statement stringlengths 1 15.9k | proof stringlengths 0 44.6k | type stringclasses 18
values | symbolic_name stringlengths 1 61 | library stringclasses 21
values | filename stringclasses 502
values | imports listlengths 0 38 | deps listlengths 0 64 | docstring stringlengths 0 500 | source_url stringclasses 1
value | commit stringclasses 1
value |
|---|---|---|---|---|---|---|---|---|---|---|
of_sbv16 mode BV16.t : t | val function | of_sbv16 | stdlib | stdlib/ieee_float.mlw | [
"Float32",
"Float64",
"Float_BV_Converter",
"GenericFloat",
"RoundingMode",
"bv.BV16",
"bv.BV32",
"bv.BV64",
"bv.BV8",
"bv.Pow2int",
"int.Int",
"real.Abs",
"real.FromInt",
"real.Real",
"real.RealInfix",
"real.Square",
"real.Truncate"
] | [
"mode"
] | https://gitlab.inria.fr/why3/why3 | 7c59064b4eed9a4059292599f3a657716aa34784 | ||
of_sbv32 mode BV32.t : t | val function | of_sbv32 | stdlib | stdlib/ieee_float.mlw | [
"Float32",
"Float64",
"Float_BV_Converter",
"GenericFloat",
"RoundingMode",
"bv.BV16",
"bv.BV32",
"bv.BV64",
"bv.BV8",
"bv.Pow2int",
"int.Int",
"real.Abs",
"real.FromInt",
"real.Real",
"real.RealInfix",
"real.Square",
"real.Truncate"
] | [
"mode"
] | https://gitlab.inria.fr/why3/why3 | 7c59064b4eed9a4059292599f3a657716aa34784 | ||
of_sbv64 mode BV64.t : t | val function | of_sbv64 | stdlib | stdlib/ieee_float.mlw | [
"Float32",
"Float64",
"Float_BV_Converter",
"GenericFloat",
"RoundingMode",
"bv.BV16",
"bv.BV32",
"bv.BV64",
"bv.BV8",
"bv.Pow2int",
"int.Int",
"real.Abs",
"real.FromInt",
"real.Real",
"real.RealInfix",
"real.Square",
"real.Truncate"
] | [
"mode"
] | https://gitlab.inria.fr/why3/why3 | 7c59064b4eed9a4059292599f3a657716aa34784 | ||
to_sbv8 mode BV8.t : t | val function | to_sbv8 | stdlib | stdlib/ieee_float.mlw | [
"Float32",
"Float64",
"Float_BV_Converter",
"GenericFloat",
"RoundingMode",
"bv.BV16",
"bv.BV32",
"bv.BV64",
"bv.BV8",
"bv.Pow2int",
"int.Int",
"real.Abs",
"real.FromInt",
"real.Real",
"real.RealInfix",
"real.Square",
"real.Truncate"
] | [
"mode"
] | convert to signed bitvector | https://gitlab.inria.fr/why3/why3 | 7c59064b4eed9a4059292599f3a657716aa34784 | |
to_sbv16 mode BV16.t : t | val function | to_sbv16 | stdlib | stdlib/ieee_float.mlw | [
"Float32",
"Float64",
"Float_BV_Converter",
"GenericFloat",
"RoundingMode",
"bv.BV16",
"bv.BV32",
"bv.BV64",
"bv.BV8",
"bv.Pow2int",
"int.Int",
"real.Abs",
"real.FromInt",
"real.Real",
"real.RealInfix",
"real.Square",
"real.Truncate"
] | [
"mode"
] | https://gitlab.inria.fr/why3/why3 | 7c59064b4eed9a4059292599f3a657716aa34784 | ||
to_sbv32 mode BV32.t : t | val function | to_sbv32 | stdlib | stdlib/ieee_float.mlw | [
"Float32",
"Float64",
"Float_BV_Converter",
"GenericFloat",
"RoundingMode",
"bv.BV16",
"bv.BV32",
"bv.BV64",
"bv.BV8",
"bv.Pow2int",
"int.Int",
"real.Abs",
"real.FromInt",
"real.Real",
"real.RealInfix",
"real.Square",
"real.Truncate"
] | [
"mode"
] | https://gitlab.inria.fr/why3/why3 | 7c59064b4eed9a4059292599f3a657716aa34784 | ||
to_sbv64 mode BV64.t : t | val function | to_sbv64 | stdlib | stdlib/ieee_float.mlw | [
"Float32",
"Float64",
"Float_BV_Converter",
"GenericFloat",
"RoundingMode",
"bv.BV16",
"bv.BV32",
"bv.BV64",
"bv.BV8",
"bv.Pow2int",
"int.Int",
"real.Abs",
"real.FromInt",
"real.Real",
"real.RealInfix",
"real.Square",
"real.Truncate"
] | [
"mode"
] | https://gitlab.inria.fr/why3/why3 | 7c59064b4eed9a4059292599f3a657716aa34784 | ||
of_ubv8 mode BV8.t : t | val function | of_ubv8 | stdlib | stdlib/ieee_float.mlw | [
"Float32",
"Float64",
"Float_BV_Converter",
"GenericFloat",
"RoundingMode",
"bv.BV16",
"bv.BV32",
"bv.BV64",
"bv.BV8",
"bv.Pow2int",
"int.Int",
"real.Abs",
"real.FromInt",
"real.Real",
"real.RealInfix",
"real.Square",
"real.Truncate"
] | [
"mode"
] | convert from unsigned bitvector | https://gitlab.inria.fr/why3/why3 | 7c59064b4eed9a4059292599f3a657716aa34784 | |
of_ubv16 mode BV16.t : t | val function | of_ubv16 | stdlib | stdlib/ieee_float.mlw | [
"Float32",
"Float64",
"Float_BV_Converter",
"GenericFloat",
"RoundingMode",
"bv.BV16",
"bv.BV32",
"bv.BV64",
"bv.BV8",
"bv.Pow2int",
"int.Int",
"real.Abs",
"real.FromInt",
"real.Real",
"real.RealInfix",
"real.Square",
"real.Truncate"
] | [
"mode"
] | https://gitlab.inria.fr/why3/why3 | 7c59064b4eed9a4059292599f3a657716aa34784 | ||
of_ubv32 mode BV32.t : t | val function | of_ubv32 | stdlib | stdlib/ieee_float.mlw | [
"Float32",
"Float64",
"Float_BV_Converter",
"GenericFloat",
"RoundingMode",
"bv.BV16",
"bv.BV32",
"bv.BV64",
"bv.BV8",
"bv.Pow2int",
"int.Int",
"real.Abs",
"real.FromInt",
"real.Real",
"real.RealInfix",
"real.Square",
"real.Truncate"
] | [
"mode"
] | https://gitlab.inria.fr/why3/why3 | 7c59064b4eed9a4059292599f3a657716aa34784 | ||
of_ubv64 mode BV64.t : t | val function | of_ubv64 | stdlib | stdlib/ieee_float.mlw | [
"Float32",
"Float64",
"Float_BV_Converter",
"GenericFloat",
"RoundingMode",
"bv.BV16",
"bv.BV32",
"bv.BV64",
"bv.BV8",
"bv.Pow2int",
"int.Int",
"real.Abs",
"real.FromInt",
"real.Real",
"real.RealInfix",
"real.Square",
"real.Truncate"
] | [
"mode"
] | https://gitlab.inria.fr/why3/why3 | 7c59064b4eed9a4059292599f3a657716aa34784 | ||
to_ubv8 mode t : BV8.t | val function | to_ubv8 | stdlib | stdlib/ieee_float.mlw | [
"Float32",
"Float64",
"Float_BV_Converter",
"GenericFloat",
"RoundingMode",
"bv.BV16",
"bv.BV32",
"bv.BV64",
"bv.BV8",
"bv.Pow2int",
"int.Int",
"real.Abs",
"real.FromInt",
"real.Real",
"real.RealInfix",
