state stringlengths 0 159k | srcUpToTactic stringlengths 387 167k | nextTactic stringlengths 3 9k | declUpToTactic stringlengths 22 11.5k | declId stringlengths 38 95 | decl stringlengths 16 1.89k | file_tag stringlengths 17 73 |
|---|---|---|---|---|---|---|
a : Primrec fun a => ofNat (ℕ × Code) (List.length a)
k✝¹ : Primrec fun a => (ofNat (ℕ × Code) (List.length a.1)).1
n✝¹ : Primrec Prod.snd
k✝ : Primrec fun a => (ofNat (ℕ × Code) (List.length a.1.1)).1
n✝ : Primrec fun a => a.1.2
k' : Primrec Prod.snd
c : Primrec fun a => (ofNat (ℕ × Code) (List.length a.1.1)).2
L : Pr... | /-
Copyright (c) 2018 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro
-/
import Mathlib.Computability.Partrec
#align_import computability.partrec_code from "leanprover-community/mathlib"@"6155d4351090a6fad236e3d2e4e0e4e7342668e8"
/-!
# G... | congr
· ext p
dsimp only []
erw [Option.bind_eq_bind, ← Option.map_eq_bind] | private theorem hG : Primrec G := by
have a := (Primrec.ofNat (ℕ × Code)).comp (Primrec.list_length (α := List (Option ℕ)))
have k := Primrec.fst.comp a
refine' Primrec.option_some.comp (Primrec.list_map (Primrec.list_range.comp k) (_ : Primrec _))
replace k := k.comp (Primrec.fst (β := ℕ))
have n := Primrec.... | Mathlib.Computability.PartrecCode.976_0.A3c3Aev6SyIRjCJ | private theorem hG : Primrec G | Mathlib_Computability_PartrecCode |
a : Primrec fun a => ofNat (ℕ × Code) (List.length a)
k✝¹ : Primrec fun a => (ofNat (ℕ × Code) (List.length a.1)).1
n✝¹ : Primrec Prod.snd
k✝ : Primrec fun a => (ofNat (ℕ × Code) (List.length a.1.1)).1
n✝ : Primrec fun a => a.1.2
k' : Primrec Prod.snd
c : Primrec fun a => (ofNat (ℕ × Code) (List.length a.1.1)).2
L : Pr... | /-
Copyright (c) 2018 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro
-/
import Mathlib.Computability.Partrec
#align_import computability.partrec_code from "leanprover-community/mathlib"@"6155d4351090a6fad236e3d2e4e0e4e7342668e8"
/-!
# G... | congr
· ext p
dsimp only []
erw [Option.bind_eq_bind, ← Option.map_eq_bind] | private theorem hG : Primrec G := by
have a := (Primrec.ofNat (ℕ × Code)).comp (Primrec.list_length (α := List (Option ℕ)))
have k := Primrec.fst.comp a
refine' Primrec.option_some.comp (Primrec.list_map (Primrec.list_range.comp k) (_ : Primrec _))
replace k := k.comp (Primrec.fst (β := ℕ))
have n := Primrec.... | Mathlib.Computability.PartrecCode.976_0.A3c3Aev6SyIRjCJ | private theorem hG : Primrec G | Mathlib_Computability_PartrecCode |
a : Primrec fun a => ofNat (ℕ × Code) (List.length a)
k✝¹ : Primrec fun a => (ofNat (ℕ × Code) (List.length a.1)).1
n✝¹ : Primrec Prod.snd
k✝ : Primrec fun a => (ofNat (ℕ × Code) (List.length a.1.1)).1
n✝ : Primrec fun a => a.1.2
k' : Primrec Prod.snd
c : Primrec fun a => (ofNat (ℕ × Code) (List.length a.1.1)).2
L : Pr... | /-
Copyright (c) 2018 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro
-/
import Mathlib.Computability.Partrec
#align_import computability.partrec_code from "leanprover-community/mathlib"@"6155d4351090a6fad236e3d2e4e0e4e7342668e8"
/-!
# G... | congr | private theorem hG : Primrec G := by
have a := (Primrec.ofNat (ℕ × Code)).comp (Primrec.list_length (α := List (Option ℕ)))
have k := Primrec.fst.comp a
refine' Primrec.option_some.comp (Primrec.list_map (Primrec.list_range.comp k) (_ : Primrec _))
replace k := k.comp (Primrec.fst (β := ℕ))
have n := Primrec.... | Mathlib.Computability.PartrecCode.976_0.A3c3Aev6SyIRjCJ | private theorem hG : Primrec G | Mathlib_Computability_PartrecCode |
case f
a : Primrec fun a => ofNat (ℕ × Code) (List.length a)
k✝¹ : Primrec fun a => (ofNat (ℕ × Code) (List.length a.1)).1
n✝¹ : Primrec Prod.snd
k✝ : Primrec fun a => (ofNat (ℕ × Code) (List.length a.1.1)).1
n✝ : Primrec fun a => a.1.2
k' : Primrec Prod.snd
c : Primrec fun a => (ofNat (ℕ × Code) (List.length a.1.1)).2... | /-
Copyright (c) 2018 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro
-/
import Mathlib.Computability.Partrec
#align_import computability.partrec_code from "leanprover-community/mathlib"@"6155d4351090a6fad236e3d2e4e0e4e7342668e8"
/-!
# G... | · ext p
dsimp only []
erw [Option.bind_eq_bind, ← Option.map_eq_bind] | private theorem hG : Primrec G := by
have a := (Primrec.ofNat (ℕ × Code)).comp (Primrec.list_length (α := List (Option ℕ)))
have k := Primrec.fst.comp a
refine' Primrec.option_some.comp (Primrec.list_map (Primrec.list_range.comp k) (_ : Primrec _))
replace k := k.comp (Primrec.fst (β := ℕ))
have n := Primrec.... | Mathlib.Computability.PartrecCode.976_0.A3c3Aev6SyIRjCJ | private theorem hG : Primrec G | Mathlib_Computability_PartrecCode |
case f
a : Primrec fun a => ofNat (ℕ × Code) (List.length a)
k✝¹ : Primrec fun a => (ofNat (ℕ × Code) (List.length a.1)).1
n✝¹ : Primrec Prod.snd
k✝ : Primrec fun a => (ofNat (ℕ × Code) (List.length a.1.1)).1
n✝ : Primrec fun a => a.1.2
k' : Primrec Prod.snd
c : Primrec fun a => (ofNat (ℕ × Code) (List.length a.1.1)).2... | /-
Copyright (c) 2018 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro
-/
import Mathlib.Computability.Partrec
#align_import computability.partrec_code from "leanprover-community/mathlib"@"6155d4351090a6fad236e3d2e4e0e4e7342668e8"
/-!
# G... | ext p
dsimp only []
erw [Option.bind_eq_bind, ← Option.map_eq_bind] | private theorem hG : Primrec G := by
have a := (Primrec.ofNat (ℕ × Code)).comp (Primrec.list_length (α := List (Option ℕ)))
have k := Primrec.fst.comp a
refine' Primrec.option_some.comp (Primrec.list_map (Primrec.list_range.comp k) (_ : Primrec _))
replace k := k.comp (Primrec.fst (β := ℕ))
have n := Primrec.... | Mathlib.Computability.PartrecCode.976_0.A3c3Aev6SyIRjCJ | private theorem hG : Primrec G | Mathlib_Computability_PartrecCode |
case f
a : Primrec fun a => ofNat (ℕ × Code) (List.length a)
k✝¹ : Primrec fun a => (ofNat (ℕ × Code) (List.length a.1)).1
n✝¹ : Primrec Prod.snd
k✝ : Primrec fun a => (ofNat (ℕ × Code) (List.length a.1.1)).1
n✝ : Primrec fun a => a.1.2
k' : Primrec Prod.snd
c : Primrec fun a => (ofNat (ℕ × Code) (List.length a.1.1)).2... | /-
Copyright (c) 2018 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro
-/
import Mathlib.Computability.Partrec
#align_import computability.partrec_code from "leanprover-community/mathlib"@"6155d4351090a6fad236e3d2e4e0e4e7342668e8"
/-!
