statement stringlengths 1 11.7k | proof stringlengths 0 214k | type stringclasses 28
values | symbolic_name stringlengths 1 301 | library stringclasses 77
values | filename stringlengths 9 65 | imports listlengths 0 60 | deps listlengths 0 64 | docstring stringlengths 0 28.4k | source_url stringclasses 1
value | commit stringclasses 1
value |
|---|---|---|---|---|---|---|---|---|---|---|
pose_Zlength l H | :=
lazymatch goal with
| f : Zlength_fact (Zlength l = _) |- _ =>
pose proof (Zlength_fact_elim _ f) as H
end. | Ltac | pose_Zlength | zlist | zlist/Zlength_solver.v | [
"Stdlib",
"ZArith",
"Znumtheory",
"Stdlib.Lists.List",
"Lia",
"ListNotations",
"VST.zlist.sublist",
"SublistInternalLib"
] | [
"Zlength_fact",
"Zlength_fact_elim"
] | Arguments:
l - the list to calculate length
H - the name for result | https://github.com/PrincetonUniversity/VST | dcb836404f5e65b4fe565837b61d42cf7d0b0f2c |
get_Zlength l | :=
lazymatch goal with
| f : Zlength_fact (Zlength l = _) |- _ =>
constr:(Zlength_fact_elim _ f)
end. | Ltac | get_Zlength | zlist | zlist/Zlength_solver.v | [
"Stdlib",
"ZArith",
"Znumtheory",
"Stdlib.Lists.List",
"Lia",
"ListNotations",
"VST.zlist.sublist",
"SublistInternalLib"
] | [
"Zlength_fact",
"Zlength_fact_elim"
] | https://github.com/PrincetonUniversity/VST | dcb836404f5e65b4fe565837b61d42cf7d0b0f2c | |
calc_Zlength_var : forall A (l : list A),
Zlength l = Zlength l. | Proof.
auto.
Qed. | Lemma | calc_Zlength_var | zlist | zlist/Zlength_solver.v | [
"Stdlib",
"ZArith",
"Znumtheory",
"Stdlib.Lists.List",
"Lia",
"ListNotations",
"VST.zlist.sublist",
"SublistInternalLib"
] | [
"Proof"
] | https://github.com/PrincetonUniversity/VST | dcb836404f5e65b4fe565837b61d42cf7d0b0f2c | |
calc_Zlength_nil : forall A,
Zlength (@nil A) = 0. | Proof.
auto.
Qed. | Lemma | calc_Zlength_nil | zlist | zlist/Zlength_solver.v | [
"Stdlib",
"ZArith",
"Znumtheory",
"Stdlib.Lists.List",
"Lia",
"ListNotations",
"VST.zlist.sublist",
"SublistInternalLib"
] | [
"Proof"
] | https://github.com/PrincetonUniversity/VST | dcb836404f5e65b4fe565837b61d42cf7d0b0f2c | |
calc_Zlength_cons : forall A (l : list A) len x,
Zlength l = len ->
Zlength (x :: l) = 1 + len. | Proof.
intros.
rewrite Zlength_cons.
lia.
Qed. | Lemma | calc_Zlength_cons | zlist | zlist/Zlength_solver.v | [
"Stdlib",
"ZArith",
"Znumtheory",
"Stdlib.Lists.List",
"Lia",
"ListNotations",
"VST.zlist.sublist",
"SublistInternalLib"
] | [
"Proof"
] | https://github.com/PrincetonUniversity/VST | dcb836404f5e65b4fe565837b61d42cf7d0b0f2c | |
calc_Zlength_app : forall A (al bl : list A) alen blen,
Zlength al = alen ->
Zlength bl = blen ->
Zlength (al ++ bl) = alen + blen. | Proof.
intros.
rewrite Zlength_app.
lia.
Qed. | Lemma | calc_Zlength_app | zlist | zlist/Zlength_solver.v | [
"Stdlib",
"ZArith",
"Znumtheory",
"Stdlib.Lists.List",
"Lia",
"ListNotations",
"VST.zlist.sublist",
"SublistInternalLib"
] | [
"Proof",
"Zlength_app"
] | https://github.com/PrincetonUniversity/VST | dcb836404f5e65b4fe565837b61d42cf7d0b0f2c | |
calc_Zlength_sublist : forall A (l : list A) len lo hi,
Zlength l = len ->
0 <= lo <= hi ->
hi <= len ->
Zlength (sublist lo hi l) = hi - lo. | Proof.
intros.
rewrite Zlength_sublist;
lia.
