Fixprime.step_found: def of bend-collections-laws-math@1.0.0.0
Import: import bend-collections-laws-math@1.0.0.0/proofs/math/number/fixprime.bend as Fixprime
Lines 91-100 of bend-collections-laws-math@1.0.0.0/proofs/math/number/fixprime.bend: https://jend.leeeet.dev/read.txt?path=bend-collections-laws-math@1.0.0.0/proofs/math/number/fixprime.bend&start_line=91&end_line=100

import Base
import bend-collections-laws-math@1.0.0.0/spec/math/fixed.bend as SF
import bend-collections-laws-math@1.0.0.0/spec/math/number.bend as SN
import bend-collections-laws-math@1.0.0.0/proofs/lib/nat.bend as N
import bend-collections-laws-math@1.0.0.0/proofs/lib/logic.bend as L
import bend-collections-laws-math@1.0.0.0/proofs/math/number/prime.bend as PR

def step_found(+t: Nat, +q: Nat, +pt: {SN.prime(t) == False{} : Bool}, +ih: {Bool.and(Bool.and(Nat.is_le(1n+t, q), SN.prime(q)), SF.no_prime(Nat.sub(q, 1n+t), 1n+t)) == True{} : Bool}) -> {Bool.and(Bool.and(Nat.is_le(t, q), SN.prime(q)), SF.no_prime(Nat.sub(q, t), t)) == True{} : Bool}:
  +a12 = L.and_left(Bool.and(Nat.is_le(1n+t, q), SN.prime(q)), SF.no_prime(Nat.sub(q, 1n+t), 1n+t), ih)
  +a1 = L.and_left(Nat.is_le(1n+t, q), SN.prime(q), a12)
  +a2 = L.and_right(Nat.is_le(1n+t, q), SN.prime(q), a12)
  +a3 = L.and_right(Bool.and(Nat.is_le(1n+t, q), SN.prime(q)), SF.no_prime(Nat.sub(q, 1n+t), 1n+t), ih)
  +le = N.le_trans(t, 1n+t, q, N.le_succ(t), a1)
  +es = PR.sub_split(q, t, N.succ_le_lt(t, q, a1))
  %Equal.sym(Nat, Nat.sub(q, t), 1n+Nat.sub(q, 1n+t), es) : {Bool.and(Bool.and(Nat.is_le(t, q), SN.prime(q)), SF.no_prime(_, t)) == True{} : Bool}
  %Equal.sym(Bool, SN.prime(t), False{}, pt) : {Bool.and(Bool.and(Nat.is_le(t, q), SN.prime(q)), Bool.and(Bool.not(_), SF.no_prime(Nat.sub(q, 1n+t), 1n+t))) == True{} : Bool}
  L.and_intro(Bool.and(Nat.is_le(t, q), SN.prime(q)), Bool.and(True{}, SF.no_prime(Nat.sub(q, 1n+t), 1n+t)), L.and_intro(Nat.is_le(t, q), SN.prime(q), le, a2), a3)

Uses (16):
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Bool
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Bool.and
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Bool.not
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Equal.sym
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat.is_le
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat.sub
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/proofs/lib/logic.bend&name=and_intro
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/proofs/lib/logic.bend&name=and_left
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/proofs/lib/logic.bend&name=and_right
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/proofs/lib/nat.bend&name=le_succ
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/proofs/lib/nat.bend&name=le_trans
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/proofs/lib/nat.bend&name=succ_le_lt
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/proofs/math/number/prime.bend&name=sub_split
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/spec/math/fixed.bend&name=no_prime
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/spec/math/number.bend&name=prime