Negate.neg_t: def of bend-collections-laws-crypto@1.0.0.0
Import: import bend-collections-laws-crypto@1.0.0.0/proofs/crypto/secp256k1/negate.bend as Negate
Lines 147-159 of bend-collections-laws-crypto@1.0.0.0/proofs/crypto/secp256k1/negate.bend: https://jend.leeeet.dev/read.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/crypto/secp256k1/negate.bend&start_line=147&end_line=159

import Base
import bend-collections-laws-crypto@1.0.0.0/spec/lib/common.bend as C
import bend-collections-laws-crypto@1.0.0.0/src/crypto/secp256k1/limbs.bend as L
import bend-collections-laws-crypto@1.0.0.0/proofs/lib/lemmas/proofs/nat_algebra.bend as NA
import bend-collections-laws-crypto@1.0.0.0/proofs/math/typed/width.bend as WW
import bend-collections-laws-crypto@1.0.0.0/proofs/crypto/secp256k1/limbs.bend as LV
import bend-collections-laws-crypto@1.0.0.0/proofs/crypto/secp256k1/bounds.bend as B

# neg_raw(c, b) + b + c = 2^256
def neg_t(+one: Nat, +h1: {one == 1n : Nat}, +c: List<&2, Nat>, +b: List<&2, Nat>, +hbc: {Nat.is_lt(Nat.add(LV.ev(b), LV.ev(c)), C.shift(256n, one)) == True{} : Bool}) -> {Nat.add(LV.ev(L.neg_raw(c, b)), Nat.add(LV.ev(b), LV.ev(c))) == C.shift(256n, one) : Nat}:
  %Equal.sym(Nat, LV.ev(L.add(L.comp(L.norm16(L.add(b, c))), [1n])), Nat.add(LV.ev(L.comp(L.norm16(L.add(b, c)))), LV.ev([1n])), LV.add_v(L.comp(L.norm16(L.add(b, c))), [1n])) : {Nat.add(_, Nat.add(LV.ev(b), LV.ev(c))) == C.shift(256n, one) : Nat}
  %Equal.sym(Nat, Nat.add(LV.ev(b), LV.ev(c)), LV.ev(L.norm16(L.add(b, c))), Equal.sym(Nat, LV.ev(L.norm16(L.add(b, c))), Nat.add(LV.ev(b), LV.ev(c)), bc_v(one, h1, c, b, hbc))) : {Nat.add(Nat.add(LV.ev(L.comp(L.norm16(L.add(b, c)))), LV.ev([1n])), _) == C.shift(256n, one) : Nat}
  %Equal.sym(Nat, C.shift(256n, one), LV.pos(16n, one), Equal.sym(Nat, LV.pos(16n, one), C.shift(256n, one), B.pos16(one))) : {Nat.add(Nat.add(LV.ev(L.comp(L.norm16(L.add(b, c)))), LV.ev([1n])), LV.ev(L.norm16(L.add(b, c)))) == _ : Nat}
  %Equal.sym(Nat, LV.pos(16n, one), Nat.add(Nat.add(LV.ev(L.comp(L.norm16(L.add(b, c)))), LV.ev(L.norm16(L.add(b, c)))), one), Equal.sym(Nat, Nat.add(Nat.add(LV.ev(L.comp(L.norm16(L.add(b, c)))), LV.ev(L.norm16(L.add(b, c)))), one), LV.pos(16n, one), comp_v(one, h1, 16n, L.norm16(L.add(b, c)), bc_limbs(one, h1, c, b)))) : {Nat.add(Nat.add(LV.ev(L.comp(L.norm16(L.add(b, c)))), LV.ev([1n])), LV.ev(L.norm16(L.add(b, c)))) == _ : Nat}
  %Equal.sym(Nat, one, 1n, h1) : {Nat.add(Nat.add(LV.ev(L.comp(L.norm16(L.add(b, c)))), LV.ev([1n])), LV.ev(L.norm16(L.add(b, c)))) == Nat.add(Nat.add(LV.ev(L.comp(L.norm16(L.add(b, c)))), LV.ev(L.norm16(L.add(b, c)))), _) : Nat}
  %Equal.sym(Nat, C.shift(16n, 0n), 0n, WW.shift_zero(16n)) : {Nat.add(Nat.add(LV.ev(L.comp(L.norm16(L.add(b, c)))), Nat.add(1n, _)), LV.ev(L.norm16(L.add(b, c)))) == Nat.add(Nat.add(LV.ev(L.comp(L.norm16(L.add(b, c)))), LV.ev(L.norm16(L.add(b, c)))), 1n) : Nat}
