diff options
author | Jason Gross <jgross@mit.edu> | 2017-04-03 15:14:17 -0400 |
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committer | Jason Gross <jgross@mit.edu> | 2017-04-03 15:14:17 -0400 |
commit | 9009ddf4261bbf489874c4619a8c0397eb3f989d (patch) | |
tree | b1fa7b5ff05300f1cca6f1eaf19b9fe3c601f6bf /src/Util | |
parent | eb20555b72dc38d4675cfb1e68203ad9be56a3d3 (diff) |
Split off liftn_sig, add lift{3,4}_sig
Diffstat (limited to 'src/Util')
-rw-r--r-- | src/Util/Sigma.v | 19 | ||||
-rw-r--r-- | src/Util/Sigma/Associativity.v (renamed from src/Util/SigmaAssoc.v) | 0 | ||||
-rw-r--r-- | src/Util/Sigma/Lift.v | 33 |
3 files changed, 33 insertions, 19 deletions
diff --git a/src/Util/Sigma.v b/src/Util/Sigma.v index 693b8ef00..1c30219b7 100644 --- a/src/Util/Sigma.v +++ b/src/Util/Sigma.v @@ -211,25 +211,6 @@ Section ex. Defined. End ex. -(* Lift foralls out of sig proofs *) -Definition lift1_sig {A C} (P:A->C->Prop) - (op_sig : forall (a:A), {c | P a c}) : - { op : A -> C | forall (a:A), P a (op a) } - := exist - (fun op => forall a, P a (op a)) - (fun a => proj1_sig (op_sig a)) - (fun a => proj2_sig (op_sig a)) -. - -(* Lift foralls out of sig proofs *) -Definition lift2_sig {A B C} (P:A->B->C->Prop) - (op_sig : forall (a:A) (b:B), {c | P a b c}) : - { op : A -> B -> C | forall (a:A) (b:B), P a b (op a b) } - := exist - (fun op => forall a b, P a b (op a b)) - (fun a b => proj1_sig (op_sig a b)) - (fun a b => proj2_sig (op_sig a b)). - Definition projT2_map {A P Q} (f : forall a, P a -> Q a) (x : @sigT A P) : @sigT A Q := let 'existT a p := x in existT Q a (f a p). Definition proj2_sig_map {A} {P Q : A -> Prop} (f : forall a, P a -> Q a) (x : @sig A P) : @sig A Q diff --git a/src/Util/SigmaAssoc.v b/src/Util/Sigma/Associativity.v index fbebf2584..fbebf2584 100644 --- a/src/Util/SigmaAssoc.v +++ b/src/Util/Sigma/Associativity.v diff --git a/src/Util/Sigma/Lift.v b/src/Util/Sigma/Lift.v new file mode 100644 index 000000000..c57172029 --- /dev/null +++ b/src/Util/Sigma/Lift.v @@ -0,0 +1,33 @@ +(** * Lift foralls out of sig proofs *) + +Definition lift1_sig {A C} (P:A->C->Prop) + (op_sig : forall (a:A), {c | P a c}) +: { op : A -> C | forall (a:A), P a (op a) } +:= exist + (fun op => forall a, P a (op a)) + (fun a => proj1_sig (op_sig a)) + (fun a => proj2_sig (op_sig a)). + +Definition lift2_sig {A B C} (P:A->B->C->Prop) + (op_sig : forall (a:A) (b:B), {c | P a b c}) + : { op : A -> B -> C | forall (a:A) (b:B), P a b (op a b) } + := exist + (fun op => forall a b, P a b (op a b)) + (fun a b => proj1_sig (op_sig a b)) + (fun a b => proj2_sig (op_sig a b)). + +Definition lift3_sig {A B C D} (P:A->B->C->D->Prop) + (op_sig : forall (a:A) (b:B) (c:C), {d | P a b c d}) + : { op : A -> B -> C -> D | forall (a:A) (b:B) (c:C), P a b c (op a b c) } + := exist + (fun op => forall a b c, P a b c (op a b c)) + (fun a b c => proj1_sig (op_sig a b c)) + (fun a b c => proj2_sig (op_sig a b c)). + +Definition lift4_sig {A B C D E} (P:A->B->C->D->E->Prop) + (op_sig : forall (a:A) (b:B) (c:C) (d:D), {e | P a b c d e}) + : { op : A -> B -> C -> D -> E | forall (a:A) (b:B) (c:C) (d:D), P a b c d (op a b c d) } + := exist + (fun op => forall a b c d, P a b c d (op a b c d)) + (fun a b c d => proj1_sig (op_sig a b c d)) + (fun a b c d => proj2_sig (op_sig a b c d)). |