"real.Square",
"real.Truncate"
] | [
"mode"
] | convert to unsigned bitvector | https://gitlab.inria.fr/why3/why3 | 7c59064b4eed9a4059292599f3a657716aa34784 | |
to_ubv16 mode t : BV16.t | val function | to_ubv16 | stdlib | stdlib/ieee_float.mlw | [
"Float32",
"Float64",
"Float_BV_Converter",
"GenericFloat",
"RoundingMode",
"bv.BV16",
"bv.BV32",
"bv.BV64",
"bv.BV8",
"bv.Pow2int",
"int.Int",
"real.Abs",
"real.FromInt",
"real.Real",
"real.RealInfix",
"real.Square",
"real.Truncate"
] | [
"mode"
] | https://gitlab.inria.fr/why3/why3 | 7c59064b4eed9a4059292599f3a657716aa34784 | ||
to_ubv32 mode t : BV32.t | val function | to_ubv32 | stdlib | stdlib/ieee_float.mlw | [
"Float32",
"Float64",
"Float_BV_Converter",
"GenericFloat",
"RoundingMode",
"bv.BV16",
"bv.BV32",
"bv.BV64",
"bv.BV8",
"bv.Pow2int",
"int.Int",
"real.Abs",
"real.FromInt",
"real.Real",
"real.RealInfix",
"real.Square",
"real.Truncate"
] | [
"mode"
] | https://gitlab.inria.fr/why3/why3 | 7c59064b4eed9a4059292599f3a657716aa34784 | ||
to_ubv64 mode t : BV64.t | val function | to_ubv64 | stdlib | stdlib/ieee_float.mlw | [
"Float32",
"Float64",
"Float_BV_Converter",
"GenericFloat",
"RoundingMode",
"bv.BV16",
"bv.BV32",
"bv.BV64",
"bv.BV8",
"bv.Pow2int",
"int.Int",
"real.Abs",
"real.FromInt",
"real.Real",
"real.RealInfix",
"real.Square",
"real.Truncate"
] | [
"mode"
] | https://gitlab.inria.fr/why3/why3 | 7c59064b4eed9a4059292599f3a657716aa34784 | ||
of_ubv8_is_finite : forall m, x. is_finite (of_ubv8 m x) | axiom | of_ubv8_is_finite | stdlib | stdlib/ieee_float.mlw | [
"Float32",
"Float64",
"Float_BV_Converter",
"GenericFloat",
"RoundingMode",
"bv.BV16",
"bv.BV32",
"bv.BV64",
"bv.BV8",
"bv.Pow2int",
"int.Int",
"real.Abs",
"real.FromInt",
"real.Real",
"real.RealInfix",
"real.Square",
"real.Truncate"
] | [
"is_finite",
"of_ubv8"
] | only true for big enough floats... | https://gitlab.inria.fr/why3/why3 | 7c59064b4eed9a4059292599f3a657716aa34784 | |
of_ubv16_is_finite: forall m, x. is_finite (of_ubv16 m x) | axiom | of_ubv16_is_finite | stdlib | stdlib/ieee_float.mlw | [
"Float32",
"Float64",
"Float_BV_Converter",
"GenericFloat",
"RoundingMode",
"bv.BV16",
"bv.BV32",
"bv.BV64",
"bv.BV8",
"bv.Pow2int",
"int.Int",
"real.Abs",
"real.FromInt",
"real.Real",
"real.RealInfix",
"real.Square",
"real.Truncate"
] | [
"is_finite",
"of_ubv16"
] | https://gitlab.inria.fr/why3/why3 | 7c59064b4eed9a4059292599f3a657716aa34784 | ||
of_ubv32_is_finite: forall m, x. is_finite (of_ubv32 m x) | axiom | of_ubv32_is_finite | stdlib | stdlib/ieee_float.mlw | [
"Float32",
"Float64",
"Float_BV_Converter",
"GenericFloat",
"RoundingMode",
"bv.BV16",
"bv.BV32",
"bv.BV64",
"bv.BV8",
"bv.Pow2int",
"int.Int",
"real.Abs",
"real.FromInt",
"real.Real",
"real.RealInfix",
"real.Square",
"real.Truncate"
] | [
"is_finite",
"of_ubv32"
] | https://gitlab.inria.fr/why3/why3 | 7c59064b4eed9a4059292599f3a657716aa34784 | ||
of_ubv64_is_finite: forall m, x. is_finite (of_ubv64 m x) | axiom | of_ubv64_is_finite | stdlib | stdlib/ieee_float.mlw | [
"Float32",
"Float64",
"Float_BV_Converter",
"GenericFloat",
"RoundingMode",
"bv.BV16",
"bv.BV32",
"bv.BV64",
"bv.BV8",
"bv.Pow2int",
"int.Int",
"real.Abs",
"real.FromInt",
"real.Real",
"real.RealInfix",
"real.Square",
"real.Truncate"
] | [
"is_finite",
"of_ubv64"
] | https://gitlab.inria.fr/why3/why3 | 7c59064b4eed9a4059292599f3a657716aa34784 | ||
of_ubv8_monotonic :
forall m, x y. BV8.ule x y -> le (of_ubv8 m x) (of_ubv8 m y) | axiom | of_ubv8_monotonic | stdlib | stdlib/ieee_float.mlw | [
"Float32",
"Float64",
"Float_BV_Converter",
"GenericFloat",
"RoundingMode",
"bv.BV16",
"bv.BV32",
"bv.BV64",
"bv.BV8",
"bv.Pow2int",
"int.Int",
"real.Abs",
"real.FromInt",
"real.Real",
"real.RealInfix",
"real.Square",
"real.Truncate"
] | [
"le",
"of_ubv8",
"ule"
] | https://gitlab.inria.fr/why3/why3 | 7c59064b4eed9a4059292599f3a657716aa34784 | ||
of_ubv16_monotonic:
forall m, x y. BV16.ule x y -> le (of_ubv16 m x) (of_ubv16 m y) | axiom | of_ubv16_monotonic | stdlib | stdlib/ieee_float.mlw | [
"Float32",
"Float64",
"Float_BV_Converter",
"GenericFloat",
"RoundingMode",
"bv.BV16",
"bv.BV32",
"bv.BV64",
"bv.BV8",
"bv.Pow2int",
"int.Int",
"real.Abs",
"real.FromInt",
"real.Real",
"real.RealInfix",
"real.Square",
"real.Truncate"
] | [
"le",
"of_ubv16",
"ule"
] | https://gitlab.inria.fr/why3/why3 | 7c59064b4eed9a4059292599f3a657716aa34784 | ||
of_ubv32_monotonic:
forall m, x y. BV32.ule x y -> le (of_ubv32 m x) (of_ubv32 m y) | axiom | of_ubv32_monotonic | stdlib | stdlib/ieee_float.mlw | [
"Float32",
"Float64",
"Float_BV_Converter",
"GenericFloat",
"RoundingMode",
"bv.BV16",
"bv.BV32",
"bv.BV64",
"bv.BV8",
"bv.Pow2int",
"int.Int",
"real.Abs",
"real.FromInt",
"real.Real",
"real.RealInfix",
"real.Square",
"real.Truncate"
] | [
"le",
"of_ubv32",
"ule"
] | https://gitlab.inria.fr/why3/why3 | 7c59064b4eed9a4059292599f3a657716aa34784 | ||
of_ubv64_monotonic:
forall m, x y. BV64.ule x y -> le (of_ubv64 m x) (of_ubv64 m y) | axiom | of_ubv64_monotonic | stdlib | stdlib/ieee_float.mlw | [
"Float32",
"Float64",
"Float_BV_Converter",
"GenericFloat",
"RoundingMode",
"bv.BV16",
"bv.BV32",
"bv.BV64",
"bv.BV8",
"bv.Pow2int",
"int.Int",
"real.Abs",
"real.FromInt",
"real.Real",
"real.RealInfix",
"real.Square",
"real.Truncate"
] | [
"le",
"of_ubv64",
"ule"
] | https://gitlab.inria.fr/why3/why3 | 7c59064b4eed9a4059292599f3a657716aa34784 | ||
of_ubv8_to_real : forall m, x.