# G... | ext p
dsimp only []
erw [Option.bind_eq_bind, ← Option.map_eq_bind] | private theorem hG : Primrec G := by
have a := (Primrec.ofNat (ℕ × Code)).comp (Primrec.list_length (α := List (Option ℕ)))
have k := Primrec.fst.comp a
refine' Primrec.option_some.comp (Primrec.list_map (Primrec.list_range.comp k) (_ : Primrec _))
replace k := k.comp (Primrec.fst (β := ℕ))
have n := Primrec.... | Mathlib.Computability.PartrecCode.976_0.A3c3Aev6SyIRjCJ | private theorem hG : Primrec G | Mathlib_Computability_PartrecCode |
case f
a : Primrec fun a => ofNat (ℕ × Code) (List.length a)
k✝¹ : Primrec fun a => (ofNat (ℕ × Code) (List.length a.1)).1
n✝¹ : Primrec Prod.snd
k✝ : Primrec fun a => (ofNat (ℕ × Code) (List.length a.1.1)).1
n✝ : Primrec fun a => a.1.2
k' : Primrec Prod.snd
c : Primrec fun a => (ofNat (ℕ × Code) (List.length a.1.1)).2... | /-
Copyright (c) 2018 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro
-/
import Mathlib.Computability.Partrec
#align_import computability.partrec_code from "leanprover-community/mathlib"@"6155d4351090a6fad236e3d2e4e0e4e7342668e8"
/-!
# G... | ext p | private theorem hG : Primrec G := by
have a := (Primrec.ofNat (ℕ × Code)).comp (Primrec.list_length (α := List (Option ℕ)))
have k := Primrec.fst.comp a
refine' Primrec.option_some.comp (Primrec.list_map (Primrec.list_range.comp k) (_ : Primrec _))
replace k := k.comp (Primrec.fst (β := ℕ))
have n := Primrec.... | Mathlib.Computability.PartrecCode.976_0.A3c3Aev6SyIRjCJ | private theorem hG : Primrec G | Mathlib_Computability_PartrecCode |
case f.h
a : Primrec fun a => ofNat (ℕ × Code) (List.length a)
k✝¹ : Primrec fun a => (ofNat (ℕ × Code) (List.length a.1)).1
n✝¹ : Primrec Prod.snd
k✝ : Primrec fun a => (ofNat (ℕ × Code) (List.length a.1.1)).1
n✝ : Primrec fun a => a.1.2
k' : Primrec Prod.snd
c : Primrec fun a => (ofNat (ℕ × Code) (List.length a.1.1))... | /-
Copyright (c) 2018 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro
-/
import Mathlib.Computability.Partrec
#align_import computability.partrec_code from "leanprover-community/mathlib"@"6155d4351090a6fad236e3d2e4e0e4e7342668e8"
/-!
# G... | dsimp only [] | private theorem hG : Primrec G := by
have a := (Primrec.ofNat (ℕ × Code)).comp (Primrec.list_length (α := List (Option ℕ)))
have k := Primrec.fst.comp a
refine' Primrec.option_some.comp (Primrec.list_map (Primrec.list_range.comp k) (_ : Primrec _))
replace k := k.comp (Primrec.fst (β := ℕ))
have n := Primrec.... | Mathlib.Computability.PartrecCode.976_0.A3c3Aev6SyIRjCJ | private theorem hG : Primrec G | Mathlib_Computability_PartrecCode |
case f.h
a : Primrec fun a => ofNat (ℕ × Code) (List.length a)
k✝¹ : Primrec fun a => (ofNat (ℕ × Code) (List.length a.1)).1
n✝¹ : Primrec Prod.snd
k✝ : Primrec fun a => (ofNat (ℕ × Code) (List.length a.1.1)).1
n✝ : Primrec fun a => a.1.2
k' : Primrec Prod.snd
c : Primrec fun a => (ofNat (ℕ × Code) (List.length a.1.1))... | /-
Copyright (c) 2018 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro
-/
import Mathlib.Computability.Partrec
#align_import computability.partrec_code from "leanprover-community/mathlib"@"6155d4351090a6fad236e3d2e4e0e4e7342668e8"
/-!
# G... | erw [Option.bind_eq_bind, ← Option.map_eq_bind] | private theorem hG : Primrec G := by
have a := (Primrec.ofNat (ℕ × Code)).comp (Primrec.list_length (α := List (Option ℕ)))
have k := Primrec.fst.comp a
refine' Primrec.option_some.comp (Primrec.list_map (Primrec.list_range.comp k) (_ : Primrec _))
replace k := k.comp (Primrec.fst (β := ℕ))
have n := Primrec.... | Mathlib.Computability.PartrecCode.976_0.A3c3Aev6SyIRjCJ | private theorem hG : Primrec G | Mathlib_Computability_PartrecCode |
case hpr
a : Primrec fun a => ofNat (ℕ × Code) (List.length a)
k✝¹ : Primrec fun a => (ofNat (ℕ × Code) (List.length a.1)).1
n✝¹ : Primrec Prod.snd
k✝ : Primrec fun a => (ofNat (ℕ × Code) (List.length a.1.1)).1
n✝ : Primrec fun a => a.1.2
k' : Primrec Prod.snd
c : Primrec fun a => (ofNat (ℕ × Code) (List.length a.1.1))... | /-
Copyright (c) 2018 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro
-/
import Mathlib.Computability.Partrec
#align_import computability.partrec_code from "leanprover-community/mathlib"@"6155d4351090a6fad236e3d2e4e0e4e7342668e8"
/-!
# G... | refine Primrec.option_map ((hlup.comp <| L.pair <| (k.pair cg).pair n).comp Primrec.fst) ?_ | private theorem hG : Primrec G := by
have a := (Primrec.ofNat (ℕ × Code)).comp (Primrec.list_length (α := List (Option ℕ)))
have k := Primrec.fst.comp a
refine' Primrec.option_some.comp (Primrec.list_map (Primrec.list_range.comp k) (_ : Primrec _))
replace k := k.comp (Primrec.fst (β := ℕ))
have n := Primrec.... | Mathlib.Computability.PartrecCode.976_0.A3c3Aev6SyIRjCJ | private theorem hG : Primrec G | Mathlib_Computability_PartrecCode |
case hpr
a : Primrec fun a => ofNat (ℕ × Code) (List.length a)
k✝¹ : Primrec fun a => (ofNat (ℕ × Code) (List.length a.1)).1
n✝¹ : Primrec Prod.snd
k✝ : Primrec fun a => (ofNat (ℕ × Code) (List.length a.1.1)).1
n✝ : Primrec fun a => a.1.2
k' : Primrec Prod.snd
c : Primrec fun a => (ofNat (ℕ × Code) (List.length a.1.1))... | /-
Copyright (c) 2018 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro
-/
import Mathlib.Computability.Partrec
#align_import computability.partrec_code from "leanprover-community/mathlib"@"6155d4351090a6fad236e3d2e4e0e4e7342668e8"
/-!
# G... | unfold Primrec₂ | private theorem hG : Primrec G := by
have a := (Primrec.ofNat (ℕ × Code)).comp (Primrec.list_length (α := List (Option ℕ)))
have k := Primrec.fst.comp a
refine' Primrec.option_some.comp (Primrec.list_map (Primrec.list_range.comp k) (_ : Primrec _))
replace k := k.comp (Primrec.fst (β := ℕ))
have n := Primrec.... | Mathlib.Computability.PartrecCode.976_0.A3c3Aev6SyIRjCJ | private theorem hG : Primrec G | Mathlib_Computability_PartrecCode |
case hpr
a : Primrec fun a => ofNat (ℕ × Code) (List.length a)
k✝¹ : Primrec fun a => (ofNat (ℕ × Code) (List.length a.1)).1
n✝¹ : Primrec Prod.snd
k✝ : Primrec fun a => (ofNat (ℕ × Code) (List.length a.1.1)).1
n✝ : Primrec fun a => a.1.2
k' : Primrec Prod.snd
c : Primrec fun a => (ofNat (ℕ × Code) (List.length a.1.1))... | /-
Copyright (c) 2018 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro
-/
import Mathlib.Computability.Partrec
#align_import computability.partrec_code from "leanprover-community/mathlib"@"6155d4351090a6fad236e3d2e4e0e4e7342668e8"
/-!
