dfy | EqEntityDiffSafe | lemma EqEntityDiffSafe(r: Request, s: EntityStore, E: EntityUID, E': EntityUID)
requires E != E'
ensures IsFalse(r,s,Expr.BinaryApp(BinaryOp.Eq,PrimitiveLit(Primitive.EntityUID(E)),PrimitiveLit(Primitive.EntityUID(E'))))
{
reveal IsSafe();
var e := Expr.BinaryApp(BinaryOp.Eq,PrimitiveLit(Primitive.E... | lemma EqEntityDiffSafe(r: Request, s: EntityStore, E: EntityUID, E': EntityUID)
requires E != E'
ensures IsFalse(r,s,Expr.BinaryApp(BinaryOp.Eq,PrimitiveLit(Primitive.EntityUID(E)),PrimitiveLit(Primitive.EntityUID(E'))))
{
reveal IsSafe();
var e := Expr.BinaryApp(BinaryOp.Eq,PrimitiveLit(Primitive.E... |
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