to_real (of_ubv8 m x) = FromInt.from_int (BV8.t'int x) | axiom | of_ubv8_to_real | stdlib | stdlib/ieee_float.mlw | [
"Float32",
"Float64",
"Float_BV_Converter",
"GenericFloat",
"RoundingMode",
"bv.BV16",
"bv.BV32",
"bv.BV64",
"bv.BV8",
"bv.Pow2int",
"int.Int",
"real.Abs",
"real.FromInt",
"real.Real",
"real.RealInfix",
"real.Square",
"real.Truncate"
] | [
"from_int",
"of_ubv8",
"to_real"
] | https://gitlab.inria.fr/why3/why3 | 7c59064b4eed9a4059292599f3a657716aa34784 | ||
of_ubv16_to_real: forall m, x.
to_real (of_ubv16 m x) = FromInt.from_int (BV16.t'int x) | axiom | of_ubv16_to_real | stdlib | stdlib/ieee_float.mlw | [
"Float32",
"Float64",
"Float_BV_Converter",
"GenericFloat",
"RoundingMode",
"bv.BV16",
"bv.BV32",
"bv.BV64",
"bv.BV8",
"bv.Pow2int",
"int.Int",
"real.Abs",
"real.FromInt",
"real.Real",
"real.RealInfix",
"real.Square",
"real.Truncate"
] | [
"from_int",
"of_ubv16",
"to_real"
] | https://gitlab.inria.fr/why3/why3 | 7c59064b4eed9a4059292599f3a657716aa34784 | ||
of_ubv64_to_real: forall m, x.
to_real (of_ubv64 m x) = round m (FromInt.from_int (BV64.t'int x)) | axiom | of_ubv64_to_real | stdlib | stdlib/ieee_float.mlw | [
"Float32",
"Float64",
"Float_BV_Converter",
"GenericFloat",
"RoundingMode",
"bv.BV16",
"bv.BV32",
"bv.BV64",
"bv.BV8",
"bv.Pow2int",
"int.Int",
"real.Abs",
"real.FromInt",
"real.Real",
"real.RealInfix",
"real.Square",
"real.Truncate"
] | [
"from_int",
"of_ubv64",
"round",
"to_real"
] | of_ubv32_to_real is defined at cloning | https://gitlab.inria.fr/why3/why3 | 7c59064b4eed9a4059292599f3a657716aa34784 | |
t | = < float 8 24 > | type | t | stdlib | stdlib/ieee_float.mlw | [
"Float32",
"Float64",
"Float_BV_Converter",
"GenericFloat",
"RoundingMode",
"bv.BV16",
"bv.BV32",
"bv.BV64",
"bv.BV8",
"bv.Pow2int",
"int.Int",
"real.Abs",
"real.FromInt",
"real.Real",
"real.RealInfix",
"real.Square",
"real.Truncate"
] | [] | https://gitlab.inria.fr/why3/why3 | 7c59064b4eed9a4059292599f3a657716aa34784 | |
pow2sb : int | = 16777216 | constant | pow2sb | stdlib | stdlib/ieee_float.mlw | [
"Float32",
"Float64",
"Float_BV_Converter",
"GenericFloat",
"RoundingMode",
"bv.BV16",
"bv.BV32",
"bv.BV64",
"bv.BV8",
"bv.Pow2int",
"int.Int",
"real.Abs",
"real.FromInt",
"real.Real",
"real.RealInfix",
"real.Square",
"real.Truncate"
] | [
"int"
] | https://gitlab.inria.fr/why3/why3 | 7c59064b4eed9a4059292599f3a657716aa34784 | |
max_int : int | = 0xFFFF_FF00_0000_0000_0000_0000_0000_0000 | constant | max_int | stdlib | stdlib/ieee_float.mlw | [
"Float32",
"Float64",
"Float_BV_Converter",
"GenericFloat",
"RoundingMode",
"bv.BV16",
"bv.BV32",
"bv.BV64",
"bv.BV8",
"bv.Pow2int",
"int.Int",
"real.Abs",
"real.FromInt",
"real.Real",
"real.RealInfix",
"real.Square",
"real.Truncate"
] | [
"int"
] | https://gitlab.inria.fr/why3/why3 | 7c59064b4eed9a4059292599f3a657716aa34784 | |
max_real : real | = 0x1.FFFFFEp127 | constant | max_real | stdlib | stdlib/ieee_float.mlw | [
"Float32",
"Float64",
"Float_BV_Converter",
"GenericFloat",
"RoundingMode",
"bv.BV16",
"bv.BV32",
"bv.BV64",
"bv.BV8",
"bv.Pow2int",
"int.Int",
"real.Abs",
"real.FromInt",
"real.Real",
"real.RealInfix",
"real.Square",
"real.Truncate"
] | [] | https://gitlab.inria.fr/why3/why3 | 7c59064b4eed9a4059292599f3a657716aa34784 | |
round_bound_ne :
forall x:real [round RNE x].
no_overflow RNE x ->
x - 0x1p-24 * Abs.abs(x) - 0x1p-150 <= round RNE x <= x + 0x1p-24 * Abs.abs(x) + 0x1p-150 | lemma | round_bound_ne | stdlib | stdlib/ieee_float.mlw | [
"Float32",
"Float64",
"Float_BV_Converter",
"GenericFloat",
"RoundingMode",
"bv.BV16",
"bv.BV32",
"bv.BV64",
"bv.BV8",
"bv.Pow2int",
"int.Int",
"real.Abs",
"real.FromInt",
"real.Real",
"real.RealInfix",
"real.Square",
"real.Truncate"
] | [
"abs",
"no_overflow",
"round"
] | TODO: "lemma"? "goal"? | https://gitlab.inria.fr/why3/why3 | 7c59064b4eed9a4059292599f3a657716aa34784 | |
round_bound :
forall m:mode, x:real [round m x].