# G... | exact Primrec₂.natPair.comp (Primrec.snd.comp Primrec.fst) Primrec.snd | private theorem hG : Primrec G := by
have a := (Primrec.ofNat (ℕ × Code)).comp (Primrec.list_length (α := List (Option ℕ)))
have k := Primrec.fst.comp a
refine' Primrec.option_some.comp (Primrec.list_map (Primrec.list_range.comp k) (_ : Primrec _))
replace k := k.comp (Primrec.fst (β := ℕ))
have n := Primrec.... | Mathlib.Computability.PartrecCode.976_0.A3c3Aev6SyIRjCJ | private theorem hG : Primrec G | Mathlib_Computability_PartrecCode |
case hco
a : Primrec fun a => ofNat (ℕ × Code) (List.length a)
k✝ : Primrec fun a => (ofNat (ℕ × Code) (List.length a.1)).1
n✝ : Primrec Prod.snd
k : Primrec fun a => (ofNat (ℕ × Code) (List.length a.1.1)).1
n : Primrec fun a => a.1.2
k' : Primrec Prod.snd
c : Primrec fun a => (ofNat (ℕ × Code) (List.length a.1.1)).2
⊢... | /-
Copyright (c) 2018 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro
-/
import Mathlib.Computability.Partrec
#align_import computability.partrec_code from "leanprover-community/mathlib"@"6155d4351090a6fad236e3d2e4e0e4e7342668e8"
/-!
# G... | have L := (Primrec.fst.comp Primrec.fst).comp
(Primrec.fst (α := (List (List (Option ℕ)) × ℕ) × ℕ)
(β := Code × Code × Option ℕ × Option ℕ)) | private theorem hG : Primrec G := by
have a := (Primrec.ofNat (ℕ × Code)).comp (Primrec.list_length (α := List (Option ℕ)))
have k := Primrec.fst.comp a
refine' Primrec.option_some.comp (Primrec.list_map (Primrec.list_range.comp k) (_ : Primrec _))
replace k := k.comp (Primrec.fst (β := ℕ))
have n := Primrec.... | Mathlib.Computability.PartrecCode.976_0.A3c3Aev6SyIRjCJ | private theorem hG : Primrec G | Mathlib_Computability_PartrecCode |
case hco
a : Primrec fun a => ofNat (ℕ × Code) (List.length a)
k✝ : Primrec fun a => (ofNat (ℕ × Code) (List.length a.1)).1
n✝ : Primrec Prod.snd
k : Primrec fun a => (ofNat (ℕ × Code) (List.length a.1.1)).1
n : Primrec fun a => a.1.2
k' : Primrec Prod.snd
c : Primrec fun a => (ofNat (ℕ × Code) (List.length a.1.1)).2
L... | /-
Copyright (c) 2018 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro
-/
import Mathlib.Computability.Partrec
#align_import computability.partrec_code from "leanprover-community/mathlib"@"6155d4351090a6fad236e3d2e4e0e4e7342668e8"
/-!
# G... | have k := k.comp (Primrec.fst (β := Code × Code × Option ℕ × Option ℕ)) | private theorem hG : Primrec G := by
have a := (Primrec.ofNat (ℕ × Code)).comp (Primrec.list_length (α := List (Option ℕ)))
have k := Primrec.fst.comp a
refine' Primrec.option_some.comp (Primrec.list_map (Primrec.list_range.comp k) (_ : Primrec _))
replace k := k.comp (Primrec.fst (β := ℕ))
have n := Primrec.... | Mathlib.Computability.PartrecCode.976_0.A3c3Aev6SyIRjCJ | private theorem hG : Primrec G | Mathlib_Computability_PartrecCode |
case hco
a : Primrec fun a => ofNat (ℕ × Code) (List.length a)
k✝¹ : Primrec fun a => (ofNat (ℕ × Code) (List.length a.1)).1
n✝ : Primrec Prod.snd
k✝ : Primrec fun a => (ofNat (ℕ × Code) (List.length a.1.1)).1
n : Primrec fun a => a.1.2
k' : Primrec Prod.snd
c : Primrec fun a => (ofNat (ℕ × Code) (List.length a.1.1)).2... | /-
Copyright (c) 2018 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro
-/
import Mathlib.Computability.Partrec
#align_import computability.partrec_code from "leanprover-community/mathlib"@"6155d4351090a6fad236e3d2e4e0e4e7342668e8"
/-!
# G... | have n := n.comp (Primrec.fst (β := Code × Code × Option ℕ × Option ℕ)) | private theorem hG : Primrec G := by
have a := (Primrec.ofNat (ℕ × Code)).comp (Primrec.list_length (α := List (Option ℕ)))
have k := Primrec.fst.comp a
refine' Primrec.option_some.comp (Primrec.list_map (Primrec.list_range.comp k) (_ : Primrec _))
replace k := k.comp (Primrec.fst (β := ℕ))
have n := Primrec.... | Mathlib.Computability.PartrecCode.976_0.A3c3Aev6SyIRjCJ | private theorem hG : Primrec G | Mathlib_Computability_PartrecCode |
case hco
a : Primrec fun a => ofNat (ℕ × Code) (List.length a)
k✝¹ : Primrec fun a => (ofNat (ℕ × Code) (List.length a.1)).1
n✝¹ : Primrec Prod.snd
k✝ : Primrec fun a => (ofNat (ℕ × Code) (List.length a.1.1)).1
n✝ : Primrec fun a => a.1.2
k' : Primrec Prod.snd
c : Primrec fun a => (ofNat (ℕ × Code) (List.length a.1.1))... | /-
Copyright (c) 2018 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro
-/
import Mathlib.Computability.Partrec
#align_import computability.partrec_code from "leanprover-community/mathlib"@"6155d4351090a6fad236e3d2e4e0e4e7342668e8"
/-!
# G... | have cf := Primrec.fst.comp (Primrec.snd (α := (List (List (Option ℕ)) × ℕ) × ℕ)
(β := Code × Code × Option ℕ × Option ℕ)) | private theorem hG : Primrec G := by
have a := (Primrec.ofNat (ℕ × Code)).comp (Primrec.list_length (α := List (Option ℕ)))
have k := Primrec.fst.comp a
refine' Primrec.option_some.comp (Primrec.list_map (Primrec.list_range.comp k) (_ : Primrec _))
replace k := k.comp (Primrec.fst (β := ℕ))
have n := Primrec.... | Mathlib.Computability.PartrecCode.976_0.A3c3Aev6SyIRjCJ | private theorem hG : Primrec G | Mathlib_Computability_PartrecCode |
case hco
a : Primrec fun a => ofNat (ℕ × Code) (List.length a)
k✝¹ : Primrec fun a => (ofNat (ℕ × Code) (List.length a.1)).1
n✝¹ : Primrec Prod.snd
k✝ : Primrec fun a => (ofNat (ℕ × Code) (List.length a.1.1)).1
n✝ : Primrec fun a => a.1.2
k' : Primrec Prod.snd
c : Primrec fun a => (ofNat (ℕ × Code) (List.length a.1.1))... | /-
Copyright (c) 2018 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro
-/
import Mathlib.Computability.Partrec
#align_import computability.partrec_code from "leanprover-community/mathlib"@"6155d4351090a6fad236e3d2e4e0e4e7342668e8"
/-!
# G... | have cg := (Primrec.fst.comp Primrec.snd).comp
(Primrec.snd (α := (List (List (Option ℕ)) × ℕ) × ℕ)
(β := Code × Code × Option ℕ × Option ℕ)) | private theorem hG : Primrec G := by
have a := (Primrec.ofNat (ℕ × Code)).comp (Primrec.list_length (α := List (Option ℕ)))
have k := Primrec.fst.comp a
refine' Primrec.option_some.comp (Primrec.list_map (Primrec.list_range.comp k) (_ : Primrec _))
replace k := k.comp (Primrec.fst (β := ℕ))
have n := Primrec.... | Mathlib.Computability.PartrecCode.976_0.A3c3Aev6SyIRjCJ | private theorem hG : Primrec G | Mathlib_Computability_PartrecCode |
case hco
a : Primrec fun a => ofNat (ℕ × Code) (List.length a)
k✝¹ : Primrec fun a => (ofNat (ℕ × Code) (List.length a.1)).1
n✝¹ : Primrec Prod.snd
k✝ : Primrec fun a => (ofNat (ℕ × Code) (List.length a.1.1)).1
n✝ : Primrec fun a => a.1.2
k' : Primrec Prod.snd
c : Primrec fun a => (ofNat (ℕ × Code) (List.length a.1.1))... | /-
Copyright (c) 2018 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro
-/
import Mathlib.Computability.Partrec
#align_import computability.partrec_code from "leanprover-community/mathlib"@"6155d4351090a6fad236e3d2e4e0e4e7342668e8"
/-!
