PROOF.tl.nzpick: def of bend-osdev-gf@0.1.1.0
Import: import bend-osdev-gf@0.1.1.0/PROOF.bend as PROOF
Lines 7873-7879 of bend-osdev-gf@0.1.1.0/PROOF.bend: https://jend.leeeet.dev/read.txt?path=bend-osdev-gf@0.1.1.0/PROOF.bend&start_line=7873&end_line=7879

import Base
import bend-osdev-gf@0.1.1.0/gf.bend as G
import bend-osdev-gf@0.1.1.0/tables.bend as T
import bend-osdev-array@0.1.0.1/array.bend as A
import bend-osdev-array@0.1.0.1/LAWS.bend as AL
import bend-osdev-gf@0.1.1.0/proof_tab.bend as GT

# both factors nonzero: the table's product, through its three reads
def tl.nzpick(+f: G.Gf8Field, +l: List<&2, U32>, +a: U32, +b: U32, +hl: {List.length(&2, U32, l) == A.Arrays.slots(8n) : Nat}, +hxa: {A.Arrays.nth(U32, l, A.Arrays.index(8n, G.Gf8.elt(a)), 0) == U32.from_nat(G.Gf8.log(f, a)) : U32}, +hxb: {A.Arrays.nth(U32, l, A.Arrays.index(8n, G.Gf8.elt(b)), 0) == U32.from_nat(G.Gf8.log(f, b)) : U32}, +ela: {G.Gf8.exp(f, G.Gf8.log(f, a)) == G.Gf8.elt(a) : U32}, +elb: {G.Gf8.exp(f, G.Gf8.log(f, b)) == G.Gf8.elt(b) : U32}) -> {T.gf8tab.two.pick(Bool.or(False{}, False{}), GT.gt.tab(f, l), G.Gf8.elt(a), G.Gf8.elt(b), False{}) == (GT.gt.tab(f, l), G.Gf8.mul(f, a, b)) : T.Gf8Tab & U32}:
  %Equal.sym(Array<U32> & U32, Array.get(U32, A.Arrays.of_list(U32, 8n, l, 0), G.Gf8.elt(a)), (A.Arrays.of_list(U32, 8n, l, 0), A.Arrays.nth(U32, l, A.Arrays.index(8n, G.Gf8.elt(a)), 0)), AL.of_list_get(U32, 8n, l, 0, hl, GT.gt.hd8(), G.Gf8.elt(a))) : {T.gf8tab.two.mid(A.Arrays.of_list(U32, 9n, GT.gt.elist(510n, f, 0n), 0), _, G.Gf8.elt(b), False{}) == (GT.gt.tab(f, l), G.Gf8.mul(f, a, b)) : T.Gf8Tab & U32}
  %Equal.sym(Array<U32> & U32, Array.get(U32, A.Arrays.of_list(U32, 8n, l, 0), G.Gf8.elt(b)), (A.Arrays.of_list(U32, 8n, l, 0), A.Arrays.nth(U32, l, A.Arrays.index(8n, G.Gf8.elt(b)), 0)), AL.of_list_get(U32, 8n, l, 0, hl, GT.gt.hd8(), G.Gf8.elt(b))) : {T.gf8tab.two.fin(A.Arrays.of_list(U32, 9n, GT.gt.elist(510n, f, 0n), 0), _, A.Arrays.nth(U32, l, A.Arrays.index(8n, G.Gf8.elt(a)), 0), False{}) == (GT.gt.tab(f, l), G.Gf8.mul(f, a, b)) : T.Gf8Tab & U32}
  %Equal.sym(Array<U32> & U32, Array.get(U32, A.Arrays.of_list(U32, 9n, GT.gt.elist(510n, f, 0n), 0), U32.add(A.Arrays.nth(U32, l, A.Arrays.index(8n, G.Gf8.elt(a)), 0), A.Arrays.nth(U32, l, A.Arrays.index(8n, G.Gf8.elt(b)), 0))), (A.Arrays.of_list(U32, 9n, GT.gt.elist(510n, f, 0n), 0), A.Arrays.nth(U32, GT.gt.elist(510n, f, 0n), A.Arrays.index(9n, U32.add(A.Arrays.nth(U32, l, A.Arrays.index(8n, G.Gf8.elt(a)), 0), A.Arrays.nth(U32, l, A.Arrays.index(8n, G.Gf8.elt(b)), 0))), 0)), AL.of_list_get(U32, 9n, GT.gt.elist(510n, f, 0n), 0, GT.gt.hl_elist(f), GT.gt.hd9(), U32.add(A.Arrays.nth(U32, l, A.Arrays.index(8n, G.Gf8.elt(a)), 0), A.Arrays.nth(U32, l, A.Arrays.index(8n, G.Gf8.elt(b)), 0)))) : {T.gf8tab.exp.fin(_, A.Arrays.of_list(U32, 8n, l, 0)) == (GT.gt.tab(f, l), G.Gf8.mul(f, a, b)) : T.Gf8Tab & U32}
  %Equal.sym(U32, A.Arrays.nth(U32, GT.gt.elist(510n, f, 0n), A.Arrays.index(9n, U32.add(A.Arrays.nth(U32, l, A.Arrays.index(8n, G.Gf8.elt(a)), 0), A.Arrays.nth(U32, l, A.Arrays.index(8n, G.Gf8.elt(b)), 0))), 0), G.Gf8.mul(f, a, b), tl.nz(f, l, a, b, hxa, hxb, ela, elb)) : {(T.Gf8Tab{A.Arrays.of_list(U32, 9n, GT.gt.elist(510n, f, 0n), 0), A.Arrays.of_list(U32, 8n, l, 0)}, _) == (GT.gt.tab(f, l), G.Gf8.mul(f, a, b)) : T.Gf8Tab & U32}
  {==}

Uses (34):
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Array
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Array.get
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Bool
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Bool.or
  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=List.length
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Pair
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Sigma
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=U32
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=U32.add
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=U32.from_nat
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-array@0.1.0.1/LAWS.bend&name=of_list_get
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-array@0.1.0.1/array.bend&name=Arrays.index
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-array@0.1.0.1/array.bend&name=Arrays.nth
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-array@0.1.0.1/array.bend&name=Arrays.of_list
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-array@0.1.0.1/array.bend&name=Arrays.slots
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-gf@0.1.1.0/PROOF.bend&name=tl.nz
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-gf@0.1.1.0/gf.bend&name=Gf8.elt
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-gf@0.1.1.0/gf.bend&name=Gf8.exp
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-gf@0.1.1.0/gf.bend&name=Gf8.log
  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.elist
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-gf@0.1.1.0/proof_tab.bend&name=gt.hd8
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-gf@0.1.1.0/proof_tab.bend&name=gt.hd9
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-gf@0.1.1.0/proof_tab.bend&name=gt.hl_elist
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-gf@0.1.1.0/proof_tab.bend&name=gt.tab
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-gf@0.1.1.0/tables.bend&name=Gf8Tab
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-gf@0.1.1.0/tables.bend&name=gf8tab.exp.fin
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-gf@0.1.1.0/tables.bend&name=gf8tab.two.fin
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-gf@0.1.1.0/tables.bend&name=gf8tab.two.mid
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-gf@0.1.1.0/tables.bend&name=gf8tab.two.pick