no_overflow m x ->
x - 0x1p-23 * Abs.abs(x) - 0x1p-149 <= round m x <= x + 0x1p-23 * Abs.abs(x) + 0x1p-149 | lemma | round_bound | stdlib | stdlib/ieee_float.mlw | [
"Float32",
"Float64",
"Float_BV_Converter",
"GenericFloat",
"RoundingMode",
"bv.BV16",
"bv.BV32",
"bv.BV64",
"bv.BV8",
"bv.Pow2int",
"int.Int",
"real.Abs",
"real.FromInt",
"real.Real",
"real.RealInfix",
"real.Square",
"real.Truncate"
] | [
"abs",
"mode",
"no_overflow",
"round"
] | https://gitlab.inria.fr/why3/why3 | 7c59064b4eed9a4059292599f3a657716aa34784 | ||
t | = < float 11 53 > | type | t | stdlib | stdlib/ieee_float.mlw | [
"Float32",
"Float64",
"Float_BV_Converter",
"GenericFloat",
"RoundingMode",
"bv.BV16",
"bv.BV32",
"bv.BV64",
"bv.BV8",
"bv.Pow2int",
"int.Int",
"real.Abs",
"real.FromInt",
"real.Real",
"real.RealInfix",
"real.Square",
"real.Truncate"
] | [] | https://gitlab.inria.fr/why3/why3 | 7c59064b4eed9a4059292599f3a657716aa34784 | |
pow2sb : int | = 9007199254740992 | constant | pow2sb | stdlib | stdlib/ieee_float.mlw | [
"Float32",
"Float64",
"Float_BV_Converter",
"GenericFloat",
"RoundingMode",
"bv.BV16",
"bv.BV32",
"bv.BV64",
"bv.BV8",
"bv.Pow2int",
"int.Int",
"real.Abs",
"real.FromInt",
"real.Real",
"real.RealInfix",
"real.Square",
"real.Truncate"
] | [
"int"
] | https://gitlab.inria.fr/why3/why3 | 7c59064b4eed9a4059292599f3a657716aa34784 | |
max_int : int | = 0xFFFF_FFFF_FFFF_F800_0000_0000_0000_0000_0000_0000_0000_0000_0000_0000_0000_0000_0000_0000_0000_0000_0000_0000_0000_0000_0000_0000_0000_0000_0000_0000_0000_0000_0000_0000_0000_0000_0000_0000_0000_0000_0000_0000_0000_0000_0000_0000_0000_0000_0000_0000_0000_0000_0000_0000_0000_0000_0000_0000_0000_0000_0000_0000_0000_0... | constant | max_int | stdlib | stdlib/ieee_float.mlw | [
"Float32",
"Float64",
"Float_BV_Converter",
"GenericFloat",
"RoundingMode",
"bv.BV16",
"bv.BV32",
"bv.BV64",
"bv.BV8",
"bv.Pow2int",
"int.Int",
"real.Abs",
"real.FromInt",
"real.Real",
"real.RealInfix",
"real.Square",
"real.Truncate"
] | [
"int"
] | 242 | https://gitlab.inria.fr/why3/why3 | 7c59064b4eed9a4059292599f3a657716aa34784 |
max_real : real | = 0x1.FFFFFFFFFFFFFp1023 | constant | max_real | stdlib | stdlib/ieee_float.mlw | [
"Float32",
"Float64",
"Float_BV_Converter",
"GenericFloat",
"RoundingMode",
"bv.BV16",
"bv.BV32",
"bv.BV64",
"bv.BV8",
"bv.Pow2int",
"int.Int",
"real.Abs",
"real.FromInt",
"real.Real",
"real.RealInfix",
"real.Square",
"real.Truncate"
] | [] | https://gitlab.inria.fr/why3/why3 | 7c59064b4eed9a4059292599f3a657716aa34784 | |
round_bound_ne :
forall x:real [round RNE x].
no_overflow RNE x ->
x - 0x1p-53 * Abs.abs(x) - 0x1p-1075 <= round RNE x <= x + 0x1p-53 * Abs.abs(x) + 0x1p-1075 | lemma | round_bound_ne | stdlib | stdlib/ieee_float.mlw | [
"Float32",
"Float64",
"Float_BV_Converter",
"GenericFloat",
"RoundingMode",
"bv.BV16",
"bv.BV32",
"bv.BV64",
"bv.BV8",
"bv.Pow2int",
"int.Int",
"real.Abs",
"real.FromInt",
"real.Real",
"real.RealInfix",
"real.Square",
"real.Truncate"
] | [
"abs",
"no_overflow",
"round"
] | TODO: "lemma"? "goal"? | https://gitlab.inria.fr/why3/why3 | 7c59064b4eed9a4059292599f3a657716aa34784 | |
round_bound :
forall m:mode, x:real [round m x].
no_overflow m x ->
x - 0x1p-52 * Abs.abs(x) - 0x1p-1074 <= round m x <= x + 0x1p-52 * Abs.abs(x) + 0x1p-1074 | lemma | round_bound | stdlib | stdlib/ieee_float.mlw | [
"Float32",
"Float64",
"Float_BV_Converter",
"GenericFloat",
"RoundingMode",
"bv.BV16",
"bv.BV32",
"bv.BV64",
"bv.BV8",
"bv.Pow2int",
"int.Int",
"real.Abs",
"real.FromInt",
"real.Real",
"real.RealInfix",
"real.Square",
"real.Truncate"
] | [
"abs",
"mode",
"no_overflow",
"round"
] | https://gitlab.inria.fr/why3/why3 | 7c59064b4eed9a4059292599f3a657716aa34784 | ||
to_float64 mode Float32.t : Float64.t | function | to_float64 | stdlib | stdlib/ieee_float.mlw | [
"Float32",
"Float64",
"Float_BV_Converter",
"GenericFloat",
"RoundingMode",
"bv.BV16",
"bv.BV32",
"bv.BV64",
"bv.BV8",
"bv.Pow2int",
"int.Int",
"real.Abs",
"real.FromInt",
"real.Real",
"real.RealInfix",
"real.Square",
"real.Truncate"
] | [
"mode"
] | https://gitlab.inria.fr/why3/why3 | 7c59064b4eed9a4059292599f3a657716aa34784 | ||
to_float32 mode Float64.t : Float32.t | function | to_float32 | stdlib | stdlib/ieee_float.mlw | [
"Float32",
"Float64",
"Float_BV_Converter",
"GenericFloat",
"RoundingMode",
"bv.BV16",
"bv.BV32",
"bv.BV64",
"bv.BV8",
"bv.Pow2int",
"int.Int",
"real.Abs",
"real.FromInt",
"real.Real",
"real.RealInfix",
"real.Square",
"real.Truncate"
] | [
"mode"
] | https://gitlab.inria.fr/why3/why3 | 7c59064b4eed9a4059292599f3a657716aa34784 | ||
round_double_single :
forall m1 m2:mode, x:real.
Float64.round m1 (Float32.round m2 x) = Float32.round m2 x | lemma | round_double_single | stdlib | stdlib/ieee_float.mlw | [
"Float32",
"Float64",
"Float_BV_Converter",
"GenericFloat",
"RoundingMode",
"bv.BV16",
"bv.BV32",
"bv.BV64",
"bv.BV8",
"bv.Pow2int",
"int.Int",
"real.Abs",
"real.FromInt",
"real.Real",
"real.RealInfix",
"real.Square",
"real.Truncate"
] | [
"mode",
"round"
] | https://gitlab.inria.fr/why3/why3 | 7c59064b4eed9a4059292599f3a657716aa34784 | ||
to_float64_exact:
forall m:mode, x:Float32.t. Float32.t'isFinite x ->
Float64.t'isFinite (to_float64 m x)
/\ Float64.t'real (to_float64 m x) = Float32.t'real x | lemma | to_float64_exact | stdlib | stdlib/ieee_float.mlw | [
"Float32",
"Float64",
"Float_BV_Converter",
"GenericFloat",
"RoundingMode",
"bv.BV16",
"bv.BV32",
"bv.BV64",
"bv.BV8",
"bv.Pow2int",
"int.Int",
"real.Abs",
"real.FromInt",
"real.Real",
"real.RealInfix",
"real.Square",
"real.Truncate"
] | [
"mode",
"to_float64"
] | https://gitlab.inria.fr/why3/why3 | 7c59064b4eed9a4059292599f3a657716aa34784 | ||
to_float32_conv:
forall m:mode, x:Float64.t. Float64.t'isFinite x ->
Float32.no_overflow m (Float64.t'real x) ->
Float32.t'isFinite (to_float32 m x)
/\ Float32.t'real (to_float32 m x) = Float32.round m (Float64.t'real x) | lemma | to_float32_conv | stdlib | stdlib/ieee_float.mlw | [
"Float32",
"Float64",
"Float_BV_Converter",
"GenericFloat",
"RoundingMode",
"bv.BV16",
"bv.BV32",
"bv.BV64",
"bv.BV8",
"bv.Pow2int",
"int.Int",
"real.Abs",
"real.FromInt",
"real.Real",
"real.RealInfix",
"real.Square",
"real.Truncate"
] | [
"mode",
"no_overflow",
"round",
"to_float32"
] | https://gitlab.inria.fr/why3/why3 | 7c59064b4eed9a4059292599f3a657716aa34784 | ||
of_ubv32_to_real : forall m, x.