# G... | refine Primrec.option_bind (hlup.comp <| L.pair <| (k.pair cg).pair n) ?_ | private theorem hG : Primrec G := by
have a := (Primrec.ofNat (ℕ × Code)).comp (Primrec.list_length (α := List (Option ℕ)))
have k := Primrec.fst.comp a
refine' Primrec.option_some.comp (Primrec.list_map (Primrec.list_range.comp k) (_ : Primrec _))
replace k := k.comp (Primrec.fst (β := ℕ))
have n := Primrec.... | Mathlib.Computability.PartrecCode.976_0.A3c3Aev6SyIRjCJ | private theorem hG : Primrec G | Mathlib_Computability_PartrecCode |
case hco
a : Primrec fun a => ofNat (ℕ × Code) (List.length a)
k✝¹ : Primrec fun a => (ofNat (ℕ × Code) (List.length a.1)).1
n✝¹ : Primrec Prod.snd
k✝ : Primrec fun a => (ofNat (ℕ × Code) (List.length a.1.1)).1
n✝ : Primrec fun a => a.1.2
k' : Primrec Prod.snd
c : Primrec fun a => (ofNat (ℕ × Code) (List.length a.1.1))... | /-
Copyright (c) 2018 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro
-/
import Mathlib.Computability.Partrec
#align_import computability.partrec_code from "leanprover-community/mathlib"@"6155d4351090a6fad236e3d2e4e0e4e7342668e8"
/-!
# G... | unfold Primrec₂ | private theorem hG : Primrec G := by
have a := (Primrec.ofNat (ℕ × Code)).comp (Primrec.list_length (α := List (Option ℕ)))
have k := Primrec.fst.comp a
refine' Primrec.option_some.comp (Primrec.list_map (Primrec.list_range.comp k) (_ : Primrec _))
replace k := k.comp (Primrec.fst (β := ℕ))
have n := Primrec.... | Mathlib.Computability.PartrecCode.976_0.A3c3Aev6SyIRjCJ | private theorem hG : Primrec G | Mathlib_Computability_PartrecCode |
case hco
a : Primrec fun a => ofNat (ℕ × Code) (List.length a)
k✝¹ : Primrec fun a => (ofNat (ℕ × Code) (List.length a.1)).1
n✝¹ : Primrec Prod.snd
k✝ : Primrec fun a => (ofNat (ℕ × Code) (List.length a.1.1)).1
n✝ : Primrec fun a => a.1.2
k' : Primrec Prod.snd
c : Primrec fun a => (ofNat (ℕ × Code) (List.length a.1.1))... | /-
Copyright (c) 2018 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro
-/
import Mathlib.Computability.Partrec
#align_import computability.partrec_code from "leanprover-community/mathlib"@"6155d4351090a6fad236e3d2e4e0e4e7342668e8"
/-!
# G... | have h :=
hlup.comp ((L.comp Primrec.fst).pair <| ((k.pair cf).comp Primrec.fst).pair Primrec.snd) | private theorem hG : Primrec G := by
have a := (Primrec.ofNat (ℕ × Code)).comp (Primrec.list_length (α := List (Option ℕ)))
have k := Primrec.fst.comp a
refine' Primrec.option_some.comp (Primrec.list_map (Primrec.list_range.comp k) (_ : Primrec _))
replace k := k.comp (Primrec.fst (β := ℕ))
have n := Primrec.... | Mathlib.Computability.PartrecCode.976_0.A3c3Aev6SyIRjCJ | private theorem hG : Primrec G | Mathlib_Computability_PartrecCode |
case hco
a : Primrec fun a => ofNat (ℕ × Code) (List.length a)
k✝¹ : Primrec fun a => (ofNat (ℕ × Code) (List.length a.1)).1
n✝¹ : Primrec Prod.snd
k✝ : Primrec fun a => (ofNat (ℕ × Code) (List.length a.1.1)).1
n✝ : Primrec fun a => a.1.2
k' : Primrec Prod.snd
c : Primrec fun a => (ofNat (ℕ × Code) (List.length a.1.1))... | /-
Copyright (c) 2018 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro
-/
import Mathlib.Computability.Partrec
#align_import computability.partrec_code from "leanprover-community/mathlib"@"6155d4351090a6fad236e3d2e4e0e4e7342668e8"
/-!
# G... | exact h | private theorem hG : Primrec G := by
have a := (Primrec.ofNat (ℕ × Code)).comp (Primrec.list_length (α := List (Option ℕ)))
have k := Primrec.fst.comp a
refine' Primrec.option_some.comp (Primrec.list_map (Primrec.list_range.comp k) (_ : Primrec _))
replace k := k.comp (Primrec.fst (β := ℕ))
have n := Primrec.... | Mathlib.Computability.PartrecCode.976_0.A3c3Aev6SyIRjCJ | private theorem hG : Primrec G | Mathlib_Computability_PartrecCode |
case hpc
a : Primrec fun a => ofNat (ℕ × Code) (List.length a)
k✝ : Primrec fun a => (ofNat (ℕ × Code) (List.length a.1)).1
n✝ : Primrec Prod.snd
k : Primrec fun a => (ofNat (ℕ × Code) (List.length a.1.1)).1
n : Primrec fun a => a.1.2
k' : Primrec Prod.snd
c : Primrec fun a => (ofNat (ℕ × Code) (List.length a.1.1)).2
⊢... | /-
Copyright (c) 2018 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro
-/
import Mathlib.Computability.Partrec
#align_import computability.partrec_code from "leanprover-community/mathlib"@"6155d4351090a6fad236e3d2e4e0e4e7342668e8"
/-!
# G... | have L := (Primrec.fst.comp Primrec.fst).comp
(Primrec.fst (α := (List (List (Option ℕ)) × ℕ) × ℕ)
(β := Code × Code × Option ℕ × Option ℕ)) | private theorem hG : Primrec G := by
have a := (Primrec.ofNat (ℕ × Code)).comp (Primrec.list_length (α := List (Option ℕ)))
have k := Primrec.fst.comp a
refine' Primrec.option_some.comp (Primrec.list_map (Primrec.list_range.comp k) (_ : Primrec _))
replace k := k.comp (Primrec.fst (β := ℕ))
have n := Primrec.... | Mathlib.Computability.PartrecCode.976_0.A3c3Aev6SyIRjCJ | private theorem hG : Primrec G | Mathlib_Computability_PartrecCode |
case hpc
a : Primrec fun a => ofNat (ℕ × Code) (List.length a)
k✝ : Primrec fun a => (ofNat (ℕ × Code) (List.length a.1)).1
n✝ : Primrec Prod.snd
k : Primrec fun a => (ofNat (ℕ × Code) (List.length a.1.1)).1
n : Primrec fun a => a.1.2
k' : Primrec Prod.snd
c : Primrec fun a => (ofNat (ℕ × Code) (List.length a.1.1)).2
L... | /-
Copyright (c) 2018 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro
-/
import Mathlib.Computability.Partrec
#align_import computability.partrec_code from "leanprover-community/mathlib"@"6155d4351090a6fad236e3d2e4e0e4e7342668e8"
/-!