Qed. | Lemma | calc_Zlength_sublist | zlist | zlist/Zlength_solver.v | [
"Stdlib",
"ZArith",
"Znumtheory",
"Stdlib.Lists.List",
"Lia",
"ListNotations",
"VST.zlist.sublist",
"SublistInternalLib"
] | [
"Proof",
"Zlength_sublist",
"sublist"
] | https://github.com/PrincetonUniversity/VST | dcb836404f5e65b4fe565837b61d42cf7d0b0f2c | |
calc_Zlength_upd_Znth : forall A (l : list A) len i x,
Zlength l = len ->
Zlength (upd_Znth i l x) = len. | Proof.
intros; subst; apply Zlength_upd_Znth.
Qed. | Lemma | calc_Zlength_upd_Znth | zlist | zlist/Zlength_solver.v | [
"Stdlib",
"ZArith",
"Znumtheory",
"Stdlib.Lists.List",
"Lia",
"ListNotations",
"VST.zlist.sublist",
"SublistInternalLib"
] | [
"Proof",
"Zlength_upd_Znth",
"subst",
"upd_Znth"
] | https://github.com/PrincetonUniversity/VST | dcb836404f5e65b4fe565837b61d42cf7d0b0f2c | |
calc_Zlength_map : forall A B (l : list A) len (f : A -> B),
Zlength l = len ->
Zlength (map f l) = len. | Proof.
intros.
rewrite Zlength_map.
auto.
Qed. | Lemma | calc_Zlength_map | zlist | zlist/Zlength_solver.v | [
"Stdlib",
"ZArith",
"Znumtheory",
"Stdlib.Lists.List",
"Lia",
"ListNotations",
"VST.zlist.sublist",
"SublistInternalLib"
] | [
"Proof",
"Zlength_map",
"map"
] | https://github.com/PrincetonUniversity/VST | dcb836404f5e65b4fe565837b61d42cf7d0b0f2c | |
calc_Zlength | := fail "defined later". | Ltac | calc_Zlength | zlist | zlist/Zlength_solver.v | [
"Stdlib",
"ZArith",
"Znumtheory",
"Stdlib.Lists.List",
"Lia",
"ListNotations",
"VST.zlist.sublist",
"SublistInternalLib"
] | [] | https://github.com/PrincetonUniversity/VST | dcb836404f5e65b4fe565837b61d42cf7d0b0f2c | |
Zlength_simplify | :=
init_Zlength_db;
repeat match goal with
| |- context [Zlength ?l] =>
progress (
calc_Zlength l;
try progress (
let H := get_Zlength l in
rewrite !H
)
)
end. | Ltac | Zlength_simplify | zlist | zlist/Zlength_solver.v | [
"Stdlib",
"ZArith",
"Znumtheory",
"Stdlib.Lists.List",
"Lia",
"ListNotations",
"VST.zlist.sublist",
"SublistInternalLib"
] | [
"calc_Zlength",
"context",
"get_Zlength",
"init_Zlength_db",
"progress"
] | https://github.com/PrincetonUniversity/VST | dcb836404f5e65b4fe565837b61d42cf7d0b0f2c | |
Zlength_simplify_in H | :=
init_Zlength_db;
repeat match type of H with
| context [Zlength ?l] =>
progress (
calc_Zlength l;
try progress (
let H1 := get_Zlength l in
rewrite !H1 in H
)
)
end. | Ltac | Zlength_simplify_in | zlist | zlist/Zlength_solver.v | [
"Stdlib",
"ZArith",
"Znumtheory",
"Stdlib.Lists.List",
"Lia",
"ListNotations",
"VST.zlist.sublist",
"SublistInternalLib"
] | [
"calc_Zlength",
"context",
"get_Zlength",
"init_Zlength_db",
"progress",
"type"
] | https://github.com/PrincetonUniversity/VST | dcb836404f5e65b4fe565837b61d42cf7d0b0f2c | |
Zlength_simplify_in_all | :=
init_Zlength_db;
repeat match goal with
| |- context [Zlength ?l] =>