t'real (of_ubv32 m x) = round m (FromInt.from_int (BV32.t'int x)) | axiom | of_ubv32_to_real | stdlib | stdlib/ieee_float.mlw | [
"Float32",
"Float64",
"Float_BV_Converter",
"GenericFloat",
"RoundingMode",
"bv.BV16",
"bv.BV32",
"bv.BV64",
"bv.BV8",
"bv.Pow2int",
"int.Int",
"real.Abs",
"real.FromInt",
"real.Real",
"real.RealInfix",
"real.Square",
"real.Truncate"
] | [
"from_int",
"of_ubv32",
"round"
] | TODO: "lemma"? "goal"? | https://gitlab.inria.fr/why3/why3 | 7c59064b4eed9a4059292599f3a657716aa34784 | |
of_ubv32_to_real : forall m, x.
t'real (of_ubv32 m x) = FromInt.from_int (BV32.t'int x) | axiom | of_ubv32_to_real | stdlib | stdlib/ieee_float.mlw | [
"Float32",
"Float64",
"Float_BV_Converter",
"GenericFloat",
"RoundingMode",
"bv.BV16",
"bv.BV32",
"bv.BV64",
"bv.BV8",
"bv.Pow2int",
"int.Int",
"real.Abs",
"real.FromInt",
"real.Real",
"real.RealInfix",
"real.Square",
"real.Truncate"
] | [
"from_int",
"of_ubv32"
] | TODO: "lemma"? "goal"? | https://gitlab.inria.fr/why3/why3 | 7c59064b4eed9a4059292599f3a657716aa34784 | |
zero : int | = 0 | constant | zero | stdlib | stdlib/int.mlw | [
"Abs",
"Exponentiation",
"Int",
"algebra.Monoid",
"algebra.OrderedUnitaryCommutativeRing",
"relations.Lex",
"relations.MinMax",
"relations.TotalOrder",
"relations.WellFounded"
] | [
"int"
] | https://gitlab.inria.fr/why3/why3 | 7c59064b4eed9a4059292599f3a657716aa34784 | |
one : int | = 1 | constant | one | stdlib | stdlib/int.mlw | [
"Abs",
"Exponentiation",
"Int",
"algebra.Monoid",
"algebra.OrderedUnitaryCommutativeRing",
"relations.Lex",
"relations.MinMax",
"relations.TotalOrder",
"relations.WellFounded"
] | [
"int"
] | https://gitlab.inria.fr/why3/why3 | 7c59064b4eed9a4059292599f3a657716aa34784 | |
(=) (x y : int) : bool ensures { result <-> x = y } | val | (=) | stdlib | stdlib/int.mlw | [
"Abs",
"Exponentiation",
"Int",
"algebra.Monoid",
"algebra.OrderedUnitaryCommutativeRing",
"relations.Lex",
"relations.MinMax",
"relations.TotalOrder",
"relations.WellFounded"
] | [
"int"
] | https://gitlab.inria.fr/why3/why3 | 7c59064b4eed9a4059292599f3a657716aa34784 | ||
(-_) int : int | val function | (-_) | stdlib | stdlib/int.mlw | [
"Abs",
"Exponentiation",
"Int",
"algebra.Monoid",
"algebra.OrderedUnitaryCommutativeRing",
"relations.Lex",
"relations.MinMax",
"relations.TotalOrder",
"relations.WellFounded"
] | [
"int"
] | https://gitlab.inria.fr/why3/why3 | 7c59064b4eed9a4059292599f3a657716aa34784 | ||
(+) int int : int | val function | (+) | stdlib | stdlib/int.mlw | [
"Abs",
"Exponentiation",
"Int",
"algebra.Monoid",
"algebra.OrderedUnitaryCommutativeRing",
"relations.Lex",
"relations.MinMax",
"relations.TotalOrder",
"relations.WellFounded"
] | [
"int"
] | https://gitlab.inria.fr/why3/why3 | 7c59064b4eed9a4059292599f3a657716aa34784 | ||
(*) int int : int | val function | (*) | stdlib | stdlib/int.mlw | [
"Abs",
"Exponentiation",
"Int",
"algebra.Monoid",
"algebra.OrderedUnitaryCommutativeRing",
"relations.Lex",
"relations.MinMax",
"relations.TotalOrder",
"relations.WellFounded"
] | [
"int"
] | https://gitlab.inria.fr/why3/why3 | 7c59064b4eed9a4059292599f3a657716aa34784 | ||
(<) int int : bool | val predicate | (<) | stdlib | stdlib/int.mlw | [
"Abs",
"Exponentiation",
"Int",
"algebra.Monoid",
"algebra.OrderedUnitaryCommutativeRing",
"relations.Lex",
"relations.MinMax",
"relations.TotalOrder",
"relations.WellFounded"
] | [
"int"
] | https://gitlab.inria.fr/why3/why3 | 7c59064b4eed9a4059292599f3a657716aa34784 | ||
(-) (x y : int) | = x + -y | let function | (-) | stdlib | stdlib/int.mlw | [
"Abs",
"Exponentiation",
"Int",
"algebra.Monoid",
"algebra.OrderedUnitaryCommutativeRing",
"relations.Lex",
"relations.MinMax",
"relations.TotalOrder",
"relations.WellFounded"
] | [
"int"
] | https://gitlab.inria.fr/why3/why3 | 7c59064b4eed9a4059292599f3a657716aa34784 | |
(>) (x y : int) | = y < x | let predicate | (>) | stdlib | stdlib/int.mlw | [
"Abs",
"Exponentiation",
"Int",
"algebra.Monoid",
"algebra.OrderedUnitaryCommutativeRing",
"relations.Lex",
"relations.MinMax",
"relations.TotalOrder",
"relations.WellFounded"
] | [
"int"
] | https://gitlab.inria.fr/why3/why3 | 7c59064b4eed9a4059292599f3a657716aa34784 | |
(<=) (x y : int) | = x < y || x = y | let predicate | (<=) | stdlib | stdlib/int.mlw | [
"Abs",
"Exponentiation",
"Int",
"algebra.Monoid",
"algebra.OrderedUnitaryCommutativeRing",
"relations.Lex",
"relations.MinMax",
"relations.TotalOrder",
"relations.WellFounded"
] | [
"int"
] | https://gitlab.inria.fr/why3/why3 | 7c59064b4eed9a4059292599f3a657716aa34784 | |
(>=) (x y : int) | = y <= x | let predicate | (>=) | stdlib | stdlib/int.mlw | [
"Abs",
"Exponentiation",
"Int",
"algebra.Monoid",
"algebra.OrderedUnitaryCommutativeRing",
"relations.Lex",
"relations.MinMax",
"relations.TotalOrder",
"relations.WellFounded"
] | [
"int"
] | https://gitlab.inria.fr/why3/why3 | 7c59064b4eed9a4059292599f3a657716aa34784 | |
compat_order_mult (x y z:int)
requires { x <= y }
requires { 0 <= z }
ensures { x * z <= y * z } | = () | let | compat_order_mult | stdlib | stdlib/int.mlw | [
"Abs",
"Exponentiation",
"Int",
"algebra.Monoid",
"algebra.OrderedUnitaryCommutativeRing",
"relations.Lex",
"relations.MinMax",
"relations.TotalOrder",
"relations.WellFounded"
] | [
"int"
] | https://gitlab.inria.fr/why3/why3 | 7c59064b4eed9a4059292599f3a657716aa34784 | |
abs (x:int) : int | = if x >= 0 then x else -x | let function | abs | stdlib | stdlib/int.mlw | [
"Abs",
"Exponentiation",
"Int",
"algebra.Monoid",
"algebra.OrderedUnitaryCommutativeRing",
"relations.Lex",
"relations.MinMax",
"relations.TotalOrder",
"relations.WellFounded"
] | [
"int"
] | https://gitlab.inria.fr/why3/why3 | 7c59064b4eed9a4059292599f3a657716aa34784 | |
Abs_le: forall x y:int. abs x <= y <-> -y <= x <= y | lemma | Abs_le | stdlib | stdlib/int.mlw | [
"Abs",
"Exponentiation",
"Int",
"algebra.Monoid",
"algebra.OrderedUnitaryCommutativeRing",
"relations.Lex",
"relations.MinMax",
"relations.TotalOrder",
"relations.WellFounded"
] | [
"abs",
"int"
] | https://gitlab.inria.fr/why3/why3 | 7c59064b4eed9a4059292599f3a657716aa34784 | ||