# G... | have k := k.comp (Primrec.fst (β := Code × Code × Option ℕ × Option ℕ)) | private theorem hG : Primrec G := by
have a := (Primrec.ofNat (ℕ × Code)).comp (Primrec.list_length (α := List (Option ℕ)))
have k := Primrec.fst.comp a
refine' Primrec.option_some.comp (Primrec.list_map (Primrec.list_range.comp k) (_ : Primrec _))
replace k := k.comp (Primrec.fst (β := ℕ))
have n := Primrec.... | Mathlib.Computability.PartrecCode.976_0.A3c3Aev6SyIRjCJ | private theorem hG : Primrec G | Mathlib_Computability_PartrecCode |
case hpc
a : Primrec fun a => ofNat (ℕ × Code) (List.length a)
k✝¹ : Primrec fun a => (ofNat (ℕ × Code) (List.length a.1)).1
n✝ : Primrec Prod.snd
k✝ : Primrec fun a => (ofNat (ℕ × Code) (List.length a.1.1)).1
n : Primrec fun a => a.1.2
k' : Primrec Prod.snd
c : Primrec fun a => (ofNat (ℕ × Code) (List.length a.1.1)).2... | /-
Copyright (c) 2018 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro
-/
import Mathlib.Computability.Partrec
#align_import computability.partrec_code from "leanprover-community/mathlib"@"6155d4351090a6fad236e3d2e4e0e4e7342668e8"
/-!
# G... | have n := n.comp (Primrec.fst (β := Code × Code × Option ℕ × Option ℕ)) | private theorem hG : Primrec G := by
have a := (Primrec.ofNat (ℕ × Code)).comp (Primrec.list_length (α := List (Option ℕ)))
have k := Primrec.fst.comp a
refine' Primrec.option_some.comp (Primrec.list_map (Primrec.list_range.comp k) (_ : Primrec _))
replace k := k.comp (Primrec.fst (β := ℕ))
have n := Primrec.... | Mathlib.Computability.PartrecCode.976_0.A3c3Aev6SyIRjCJ | private theorem hG : Primrec G | Mathlib_Computability_PartrecCode |
case hpc
a : Primrec fun a => ofNat (ℕ × Code) (List.length a)
k✝¹ : Primrec fun a => (ofNat (ℕ × Code) (List.length a.1)).1
n✝¹ : Primrec Prod.snd
k✝ : Primrec fun a => (ofNat (ℕ × Code) (List.length a.1.1)).1
n✝ : Primrec fun a => a.1.2
k' : Primrec Prod.snd
c : Primrec fun a => (ofNat (ℕ × Code) (List.length a.1.1))... | /-
Copyright (c) 2018 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro
-/
import Mathlib.Computability.Partrec
#align_import computability.partrec_code from "leanprover-community/mathlib"@"6155d4351090a6fad236e3d2e4e0e4e7342668e8"
/-!
# G... | have cf := Primrec.fst.comp (Primrec.snd (α := (List (List (Option ℕ)) × ℕ) × ℕ)
(β := Code × Code × Option ℕ × Option ℕ)) | private theorem hG : Primrec G := by
have a := (Primrec.ofNat (ℕ × Code)).comp (Primrec.list_length (α := List (Option ℕ)))
have k := Primrec.fst.comp a
refine' Primrec.option_some.comp (Primrec.list_map (Primrec.list_range.comp k) (_ : Primrec _))
replace k := k.comp (Primrec.fst (β := ℕ))
have n := Primrec.... | Mathlib.Computability.PartrecCode.976_0.A3c3Aev6SyIRjCJ | private theorem hG : Primrec G | Mathlib_Computability_PartrecCode |
case hpc
a : Primrec fun a => ofNat (ℕ × Code) (List.length a)
k✝¹ : Primrec fun a => (ofNat (ℕ × Code) (List.length a.1)).1
n✝¹ : Primrec Prod.snd
k✝ : Primrec fun a => (ofNat (ℕ × Code) (List.length a.1.1)).1
n✝ : Primrec fun a => a.1.2
k' : Primrec Prod.snd
c : Primrec fun a => (ofNat (ℕ × Code) (List.length a.1.1))... | /-
Copyright (c) 2018 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro
-/
import Mathlib.Computability.Partrec
#align_import computability.partrec_code from "leanprover-community/mathlib"@"6155d4351090a6fad236e3d2e4e0e4e7342668e8"
/-!
# G... | have cg := (Primrec.fst.comp Primrec.snd).comp
(Primrec.snd (α := (List (List (Option ℕ)) × ℕ) × ℕ)
(β := Code × Code × Option ℕ × Option ℕ)) | private theorem hG : Primrec G := by
have a := (Primrec.ofNat (ℕ × Code)).comp (Primrec.list_length (α := List (Option ℕ)))
have k := Primrec.fst.comp a
refine' Primrec.option_some.comp (Primrec.list_map (Primrec.list_range.comp k) (_ : Primrec _))
replace k := k.comp (Primrec.fst (β := ℕ))
have n := Primrec.... | Mathlib.Computability.PartrecCode.976_0.A3c3Aev6SyIRjCJ | private theorem hG : Primrec G | Mathlib_Computability_PartrecCode |
case hpc
a : Primrec fun a => ofNat (ℕ × Code) (List.length a)
k✝¹ : Primrec fun a => (ofNat (ℕ × Code) (List.length a.1)).1
n✝¹ : Primrec Prod.snd
k✝ : Primrec fun a => (ofNat (ℕ × Code) (List.length a.1.1)).1
n✝ : Primrec fun a => a.1.2
k' : Primrec Prod.snd
c : Primrec fun a => (ofNat (ℕ × Code) (List.length a.1.1))... | /-
Copyright (c) 2018 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro
-/
import Mathlib.Computability.Partrec
#align_import computability.partrec_code from "leanprover-community/mathlib"@"6155d4351090a6fad236e3d2e4e0e4e7342668e8"
/-!
# G... | have z := Primrec.fst.comp (Primrec.unpair.comp n) | private theorem hG : Primrec G := by
have a := (Primrec.ofNat (ℕ × Code)).comp (Primrec.list_length (α := List (Option ℕ)))
have k := Primrec.fst.comp a
refine' Primrec.option_some.comp (Primrec.list_map (Primrec.list_range.comp k) (_ : Primrec _))
replace k := k.comp (Primrec.fst (β := ℕ))
have n := Primrec.... | Mathlib.Computability.PartrecCode.976_0.A3c3Aev6SyIRjCJ | private theorem hG : Primrec G | Mathlib_Computability_PartrecCode |
case hpc
a : Primrec fun a => ofNat (ℕ × Code) (List.length a)
k✝¹ : Primrec fun a => (ofNat (ℕ × Code) (List.length a.1)).1
n✝¹ : Primrec Prod.snd
k✝ : Primrec fun a => (ofNat (ℕ × Code) (List.length a.1.1)).1
n✝ : Primrec fun a => a.1.2
k' : Primrec Prod.snd
c : Primrec fun a => (ofNat (ℕ × Code) (List.length a.1.1))... | /-
Copyright (c) 2018 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro
-/
import Mathlib.Computability.Partrec
#align_import computability.partrec_code from "leanprover-community/mathlib"@"6155d4351090a6fad236e3d2e4e0e4e7342668e8"
/-!
# G... | refine'
Primrec.nat_casesOn (Primrec.snd.comp (Primrec.unpair.comp n))
(hlup.comp <| L.pair <| (k.pair cf).pair z)
(_ : Primrec _) | private theorem hG : Primrec G := by
have a := (Primrec.ofNat (ℕ × Code)).comp (Primrec.list_length (α := List (Option ℕ)))
have k := Primrec.fst.comp a
refine' Primrec.option_some.comp (Primrec.list_map (Primrec.list_range.comp k) (_ : Primrec _))
replace k := k.comp (Primrec.fst (β := ℕ))
have n := Primrec.... | Mathlib.Computability.PartrecCode.976_0.A3c3Aev6SyIRjCJ | private theorem hG : Primrec G | Mathlib_Computability_PartrecCode |
case hpc
a : Primrec fun a => ofNat (ℕ × Code) (List.length a)
k✝¹ : Primrec fun a => (ofNat (ℕ × Code) (List.length a.1)).1
n✝¹ : Primrec Prod.snd
k✝ : Primrec fun a => (ofNat (ℕ × Code) (List.length a.1.1)).1
n✝ : Primrec fun a => a.1.2
k' : Primrec Prod.snd
c : Primrec fun a => (ofNat (ℕ × Code) (List.length a.1.1))... | /-
Copyright (c) 2018 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro
-/
import Mathlib.Computability.Partrec
#align_import computability.partrec_code from "leanprover-community/mathlib"@"6155d4351090a6fad236e3d2e4e0e4e7342668e8"
/-!
