1	import Base
2	import ../../../src/crypto/secp256k1.bend as K
3	import ../../../src/crypto/secp256k1/ecdsa.bend as E
4	import ../../../spec/crypto/secp256k1/ecdsa.bend as ES
5	import ./laws_sign.bend as Laws
6	import ./psign.bend as PS
7	
8	# ECDSA signing of src/crypto/secp256k1.bend (laws.bend Sign.correct):
9	# `bend proofs/crypto/secp256k1/proof_sign.bend`.
10	
11	def compact_v(m: Maybe<&2, E.Signature>) -> {K.compact(m) == PS.msig(m) : Maybe<&2, List<&2, U32>>}:
12	  match m:
13	    case None{}:
14	      {==}
15	    case Some{sig}:
16	      match sig:
17	        case E.Signature{r, s, v}:
18	          {==}
19	
20	def sign_c(+one: Nat, +h1: {one == 1n : Nat}, +sk: List<&2, U32>, +h: List<&2, U32>) -> {K.sign_compact(sk, h) == ES.sign(one, sk, h) : Maybe<&2, List<&2, U32>>}:
21	  Equal.trans(Maybe<&2, List<&2, U32>>, K.compact(E.sign(sk, h)), PS.msig(E.sign(sk, h)), ES.sign(one, sk, h), compact_v(E.sign(sk, h)), PS.sign_v(one, h1, sk, h))
22	
23	def Laws.Sign.correct(one, h1, sk, h):
24	  sign_c(one, h1, sk, h)