Abs_pos: forall x:int. abs x >= 0 | lemma | Abs_pos | stdlib | stdlib/int.mlw | [
"Abs",
"Exponentiation",
"Int",
"algebra.Monoid",
"algebra.OrderedUnitaryCommutativeRing",
"relations.Lex",
"relations.MinMax",
"relations.TotalOrder",
"relations.WellFounded"
] | [
"abs",
"int"
] | https://gitlab.inria.fr/why3/why3 | 7c59064b4eed9a4059292599f3a657716aa34784 | ||
min (x y : int) : int
ensures { result = min x y } | = if x <= y then x else y | let | min | stdlib | stdlib/int.mlw | [
"Abs",
"Exponentiation",
"Int",
"algebra.Monoid",
"algebra.OrderedUnitaryCommutativeRing",
"relations.Lex",
"relations.MinMax",
"relations.TotalOrder",
"relations.WellFounded"
] | [
"int"
] | https://gitlab.inria.fr/why3/why3 | 7c59064b4eed9a4059292599f3a657716aa34784 | |
max (x y : int) : int
ensures { result = max x y } | = if x <= y then y else x | let | max | stdlib | stdlib/int.mlw | [
"Abs",
"Exponentiation",
"Int",
"algebra.Monoid",
"algebra.OrderedUnitaryCommutativeRing",
"relations.Lex",
"relations.MinMax",
"relations.TotalOrder",
"relations.WellFounded"
] | [
"int"
] | https://gitlab.inria.fr/why3/why3 | 7c59064b4eed9a4059292599f3a657716aa34784 | |
lt_nat (x y: int) | = 0 <= y /\ x < y | predicate | lt_nat | stdlib | stdlib/int.mlw | [
"Abs",
"Exponentiation",
"Int",
"algebra.Monoid",
"algebra.OrderedUnitaryCommutativeRing",
"relations.Lex",
"relations.MinMax",
"relations.TotalOrder",
"relations.WellFounded"
] | [
"int"
] | https://gitlab.inria.fr/why3/why3 | 7c59064b4eed9a4059292599f3a657716aa34784 | |
div (x y: int) : int | function | div | stdlib | stdlib/int.mlw | [
"Abs",
"Exponentiation",
"Int",
"algebra.Monoid",
"algebra.OrderedUnitaryCommutativeRing",
"relations.Lex",
"relations.MinMax",
"relations.TotalOrder",
"relations.WellFounded"
] | [
"int"
] | https://gitlab.inria.fr/why3/why3 | 7c59064b4eed9a4059292599f3a657716aa34784 | ||
mod (x y: int) : int | function | mod | stdlib | stdlib/int.mlw | [
"Abs",
"Exponentiation",
"Int",
"algebra.Monoid",
"algebra.OrderedUnitaryCommutativeRing",
"relations.Lex",
"relations.MinMax",
"relations.TotalOrder",
"relations.WellFounded"
] | [
"int"
] | https://gitlab.inria.fr/why3/why3 | 7c59064b4eed9a4059292599f3a657716aa34784 | ||
Div_mod:
forall x y:int. y <> 0 -> x = y * div x y + mod x y | axiom | Div_mod | stdlib | stdlib/int.mlw | [
"Abs",
"Exponentiation",
"Int",
"algebra.Monoid",
"algebra.OrderedUnitaryCommutativeRing",
"relations.Lex",
"relations.MinMax",
"relations.TotalOrder",
"relations.WellFounded"
] | [
"div",
"int",
"mod"
] | https://gitlab.inria.fr/why3/why3 | 7c59064b4eed9a4059292599f3a657716aa34784 | ||
Mod_bound:
forall x y:int. y <> 0 -> 0 <= mod x y < abs y | axiom | Mod_bound | stdlib | stdlib/int.mlw | [
"Abs",
"Exponentiation",
"Int",
"algebra.Monoid",
"algebra.OrderedUnitaryCommutativeRing",
"relations.Lex",
"relations.MinMax",
"relations.TotalOrder",
"relations.WellFounded"
] | [
"abs",
"int",
"mod"
] | https://gitlab.inria.fr/why3/why3 | 7c59064b4eed9a4059292599f3a657716aa34784 | ||
Div_unique:
forall x y q:int. y > 0 -> q * y <= x < q * y + y -> div x y = q | lemma | Div_unique | stdlib | stdlib/int.mlw | [
"Abs",
"Exponentiation",
"Int",
"algebra.Monoid",
"algebra.OrderedUnitaryCommutativeRing",
"relations.Lex",
"relations.MinMax",
"relations.TotalOrder",
"relations.WellFounded"
] | [
"div",
"int"
] | https://gitlab.inria.fr/why3/why3 | 7c59064b4eed9a4059292599f3a657716aa34784 | ||
Div_bound:
forall x y:int. x >= 0 /\ y > 0 -> 0 <= div x y <= x | lemma | Div_bound | stdlib | stdlib/int.mlw | [
"Abs",
"Exponentiation",
"Int",
"algebra.Monoid",
"algebra.OrderedUnitaryCommutativeRing",
"relations.Lex",
"relations.MinMax",
"relations.TotalOrder",
"relations.WellFounded"
] | [
"div",
"int"
] | https://gitlab.inria.fr/why3/why3 | 7c59064b4eed9a4059292599f3a657716aa34784 | ||
Mod_1: forall x:int. mod x 1 = 0 | lemma | Mod_1 | stdlib | stdlib/int.mlw | [
"Abs",
"Exponentiation",
"Int",
"algebra.Monoid",
"algebra.OrderedUnitaryCommutativeRing",
"relations.Lex",
"relations.MinMax",
"relations.TotalOrder",
"relations.WellFounded"
] | [
"int",
"mod"
] | https://gitlab.inria.fr/why3/why3 | 7c59064b4eed9a4059292599f3a657716aa34784 | ||
Div_1: forall x:int. div x 1 = x | lemma | Div_1 | stdlib | stdlib/int.mlw | [
"Abs",
"Exponentiation",
"Int",
"algebra.Monoid",
"algebra.OrderedUnitaryCommutativeRing",
"relations.Lex",
"relations.MinMax",
"relations.TotalOrder",
"relations.WellFounded"
] | [
"div",
"int"
] | https://gitlab.inria.fr/why3/why3 | 7c59064b4eed9a4059292599f3a657716aa34784 | ||
Div_inf: forall x y:int. 0 <= x < y -> div x y = 0 | lemma | Div_inf | stdlib | stdlib/int.mlw | [
"Abs",
"Exponentiation",
"Int",
"algebra.Monoid",
"algebra.OrderedUnitaryCommutativeRing",
"relations.Lex",
"relations.MinMax",
"relations.TotalOrder",
"relations.WellFounded"
] | [
"div",
"int"
] | https://gitlab.inria.fr/why3/why3 | 7c59064b4eed9a4059292599f3a657716aa34784 | ||
Div_inf_neg: forall x y:int. 0 < x <= y -> div (-x) y = -1 | lemma | Div_inf_neg | stdlib | stdlib/int.mlw | [
"Abs",
"Exponentiation",
"Int",
"algebra.Monoid",
"algebra.OrderedUnitaryCommutativeRing",
"relations.Lex",
"relations.MinMax",
"relations.TotalOrder",
"relations.WellFounded"
] | [
"div",
"int"
] | https://gitlab.inria.fr/why3/why3 | 7c59064b4eed9a4059292599f3a657716aa34784 | ||
Mod_0: forall y:int. y <> 0 -> mod 0 y = 0 | lemma | Mod_0 | stdlib | stdlib/int.mlw | [
"Abs",
"Exponentiation",
"Int",
"algebra.Monoid",
"algebra.OrderedUnitaryCommutativeRing",
"relations.Lex",
"relations.MinMax",
"relations.TotalOrder",
"relations.WellFounded"
] | [
"int",
"mod"
] | https://gitlab.inria.fr/why3/why3 | 7c59064b4eed9a4059292599f3a657716aa34784 | ||
Div_1_left: forall y:int. y > 1 -> div 1 y = 0 | lemma | Div_1_left | stdlib | stdlib/int.mlw | [
"Abs",
"Exponentiation",
"Int",
"algebra.Monoid",
"algebra.OrderedUnitaryCommutativeRing",
"relations.Lex",
"relations.MinMax",
"relations.TotalOrder",
"relations.WellFounded"
] | [
"div",
"int"
] | https://gitlab.inria.fr/why3/why3 | 7c59064b4eed9a4059292599f3a657716aa34784 | ||