# G... | have L := L.comp (Primrec.fst (β := ℕ)) | private theorem hG : Primrec G := by
have a := (Primrec.ofNat (ℕ × Code)).comp (Primrec.list_length (α := List (Option ℕ)))
have k := Primrec.fst.comp a
refine' Primrec.option_some.comp (Primrec.list_map (Primrec.list_range.comp k) (_ : Primrec _))
replace k := k.comp (Primrec.fst (β := ℕ))
have n := Primrec.... | Mathlib.Computability.PartrecCode.976_0.A3c3Aev6SyIRjCJ | private theorem hG : Primrec G | Mathlib_Computability_PartrecCode |
case hpc
a : Primrec fun a => ofNat (ℕ × Code) (List.length a)
k✝¹ : Primrec fun a => (ofNat (ℕ × Code) (List.length a.1)).1
n✝¹ : Primrec Prod.snd
k✝ : Primrec fun a => (ofNat (ℕ × Code) (List.length a.1.1)).1
n✝ : Primrec fun a => a.1.2
k' : Primrec Prod.snd
c : Primrec fun a => (ofNat (ℕ × Code) (List.length a.1.1))... | /-
Copyright (c) 2018 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro
-/
import Mathlib.Computability.Partrec
#align_import computability.partrec_code from "leanprover-community/mathlib"@"6155d4351090a6fad236e3d2e4e0e4e7342668e8"
/-!
# G... | have z := z.comp (Primrec.fst (β := ℕ)) | private theorem hG : Primrec G := by
have a := (Primrec.ofNat (ℕ × Code)).comp (Primrec.list_length (α := List (Option ℕ)))
have k := Primrec.fst.comp a
refine' Primrec.option_some.comp (Primrec.list_map (Primrec.list_range.comp k) (_ : Primrec _))
replace k := k.comp (Primrec.fst (β := ℕ))
have n := Primrec.... | Mathlib.Computability.PartrecCode.976_0.A3c3Aev6SyIRjCJ | private theorem hG : Primrec G | Mathlib_Computability_PartrecCode |
case hpc
a : Primrec fun a => ofNat (ℕ × Code) (List.length a)
k✝¹ : Primrec fun a => (ofNat (ℕ × Code) (List.length a.1)).1
n✝¹ : Primrec Prod.snd
k✝ : Primrec fun a => (ofNat (ℕ × Code) (List.length a.1.1)).1
n✝ : Primrec fun a => a.1.2
k' : Primrec Prod.snd
c : Primrec fun a => (ofNat (ℕ × Code) (List.length a.1.1))... | /-
Copyright (c) 2018 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro
-/
import Mathlib.Computability.Partrec
#align_import computability.partrec_code from "leanprover-community/mathlib"@"6155d4351090a6fad236e3d2e4e0e4e7342668e8"
/-!
# G... | have y := Primrec.snd
(α := ((List (List (Option ℕ)) × ℕ) × ℕ) × Code × Code × Option ℕ × Option ℕ) (β := ℕ) | private theorem hG : Primrec G := by
have a := (Primrec.ofNat (ℕ × Code)).comp (Primrec.list_length (α := List (Option ℕ)))
have k := Primrec.fst.comp a
refine' Primrec.option_some.comp (Primrec.list_map (Primrec.list_range.comp k) (_ : Primrec _))
replace k := k.comp (Primrec.fst (β := ℕ))
have n := Primrec.... | Mathlib.Computability.PartrecCode.976_0.A3c3Aev6SyIRjCJ | private theorem hG : Primrec G | Mathlib_Computability_PartrecCode |
case hpc
a : Primrec fun a => ofNat (ℕ × Code) (List.length a)
k✝¹ : Primrec fun a => (ofNat (ℕ × Code) (List.length a.1)).1
n✝¹ : Primrec Prod.snd
k✝ : Primrec fun a => (ofNat (ℕ × Code) (List.length a.1.1)).1
n✝ : Primrec fun a => a.1.2
k' : Primrec Prod.snd
c : Primrec fun a => (ofNat (ℕ × Code) (List.length a.1.1))... | /-
Copyright (c) 2018 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro
-/
import Mathlib.Computability.Partrec
#align_import computability.partrec_code from "leanprover-community/mathlib"@"6155d4351090a6fad236e3d2e4e0e4e7342668e8"
/-!
# G... | have h₁ := hlup.comp <| L.pair <| (((k'.pair c).comp Primrec.fst).comp Primrec.fst).pair
(Primrec₂.natPair.comp z y) | private theorem hG : Primrec G := by
have a := (Primrec.ofNat (ℕ × Code)).comp (Primrec.list_length (α := List (Option ℕ)))
have k := Primrec.fst.comp a
refine' Primrec.option_some.comp (Primrec.list_map (Primrec.list_range.comp k) (_ : Primrec _))
replace k := k.comp (Primrec.fst (β := ℕ))
have n := Primrec.... | Mathlib.Computability.PartrecCode.976_0.A3c3Aev6SyIRjCJ | private theorem hG : Primrec G | Mathlib_Computability_PartrecCode |
case hpc
a : Primrec fun a => ofNat (ℕ × Code) (List.length a)
k✝¹ : Primrec fun a => (ofNat (ℕ × Code) (List.length a.1)).1
n✝¹ : Primrec Prod.snd
k✝ : Primrec fun a => (ofNat (ℕ × Code) (List.length a.1.1)).1
n✝ : Primrec fun a => a.1.2
k' : Primrec Prod.snd
c : Primrec fun a => (ofNat (ℕ × Code) (List.length a.1.1))... | /-
Copyright (c) 2018 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro
-/
import Mathlib.Computability.Partrec
#align_import computability.partrec_code from "leanprover-community/mathlib"@"6155d4351090a6fad236e3d2e4e0e4e7342668e8"
/-!
# G... | refine' Primrec.option_bind h₁ (_ : Primrec _) | private theorem hG : Primrec G := by
have a := (Primrec.ofNat (ℕ × Code)).comp (Primrec.list_length (α := List (Option ℕ)))
have k := Primrec.fst.comp a
refine' Primrec.option_some.comp (Primrec.list_map (Primrec.list_range.comp k) (_ : Primrec _))
replace k := k.comp (Primrec.fst (β := ℕ))
have n := Primrec.... | Mathlib.Computability.PartrecCode.976_0.A3c3Aev6SyIRjCJ | private theorem hG : Primrec G | Mathlib_Computability_PartrecCode |
case hpc
a : Primrec fun a => ofNat (ℕ × Code) (List.length a)
k✝¹ : Primrec fun a => (ofNat (ℕ × Code) (List.length a.1)).1
n✝¹ : Primrec Prod.snd
k✝ : Primrec fun a => (ofNat (ℕ × Code) (List.length a.1.1)).1
n✝ : Primrec fun a => a.1.2
k' : Primrec Prod.snd
c : Primrec fun a => (ofNat (ℕ × Code) (List.length a.1.1))... | /-
Copyright (c) 2018 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro
-/
import Mathlib.Computability.Partrec
#align_import computability.partrec_code from "leanprover-community/mathlib"@"6155d4351090a6fad236e3d2e4e0e4e7342668e8"
/-!
# G... | have z := z.comp (Primrec.fst (β := ℕ)) | private theorem hG : Primrec G := by
have a := (Primrec.ofNat (ℕ × Code)).comp (Primrec.list_length (α := List (Option ℕ)))
have k := Primrec.fst.comp a
refine' Primrec.option_some.comp (Primrec.list_map (Primrec.list_range.comp k) (_ : Primrec _))
replace k := k.comp (Primrec.fst (β := ℕ))
have n := Primrec.... | Mathlib.Computability.PartrecCode.976_0.A3c3Aev6SyIRjCJ | private theorem hG : Primrec G | Mathlib_Computability_PartrecCode |
case hpc
a : Primrec fun a => ofNat (ℕ × Code) (List.length a)
k✝¹ : Primrec fun a => (ofNat (ℕ × Code) (List.length a.1)).1
n✝¹ : Primrec Prod.snd
k✝ : Primrec fun a => (ofNat (ℕ × Code) (List.length a.1.1)).1
n✝ : Primrec fun a => a.1.2
k' : Primrec Prod.snd
c : Primrec fun a => (ofNat (ℕ × Code) (List.length a.1.1))... | /-
Copyright (c) 2018 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro
-/
import Mathlib.Computability.Partrec
#align_import computability.partrec_code from "leanprover-community/mathlib"@"6155d4351090a6fad236e3d2e4e0e4e7342668e8"
/-!
