ProofTab.gt.log_go_lt: def of bend-osdev-gf@0.1.1.0
Import: import bend-osdev-gf@0.1.1.0/proof_tab.bend as ProofTab
Lines 172-180 of bend-osdev-gf@0.1.1.0/proof_tab.bend: https://jend.leeeet.dev/read.txt?path=bend-osdev-gf@0.1.1.0/proof_tab.bend&start_line=172&end_line=180

import Base
import bend-osdev-gf@0.1.1.0/gf.bend as G
import bend-osdev-u32@0.1.0.0/LAWS.bend as UL

def gt.log_go_lt(+n: Nat, hit: Bool, +f: G.Gf8Field, +a: U32, +cur: U32, +i: Nat) -> {Nat.is_lt(G.Gf8.log.go(n, hit, f, a, cur, i), 1n+Nat.add(n, i)) == True{} : Bool}:
  match n hit:
    case _ True{}:
      gt.lt_self_add(n, i)
    case 0n False{}:
      {==}
    case 1n+k False{}:
      %UL.nat_add_succ(k, i) : {Nat.is_lt(G.Gf8.log.go(k, U32.is_eq(G.Gf8.mul(f, G.Gf8.gen(f), cur), a), f, a, G.Gf8.mul(f, G.Gf8.gen(f), cur), 1n+i), 1n+_) == True{} : Bool}
      gt.log_go_lt(k, U32.is_eq(G.Gf8.mul(f, G.Gf8.gen(f), cur), a), f, a, G.Gf8.mul(f, G.Gf8.gen(f), cur), 1n+i)

Uses (12):
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Bool
  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=Base/base.bend&name=U32
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=U32.is_eq
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-gf@0.1.1.0/gf.bend&name=Gf8.gen
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-gf@0.1.1.0/gf.bend&name=Gf8.log.go
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-gf@0.1.1.0/gf.bend&name=Gf8.mul
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-gf@0.1.1.0/gf.bend&name=Gf8Field
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-gf@0.1.1.0/proof_tab.bend&name=gt.lt_self_add
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-u32@0.1.0.0/LAWS.bend&name=nat_add_succ