Div_minus1_left: forall y:int. y > 1 -> div (-1) y = -1 | lemma | Div_minus1_left | stdlib | stdlib/int.mlw | [
"Abs",
"Exponentiation",
"Int",
"algebra.Monoid",
"algebra.OrderedUnitaryCommutativeRing",
"relations.Lex",
"relations.MinMax",
"relations.TotalOrder",
"relations.WellFounded"
] | [
"div",
"int"
] | https://gitlab.inria.fr/why3/why3 | 7c59064b4eed9a4059292599f3a657716aa34784 | ||
Mod_1_left: forall y:int. y > 1 -> mod 1 y = 1 | lemma | Mod_1_left | stdlib | stdlib/int.mlw | [
"Abs",
"Exponentiation",
"Int",
"algebra.Monoid",
"algebra.OrderedUnitaryCommutativeRing",
"relations.Lex",
"relations.MinMax",
"relations.TotalOrder",
"relations.WellFounded"
] | [
"int",
"mod"
] | https://gitlab.inria.fr/why3/why3 | 7c59064b4eed9a4059292599f3a657716aa34784 | ||
Mod_minus1_left: forall y:int. y > 1 -> mod (-1) y = y - 1 | lemma | Mod_minus1_left | stdlib | stdlib/int.mlw | [
"Abs",
"Exponentiation",
"Int",
"algebra.Monoid",
"algebra.OrderedUnitaryCommutativeRing",
"relations.Lex",
"relations.MinMax",
"relations.TotalOrder",
"relations.WellFounded"
] | [
"int",
"mod"
] | https://gitlab.inria.fr/why3/why3 | 7c59064b4eed9a4059292599f3a657716aa34784 | ||
Div_mult: forall x y z:int [div (x * y + z) x].
x > 0 ->
div (x * y + z) x = y + div z x | lemma | Div_mult | stdlib | stdlib/int.mlw | [
"Abs",
"Exponentiation",
"Int",
"algebra.Monoid",
"algebra.OrderedUnitaryCommutativeRing",
"relations.Lex",
"relations.MinMax",
"relations.TotalOrder",
"relations.WellFounded"
] | [
"div",
"int"
] | https://gitlab.inria.fr/why3/why3 | 7c59064b4eed9a4059292599f3a657716aa34784 | ||
Mod_mult: forall x y z:int [mod (x * y + z) x].
x > 0 ->
mod (x * y + z) x = mod z x | lemma | Mod_mult | stdlib | stdlib/int.mlw | [
"Abs",
"Exponentiation",
"Int",
"algebra.Monoid",
"algebra.OrderedUnitaryCommutativeRing",
"relations.Lex",
"relations.MinMax",
"relations.TotalOrder",
"relations.WellFounded"
] | [
"int",
"mod"
] | https://gitlab.inria.fr/why3/why3 | 7c59064b4eed9a4059292599f3a657716aa34784 | ||
div (x y:int) : int
requires { y <> 0 }
ensures { result = div x y } | val | div | stdlib | stdlib/int.mlw | [
"Abs",
"Exponentiation",
"Int",
"algebra.Monoid",
"algebra.OrderedUnitaryCommutativeRing",
"relations.Lex",
"relations.MinMax",
"relations.TotalOrder",
"relations.WellFounded"
] | [
"int"
] | https://gitlab.inria.fr/why3/why3 | 7c59064b4eed9a4059292599f3a657716aa34784 | ||
mod (x y:int) : int
requires { y <> 0 }
ensures { result = mod x y } | val | mod | stdlib | stdlib/int.mlw | [
"Abs",
"Exponentiation",
"Int",
"algebra.Monoid",
"algebra.OrderedUnitaryCommutativeRing",
"relations.Lex",
"relations.MinMax",
"relations.TotalOrder",
"relations.WellFounded"
] | [
"int"
] | https://gitlab.inria.fr/why3/why3 | 7c59064b4eed9a4059292599f3a657716aa34784 | ||
div2:
forall x: int. exists y: int. x = 2*y \/ x = 2*y+1 | lemma | div2 | stdlib | stdlib/int.mlw | [
"Abs",
"Exponentiation",
"Int",
"algebra.Monoid",
"algebra.OrderedUnitaryCommutativeRing",
"relations.Lex",
"relations.MinMax",
"relations.TotalOrder",
"relations.WellFounded"
] | [
"int"
] | https://gitlab.inria.fr/why3/why3 | 7c59064b4eed9a4059292599f3a657716aa34784 | ||
Mod_bound:
forall x y:int. y <> 0 -> - abs y < mod x y < abs y | axiom | Mod_bound | stdlib | stdlib/int.mlw | [
"Abs",
"Exponentiation",
"Int",
"algebra.Monoid",
"algebra.OrderedUnitaryCommutativeRing",
"relations.Lex",
"relations.MinMax",
"relations.TotalOrder",
"relations.WellFounded"
] | [
"abs",
"int",
"mod"
] | https://gitlab.inria.fr/why3/why3 | 7c59064b4eed9a4059292599f3a657716aa34784 | ||
Div_sign_pos:
forall x y:int. x >= 0 /\ y > 0 -> div x y >= 0 | axiom | Div_sign_pos | stdlib | stdlib/int.mlw | [
"Abs",
"Exponentiation",
"Int",
"algebra.Monoid",
"algebra.OrderedUnitaryCommutativeRing",
"relations.Lex",
"relations.MinMax",
"relations.TotalOrder",
"relations.WellFounded"
] | [
"div",
"int"
] | https://gitlab.inria.fr/why3/why3 | 7c59064b4eed9a4059292599f3a657716aa34784 | ||
Div_sign_neg:
forall x y:int. x <= 0 /\ y > 0 -> div x y <= 0 | axiom | Div_sign_neg | stdlib | stdlib/int.mlw | [
"Abs",
"Exponentiation",
"Int",
"algebra.Monoid",
"algebra.OrderedUnitaryCommutativeRing",
"relations.Lex",
"relations.MinMax",
"relations.TotalOrder",
"relations.WellFounded"
] | [
"div",
"int"
] | https://gitlab.inria.fr/why3/why3 | 7c59064b4eed9a4059292599f3a657716aa34784 | ||
Mod_sign_pos:
forall x y:int. x >= 0 /\ y <> 0 -> mod x y >= 0 | axiom | Mod_sign_pos | stdlib | stdlib/int.mlw | [
"Abs",
"Exponentiation",
"Int",
"algebra.Monoid",
"algebra.OrderedUnitaryCommutativeRing",
"relations.Lex",
"relations.MinMax",
"relations.TotalOrder",
"relations.WellFounded"
] | [
"int",
"mod"
] | https://gitlab.inria.fr/why3/why3 | 7c59064b4eed9a4059292599f3a657716aa34784 | ||
Mod_sign_neg:
forall x y:int. x <= 0 /\ y <> 0 -> mod x y <= 0 | axiom | Mod_sign_neg | stdlib | stdlib/int.mlw | [
"Abs",
"Exponentiation",
"Int",
"algebra.Monoid",
"algebra.OrderedUnitaryCommutativeRing",
"relations.Lex",
"relations.MinMax",
"relations.TotalOrder",
"relations.WellFounded"
] | [
"int",
"mod"
] | https://gitlab.inria.fr/why3/why3 | 7c59064b4eed9a4059292599f3a657716aa34784 | ||
Rounds_toward_zero:
forall x y:int. y <> 0 -> abs (div x y * y) <= abs x | lemma | Rounds_toward_zero | stdlib | stdlib/int.mlw | [
"Abs",
"Exponentiation",
"Int",
"algebra.Monoid",
"algebra.OrderedUnitaryCommutativeRing",
"relations.Lex",
"relations.MinMax",
"relations.TotalOrder",
"relations.WellFounded"
] | [
"abs",
"div",
"int"
] | https://gitlab.inria.fr/why3/why3 | 7c59064b4eed9a4059292599f3a657716aa34784 | ||
Mod_inf: forall x y:int. 0 <= x < y -> mod x y = x | lemma | Mod_inf | stdlib | stdlib/int.mlw | [
"Abs",
"Exponentiation",
"Int",
"algebra.Monoid",
"algebra.OrderedUnitaryCommutativeRing",
"relations.Lex",
"relations.MinMax",
"relations.TotalOrder",
"relations.WellFounded"
] | [
"int",
"mod"
] | https://gitlab.inria.fr/why3/why3 | 7c59064b4eed9a4059292599f3a657716aa34784 | ||
Div_mult: forall x y z:int [div (x * y + z) x].