# G... | have y := y.comp (Primrec.fst (β := ℕ)) | private theorem hG : Primrec G := by
have a := (Primrec.ofNat (ℕ × Code)).comp (Primrec.list_length (α := List (Option ℕ)))
have k := Primrec.fst.comp a
refine' Primrec.option_some.comp (Primrec.list_map (Primrec.list_range.comp k) (_ : Primrec _))
replace k := k.comp (Primrec.fst (β := ℕ))
have n := Primrec.... | Mathlib.Computability.PartrecCode.976_0.A3c3Aev6SyIRjCJ | private theorem hG : Primrec G | Mathlib_Computability_PartrecCode |
case hpc
a : Primrec fun a => ofNat (ℕ × Code) (List.length a)
k✝¹ : Primrec fun a => (ofNat (ℕ × Code) (List.length a.1)).1
n✝¹ : Primrec Prod.snd
k✝ : Primrec fun a => (ofNat (ℕ × Code) (List.length a.1.1)).1
n✝ : Primrec fun a => a.1.2
k' : Primrec Prod.snd
c : Primrec fun a => (ofNat (ℕ × Code) (List.length a.1.1))... | /-
Copyright (c) 2018 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro
-/
import Mathlib.Computability.Partrec
#align_import computability.partrec_code from "leanprover-community/mathlib"@"6155d4351090a6fad236e3d2e4e0e4e7342668e8"
/-!
# G... | have i := Primrec.snd
(α := (((List (List (Option ℕ)) × ℕ) × ℕ) × Code × Code × Option ℕ × Option ℕ) × ℕ)
(β := ℕ) | private theorem hG : Primrec G := by
have a := (Primrec.ofNat (ℕ × Code)).comp (Primrec.list_length (α := List (Option ℕ)))
have k := Primrec.fst.comp a
refine' Primrec.option_some.comp (Primrec.list_map (Primrec.list_range.comp k) (_ : Primrec _))
replace k := k.comp (Primrec.fst (β := ℕ))
have n := Primrec.... | Mathlib.Computability.PartrecCode.976_0.A3c3Aev6SyIRjCJ | private theorem hG : Primrec G | Mathlib_Computability_PartrecCode |
case hpc
a : Primrec fun a => ofNat (ℕ × Code) (List.length a)
k✝¹ : Primrec fun a => (ofNat (ℕ × Code) (List.length a.1)).1
n✝¹ : Primrec Prod.snd
k✝ : Primrec fun a => (ofNat (ℕ × Code) (List.length a.1.1)).1
n✝ : Primrec fun a => a.1.2
k' : Primrec Prod.snd
c : Primrec fun a => (ofNat (ℕ × Code) (List.length a.1.1))... | /-
Copyright (c) 2018 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro
-/
import Mathlib.Computability.Partrec
#align_import computability.partrec_code from "leanprover-community/mathlib"@"6155d4351090a6fad236e3d2e4e0e4e7342668e8"
/-!
# G... | have h₂ := hlup.comp ((L.comp Primrec.fst).pair <|
((k.pair cg).comp <| Primrec.fst.comp Primrec.fst).pair <|
Primrec₂.natPair.comp z <| Primrec₂.natPair.comp y i) | private theorem hG : Primrec G := by
have a := (Primrec.ofNat (ℕ × Code)).comp (Primrec.list_length (α := List (Option ℕ)))
have k := Primrec.fst.comp a
refine' Primrec.option_some.comp (Primrec.list_map (Primrec.list_range.comp k) (_ : Primrec _))
replace k := k.comp (Primrec.fst (β := ℕ))
have n := Primrec.... | Mathlib.Computability.PartrecCode.976_0.A3c3Aev6SyIRjCJ | private theorem hG : Primrec G | Mathlib_Computability_PartrecCode |
case hpc
a : Primrec fun a => ofNat (ℕ × Code) (List.length a)
k✝¹ : Primrec fun a => (ofNat (ℕ × Code) (List.length a.1)).1
n✝¹ : Primrec Prod.snd
k✝ : Primrec fun a => (ofNat (ℕ × Code) (List.length a.1.1)).1
n✝ : Primrec fun a => a.1.2
k' : Primrec Prod.snd
c : Primrec fun a => (ofNat (ℕ × Code) (List.length a.1.1))... | /-
Copyright (c) 2018 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro
-/
import Mathlib.Computability.Partrec
#align_import computability.partrec_code from "leanprover-community/mathlib"@"6155d4351090a6fad236e3d2e4e0e4e7342668e8"
/-!
# G... | exact h₂ | private theorem hG : Primrec G := by
have a := (Primrec.ofNat (ℕ × Code)).comp (Primrec.list_length (α := List (Option ℕ)))
have k := Primrec.fst.comp a
refine' Primrec.option_some.comp (Primrec.list_map (Primrec.list_range.comp k) (_ : Primrec _))
replace k := k.comp (Primrec.fst (β := ℕ))
have n := Primrec.... | Mathlib.Computability.PartrecCode.976_0.A3c3Aev6SyIRjCJ | private theorem hG : Primrec G | Mathlib_Computability_PartrecCode |
case hrf
a : Primrec fun a => ofNat (ℕ × Code) (List.length a)
k✝ : Primrec fun a => (ofNat (ℕ × Code) (List.length a.1)).1
n✝ : Primrec Prod.snd
k : Primrec fun a => (ofNat (ℕ × Code) (List.length a.1.1)).1
n : Primrec fun a => a.1.2
k' : Primrec Prod.snd
c : Primrec fun a => (ofNat (ℕ × Code) (List.length a.1.1)).2
⊢... | /-
Copyright (c) 2018 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro
-/
import Mathlib.Computability.Partrec
#align_import computability.partrec_code from "leanprover-community/mathlib"@"6155d4351090a6fad236e3d2e4e0e4e7342668e8"
/-!
# G... | have L := (Primrec.fst.comp Primrec.fst).comp
(Primrec.fst (α := (List (List (Option ℕ)) × ℕ) × ℕ)
(β := Code × Option ℕ)) | private theorem hG : Primrec G := by
have a := (Primrec.ofNat (ℕ × Code)).comp (Primrec.list_length (α := List (Option ℕ)))
have k := Primrec.fst.comp a
refine' Primrec.option_some.comp (Primrec.list_map (Primrec.list_range.comp k) (_ : Primrec _))
replace k := k.comp (Primrec.fst (β := ℕ))
have n := Primrec.... | Mathlib.Computability.PartrecCode.976_0.A3c3Aev6SyIRjCJ | private theorem hG : Primrec G | Mathlib_Computability_PartrecCode |
case hrf
a : Primrec fun a => ofNat (ℕ × Code) (List.length a)
k✝ : Primrec fun a => (ofNat (ℕ × Code) (List.length a.1)).1
n✝ : Primrec Prod.snd
k : Primrec fun a => (ofNat (ℕ × Code) (List.length a.1.1)).1
n : Primrec fun a => a.1.2
k' : Primrec Prod.snd
c : Primrec fun a => (ofNat (ℕ × Code) (List.length a.1.1)).2
L... | /-
Copyright (c) 2018 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro
-/
import Mathlib.Computability.Partrec
#align_import computability.partrec_code from "leanprover-community/mathlib"@"6155d4351090a6fad236e3d2e4e0e4e7342668e8"
/-!