  %Equal.sym(Nat, Nat.add(1n, 0n), 1n, {==}) : {Nat.add(Nat.add(LV.ev(L.comp(L.norm16(L.add(b, c)))), _), LV.ev(L.norm16(L.add(b, c)))) == Nat.add(Nat.add(LV.ev(L.comp(L.norm16(L.add(b, c)))), LV.ev(L.norm16(L.add(b, c)))), 1n) : Nat}
  %Equal.sym(Nat, Nat.add(Nat.add(LV.ev(L.comp(L.norm16(L.add(b, c)))), 1n), LV.ev(L.norm16(L.add(b, c)))), Nat.add(LV.ev(L.comp(L.norm16(L.add(b, c)))), Nat.add(1n, LV.ev(L.norm16(L.add(b, c))))), NA.add_assoc(LV.ev(L.comp(L.norm16(L.add(b, c)))), 1n, LV.ev(L.norm16(L.add(b, c))))) : {_ == Nat.add(Nat.add(LV.ev(L.comp(L.norm16(L.add(b, c)))), LV.ev(L.norm16(L.add(b, c)))), 1n) : Nat}
  %Equal.sym(Nat, Nat.add(1n, LV.ev(L.norm16(L.add(b, c)))), Nat.add(LV.ev(L.norm16(L.add(b, c))), 1n), NA.add_comm(1n, LV.ev(L.norm16(L.add(b, c))))) : {Nat.add(LV.ev(L.comp(L.norm16(L.add(b, c)))), _) == Nat.add(Nat.add(LV.ev(L.comp(L.norm16(L.add(b, c)))), LV.ev(L.norm16(L.add(b, c)))), 1n) : Nat}
  %Equal.sym(Nat, Nat.add(Nat.add(LV.ev(L.comp(L.norm16(L.add(b, c)))), LV.ev(L.norm16(L.add(b, c)))), 1n), Nat.add(LV.ev(L.comp(L.norm16(L.add(b, c)))), Nat.add(LV.ev(L.norm16(L.add(b, c))), 1n)), NA.add_assoc(LV.ev(L.comp(L.norm16(L.add(b, c)))), LV.ev(L.norm16(L.add(b, c))), 1n)) : {Nat.add(LV.ev(L.comp(L.norm16(L.add(b, c)))), Nat.add(LV.ev(L.norm16(L.add(b, c))), 1n)) == _ : Nat}
  {==}

Uses (21):
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Bool
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Equal.sym
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=List
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat.add
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat.is_lt
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/crypto/secp256k1/bounds.bend&name=pos16
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/crypto/secp256k1/limbs.bend&name=add_v
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/crypto/secp256k1/limbs.bend&name=ev
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/crypto/secp256k1/limbs.bend&name=pos
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/crypto/secp256k1/negate.bend&name=bc_limbs
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/crypto/secp256k1/negate.bend&name=bc_v
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/crypto/secp256k1/negate.bend&name=comp_v
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/lib/lemmas/proofs/nat_algebra.bend&name=add_assoc
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/lib/lemmas/proofs/nat_algebra.bend&name=add_comm
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/math/typed/width.bend&name=shift_zero
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/spec/lib/common.bend&name=shift
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/src/crypto/secp256k1/limbs.bend&name=add
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/src/crypto/secp256k1/limbs.bend&name=comp
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/src/crypto/secp256k1/limbs.bend&name=neg_raw
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/src/crypto/secp256k1/limbs.bend&name=norm16