x > 0 /\ y >= 0 /\ z >= 0 ->
div (x * y + z) x = y + div z x | lemma | Div_mult | stdlib | stdlib/int.mlw | [
"Abs",
"Exponentiation",
"Int",
"algebra.Monoid",
"algebra.OrderedUnitaryCommutativeRing",
"relations.Lex",
"relations.MinMax",
"relations.TotalOrder",
"relations.WellFounded"
] | [
"div",
"int"
] | https://gitlab.inria.fr/why3/why3 | 7c59064b4eed9a4059292599f3a657716aa34784 | ||
Mod_mult: forall x y z:int [mod (x * y + z) x].
x > 0 /\ y >= 0 /\ z >= 0 ->
mod (x * y + z) x = mod z x | lemma | Mod_mult | stdlib | stdlib/int.mlw | [
"Abs",
"Exponentiation",
"Int",
"algebra.Monoid",
"algebra.OrderedUnitaryCommutativeRing",
"relations.Lex",
"relations.MinMax",
"relations.TotalOrder",
"relations.WellFounded"
] | [
"int",
"mod"
] | https://gitlab.inria.fr/why3/why3 | 7c59064b4eed9a4059292599f3a657716aa34784 | ||
power t int : t | function | power | stdlib | stdlib/int.mlw | [
"Abs",
"Exponentiation",
"Int",
"algebra.Monoid",
"algebra.OrderedUnitaryCommutativeRing",
"relations.Lex",
"relations.MinMax",
"relations.TotalOrder",
"relations.WellFounded"
] | [
"int"
] | TODO: implement with let rec once let cloning is done | https://gitlab.inria.fr/why3/why3 | 7c59064b4eed9a4059292599f3a657716aa34784 | |
Power_0 : forall x: t. power x 0 = one | axiom | Power_0 | stdlib | stdlib/int.mlw | [
"Abs",
"Exponentiation",
"Int",
"algebra.Monoid",
"algebra.OrderedUnitaryCommutativeRing",
"relations.Lex",
"relations.MinMax",
"relations.TotalOrder",
"relations.WellFounded"
] | [
"one",
"power"
] | https://gitlab.inria.fr/why3/why3 | 7c59064b4eed9a4059292599f3a657716aa34784 | ||
Power_s : forall x: t, n: int. n >= 0 -> power x (n+1) = x * power x n | axiom | Power_s | stdlib | stdlib/int.mlw | [
"Abs",
"Exponentiation",
"Int",
"algebra.Monoid",
"algebra.OrderedUnitaryCommutativeRing",
"relations.Lex",
"relations.MinMax",
"relations.TotalOrder",
"relations.WellFounded"
] | [
"int",
"power"
] | https://gitlab.inria.fr/why3/why3 | 7c59064b4eed9a4059292599f3a657716aa34784 | ||
Power_s_alt: forall x: t, n: int. n > 0 -> power x n = x * power x (n-1) | lemma | Power_s_alt | stdlib | stdlib/int.mlw | [
"Abs",
"Exponentiation",
"Int",
"algebra.Monoid",
"algebra.OrderedUnitaryCommutativeRing",
"relations.Lex",
"relations.MinMax",
"relations.TotalOrder",
"relations.WellFounded"
] | [
"int",
"power"
] | https://gitlab.inria.fr/why3/why3 | 7c59064b4eed9a4059292599f3a657716aa34784 | ||
Power_1 : forall x : t. power x 1 = x | lemma | Power_1 | stdlib | stdlib/int.mlw | [
"Abs",
"Exponentiation",
"Int",
"algebra.Monoid",
"algebra.OrderedUnitaryCommutativeRing",
"relations.Lex",
"relations.MinMax",
"relations.TotalOrder",
"relations.WellFounded"
] | [
"power"
] | https://gitlab.inria.fr/why3/why3 | 7c59064b4eed9a4059292599f3a657716aa34784 | ||
Power_sum : forall x: t, n m: int. 0 <= n -> 0 <= m ->
power x (n+m) = power x n * power x m | lemma | Power_sum | stdlib | stdlib/int.mlw | [
"Abs",
"Exponentiation",
"Int",
"algebra.Monoid",
"algebra.OrderedUnitaryCommutativeRing",
"relations.Lex",
"relations.MinMax",
"relations.TotalOrder",
"relations.WellFounded"
] | [
"int",
"power"
] | https://gitlab.inria.fr/why3/why3 | 7c59064b4eed9a4059292599f3a657716aa34784 | ||
Power_mult : forall x:t, n m : int. 0 <= n -> 0 <= m ->
power x (Int.(*) n m) = power (power x n) m | lemma | Power_mult | stdlib | stdlib/int.mlw | [
"Abs",
"Exponentiation",
"Int",
"algebra.Monoid",
"algebra.OrderedUnitaryCommutativeRing",
"relations.Lex",
"relations.MinMax",
"relations.TotalOrder",
"relations.WellFounded"
] | [
"int",
"power"
] | https://gitlab.inria.fr/why3/why3 | 7c59064b4eed9a4059292599f3a657716aa34784 | ||
Power_comm1 : forall x y: t. x * y = y * x ->
forall n:int. 0 <= n ->
power x n * y = y * power x n | lemma | Power_comm1 | stdlib | stdlib/int.mlw | [
"Abs",
"Exponentiation",
"Int",
"algebra.Monoid",
"algebra.OrderedUnitaryCommutativeRing",
"relations.Lex",
"relations.MinMax",
"relations.TotalOrder",
"relations.WellFounded"
] | [
"int",
"power"
] | https://gitlab.inria.fr/why3/why3 | 7c59064b4eed9a4059292599f3a657716aa34784 |
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