Proof.inv_value: def of bend-collections-laws-crypto@1.0.0.0
Import: import bend-collections-laws-crypto@1.0.0.0/proofs/crypto/curve25519/proof.bend as Proof
Lines 84-87 of bend-collections-laws-crypto@1.0.0.0/proofs/crypto/curve25519/proof.bend: https://jend.leeeet.dev/read.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/crypto/curve25519/proof.bend&start_line=84&end_line=87

import Base
import bend-collections-laws-crypto@1.0.0.0/spec/crypto/curve25519/field.bend as FS
import bend-collections-laws-crypto@1.0.0.0/src/crypto/curve25519/field.bend as F
import bend-collections-laws-crypto@1.0.0.0/proofs/math/natural/arith.bend as NR
import bend-collections-laws-crypto@1.0.0.0/proofs/crypto/curve25519/pow.bend as PW
import bend-collections-laws-crypto@1.0.0.0/proofs/crypto/curve25519/prime.bend as PR
import bend-collections-laws-crypto@1.0.0.0/proofs/crypto/curve25519/cong.bend as G

def inv_value(+one: Nat, +h1: {one == 1n : Nat}, +a: List<&2, U32>, +ha: {FS.tight(a) == True{} : Bool}) -> FS.Inv.value(one, h1, a, ha):
  +pp = pp1(one)
  +e = G.c_trans(pp, FS.value(F.inv(a)), Nat.pow(FS.value(a), Nat.sub(1n+pp, 2n)), FS.finv(1n+pp, FS.value(a)), PW.inv_val(one, h1, pp, PR.hP(one, h1), a, ok(a, ha)), G.c_sym(pp, FS.finv(1n+pp, FS.value(a)), Nat.pow(FS.value(a), Nat.sub(1n+pp, 2n)), G.c_mod(pp, Nat.pow(FS.value(a), Nat.sub(1n+pp, 2n)))))
  at_p(one, h1, z => {Nat.mod(FS.value(F.inv(a)), z) == FS.finv(z, FS.value(a)) : Nat}, Equal.trans(Nat, Nat.mod(FS.value(F.inv(a)), 1n+pp), Nat.mod(FS.finv(1n+pp, FS.value(a)), 1n+pp), FS.finv(1n+pp, FS.value(a)), e, NR.mod_mod(pp, Nat.pow(FS.value(a), Nat.sub(1n+pp, 2n)))))

Uses (22):
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Bool
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Equal.trans
  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.mod
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat.pow
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat.sub
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=U32
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/crypto/curve25519/cong.bend&name=c_mod
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/crypto/curve25519/cong.bend&name=c_sym
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/crypto/curve25519/cong.bend&name=c_trans
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/crypto/curve25519/pow.bend&name=inv_val
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/crypto/curve25519/prime.bend&name=hP
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/crypto/curve25519/proof.bend&name=at_p
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/crypto/curve25519/proof.bend&name=ok
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/crypto/curve25519/proof.bend&name=pp1
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/math/natural/arith.bend&name=mod_mod
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/spec/crypto/curve25519/field.bend&name=Inv.value
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/spec/crypto/curve25519/field.bend&name=finv
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/spec/crypto/curve25519/field.bend&name=tight
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/spec/crypto/curve25519/field.bend&name=value
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/src/crypto/curve25519/field.bend&name=inv