progress (
calc_Zlength l;
try progress (
let H := get_Zlength l in
rewrite !H
)
)
| H : _ |- _ =>
lazymatch type of H with
| Zlength_fact _ => fail
| _ =>
match type of H with
... | Ltac | Zlength_simplify_in_all | zlist | zlist/Zlength_solver.v | [
"Stdlib",
"ZArith",
"Znumtheory",
"Stdlib.Lists.List",
"Lia",
"ListNotations",
"VST.zlist.sublist",
"SublistInternalLib"
] | [
"Zlength_fact",
"calc_Zlength",
"context",
"get_Zlength",
"init_Zlength_db",
"progress",
"type"
] | https://github.com/PrincetonUniversity/VST | dcb836404f5e65b4fe565837b61d42cf7d0b0f2c | |
calc_Zlength_by_autorewrite l | :=
let len_name := fresh "len" in
pose (Zlength l) as len_name;
let H := fresh in
eassert (len_name = Zlength l) as H by reflexivity;
progress autorewrite with Zlength in H;
Zlength_simplify_in H;
unfold len_name in H;
clear len_name;
add_Zlength_res H;
clear H. | Ltac | calc_Zlength_by_autorewrite | zlist | zlist/Zlength_solver.v | [
"Stdlib",
"ZArith",
"Znumtheory",
"Stdlib.Lists.List",
"Lia",
"ListNotations",
"VST.zlist.sublist",
"SublistInternalLib"
] | [
"Zlength_simplify_in",
"add_Zlength_res",
"fresh",
"progress"
] | https://github.com/PrincetonUniversity/VST | dcb836404f5e65b4fe565837b61d42cf7d0b0f2c | |
calc_Zlength_extra l | := fail. | Ltac | calc_Zlength_extra | zlist | zlist/Zlength_solver.v | [
"Stdlib",
"ZArith",
"Znumtheory",
"Stdlib.Lists.List",
"Lia",
"ListNotations",
"VST.zlist.sublist",
"SublistInternalLib"
] | [] | https://github.com/PrincetonUniversity/VST | dcb836404f5e65b4fe565837b61d42cf7d0b0f2c | |
calc_Zlength l : | :=
first
[ search_Zlength l
| lazymatch l with
| @nil ?A =>
add_Zlength_res (calc_Zlength_nil A)
| @cons ?A ?x ?l =>
calc_Zlength l;
let H := get_Zlength l in
add_Zlength_res (calc_Zlength_cons A l _ x H)
| @app ?A ?l1 ?l2 =>
calc_Zlength l1; calc_Zlength l2;
let H1... | Ltac | calc_Zlength | zlist | zlist/Zlength_solver.v | [
"Stdlib",
"ZArith",
"Znumtheory",
"Stdlib.Lists.List",
"Lia",
"ListNotations",
"VST.zlist.sublist",
"SublistInternalLib"
] | [
"Zlength_Zrepeat",
"Zlength_nonneg",
"Zrepeat",
"add_Zlength_res",
"calc_Zlength_app",
"calc_Zlength_by_autorewrite",
"calc_Zlength_cons",
"calc_Zlength_extra",
"calc_Zlength_map",
"calc_Zlength_nil",
"calc_Zlength_sublist",
"calc_Zlength_upd_Znth",
"calc_Zlength_var",
"get_Zlength",
"ma... | https://github.com/PrincetonUniversity/VST | dcb836404f5e65b4fe565837b61d42cf7d0b0f2c | |
Zlength_solve | :=
Zlength_simplify;
lia. | Ltac | Zlength_solve | zlist | zlist/Zlength_solver.v | [
"Stdlib",
"ZArith",
"Znumtheory",
"Stdlib.Lists.List",
"Lia",
"ListNotations",
"VST.zlist.sublist",
"SublistInternalLib"
] | [
"Zlength_simplify"
] | https://github.com/PrincetonUniversity/VST | dcb836404f5e65b4fe565837b61d42cf7d0b0f2c |
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