# G... | have k := k.comp (Primrec.fst (β := Code × Option ℕ)) | private theorem hG : Primrec G := by
have a := (Primrec.ofNat (ℕ × Code)).comp (Primrec.list_length (α := List (Option ℕ)))
have k := Primrec.fst.comp a
refine' Primrec.option_some.comp (Primrec.list_map (Primrec.list_range.comp k) (_ : Primrec _))
replace k := k.comp (Primrec.fst (β := ℕ))
have n := Primrec.... | Mathlib.Computability.PartrecCode.976_0.A3c3Aev6SyIRjCJ | private theorem hG : Primrec G | Mathlib_Computability_PartrecCode |
case hrf
a : Primrec fun a => ofNat (ℕ × Code) (List.length a)
k✝¹ : Primrec fun a => (ofNat (ℕ × Code) (List.length a.1)).1
n✝ : Primrec Prod.snd
k✝ : Primrec fun a => (ofNat (ℕ × Code) (List.length a.1.1)).1
n : Primrec fun a => a.1.2
k' : Primrec Prod.snd
c : Primrec fun a => (ofNat (ℕ × Code) (List.length a.1.1)).2... | /-
Copyright (c) 2018 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro
-/
import Mathlib.Computability.Partrec
#align_import computability.partrec_code from "leanprover-community/mathlib"@"6155d4351090a6fad236e3d2e4e0e4e7342668e8"
/-!
# G... | have n := n.comp (Primrec.fst (β := Code × Option ℕ)) | private theorem hG : Primrec G := by
have a := (Primrec.ofNat (ℕ × Code)).comp (Primrec.list_length (α := List (Option ℕ)))
have k := Primrec.fst.comp a
refine' Primrec.option_some.comp (Primrec.list_map (Primrec.list_range.comp k) (_ : Primrec _))
replace k := k.comp (Primrec.fst (β := ℕ))
have n := Primrec.... | Mathlib.Computability.PartrecCode.976_0.A3c3Aev6SyIRjCJ | private theorem hG : Primrec G | Mathlib_Computability_PartrecCode |
case hrf
a : Primrec fun a => ofNat (ℕ × Code) (List.length a)
k✝¹ : Primrec fun a => (ofNat (ℕ × Code) (List.length a.1)).1
n✝¹ : Primrec Prod.snd
k✝ : Primrec fun a => (ofNat (ℕ × Code) (List.length a.1.1)).1
n✝ : Primrec fun a => a.1.2
k' : Primrec Prod.snd
c : Primrec fun a => (ofNat (ℕ × Code) (List.length a.1.1))... | /-
Copyright (c) 2018 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro
-/
import Mathlib.Computability.Partrec
#align_import computability.partrec_code from "leanprover-community/mathlib"@"6155d4351090a6fad236e3d2e4e0e4e7342668e8"
/-!
# G... | have cf := Primrec.fst.comp (Primrec.snd (α := (List (List (Option ℕ)) × ℕ) × ℕ)
(β := Code × Option ℕ)) | private theorem hG : Primrec G := by
have a := (Primrec.ofNat (ℕ × Code)).comp (Primrec.list_length (α := List (Option ℕ)))
have k := Primrec.fst.comp a
refine' Primrec.option_some.comp (Primrec.list_map (Primrec.list_range.comp k) (_ : Primrec _))
replace k := k.comp (Primrec.fst (β := ℕ))
have n := Primrec.... | Mathlib.Computability.PartrecCode.976_0.A3c3Aev6SyIRjCJ | private theorem hG : Primrec G | Mathlib_Computability_PartrecCode |
case hrf
a : Primrec fun a => ofNat (ℕ × Code) (List.length a)
k✝¹ : Primrec fun a => (ofNat (ℕ × Code) (List.length a.1)).1
n✝¹ : Primrec Prod.snd
k✝ : Primrec fun a => (ofNat (ℕ × Code) (List.length a.1.1)).1
n✝ : Primrec fun a => a.1.2
k' : Primrec Prod.snd
c : Primrec fun a => (ofNat (ℕ × Code) (List.length a.1.1))... | /-
Copyright (c) 2018 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro
-/
import Mathlib.Computability.Partrec
#align_import computability.partrec_code from "leanprover-community/mathlib"@"6155d4351090a6fad236e3d2e4e0e4e7342668e8"
/-!
# G... | have z := Primrec.fst.comp (Primrec.unpair.comp n) | private theorem hG : Primrec G := by
have a := (Primrec.ofNat (ℕ × Code)).comp (Primrec.list_length (α := List (Option ℕ)))
have k := Primrec.fst.comp a
refine' Primrec.option_some.comp (Primrec.list_map (Primrec.list_range.comp k) (_ : Primrec _))
replace k := k.comp (Primrec.fst (β := ℕ))
have n := Primrec.... | Mathlib.Computability.PartrecCode.976_0.A3c3Aev6SyIRjCJ | private theorem hG : Primrec G | Mathlib_Computability_PartrecCode |
case hrf
a : Primrec fun a => ofNat (ℕ × Code) (List.length a)
k✝¹ : Primrec fun a => (ofNat (ℕ × Code) (List.length a.1)).1
n✝¹ : Primrec Prod.snd
k✝ : Primrec fun a => (ofNat (ℕ × Code) (List.length a.1.1)).1
n✝ : Primrec fun a => a.1.2
k' : Primrec Prod.snd
c : Primrec fun a => (ofNat (ℕ × Code) (List.length a.1.1))... | /-
Copyright (c) 2018 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro
-/
import Mathlib.Computability.Partrec
#align_import computability.partrec_code from "leanprover-community/mathlib"@"6155d4351090a6fad236e3d2e4e0e4e7342668e8"
/-!
# G... | have m := Primrec.snd.comp (Primrec.unpair.comp n) | private theorem hG : Primrec G := by
have a := (Primrec.ofNat (ℕ × Code)).comp (Primrec.list_length (α := List (Option ℕ)))
have k := Primrec.fst.comp a
refine' Primrec.option_some.comp (Primrec.list_map (Primrec.list_range.comp k) (_ : Primrec _))
replace k := k.comp (Primrec.fst (β := ℕ))
have n := Primrec.... | Mathlib.Computability.PartrecCode.976_0.A3c3Aev6SyIRjCJ | private theorem hG : Primrec G | Mathlib_Computability_PartrecCode |
case hrf
a : Primrec fun a => ofNat (ℕ × Code) (List.length a)
k✝¹ : Primrec fun a => (ofNat (ℕ × Code) (List.length a.1)).1
n✝¹ : Primrec Prod.snd
k✝ : Primrec fun a => (ofNat (ℕ × Code) (List.length a.1.1)).1
n✝ : Primrec fun a => a.1.2
k' : Primrec Prod.snd
c : Primrec fun a => (ofNat (ℕ × Code) (List.length a.1.1))... | /-
Copyright (c) 2018 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro
-/
import Mathlib.Computability.Partrec
#align_import computability.partrec_code from "leanprover-community/mathlib"@"6155d4351090a6fad236e3d2e4e0e4e7342668e8"
/-!
# G... | have h₁ := hlup.comp <| L.pair <| (k.pair cf).pair (Primrec₂.natPair.comp z m) | private theorem hG : Primrec G := by
have a := (Primrec.ofNat (ℕ × Code)).comp (Primrec.list_length (α := List (Option ℕ)))
have k := Primrec.fst.comp a
refine' Primrec.option_some.comp (Primrec.list_map (Primrec.list_range.comp k) (_ : Primrec _))
replace k := k.comp (Primrec.fst (β := ℕ))
have n := Primrec.... | Mathlib.Computability.PartrecCode.976_0.A3c3Aev6SyIRjCJ | private theorem hG : Primrec G | Mathlib_Computability_PartrecCode |
case hrf
a : Primrec fun a => ofNat (ℕ × Code) (List.length a)
k✝¹ : Primrec fun a => (ofNat (ℕ × Code) (List.length a.1)).1
n✝¹ : Primrec Prod.snd
k✝ : Primrec fun a => (ofNat (ℕ × Code) (List.length a.1.1)).1
n✝ : Primrec fun a => a.1.2
k' : Primrec Prod.snd
c : Primrec fun a => (ofNat (ℕ × Code) (List.length a.1.1))... | /-
Copyright (c) 2018 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro
-/
import Mathlib.Computability.Partrec
#align_import computability.partrec_code from "leanprover-community/mathlib"@"6155d4351090a6fad236e3d2e4e0e4e7342668e8"
/-!
# G... | refine' Primrec.option_bind h₁ (_ : Primrec _) | private theorem hG : Primrec G := by
have a := (Primrec.ofNat (ℕ × Code)).comp (Primrec.list_length (α := List (Option ℕ)))
have k := Primrec.fst.comp a
refine' Primrec.option_some.comp (Primrec.list_map (Primrec.list_range.comp k) (_ : Primrec _))
replace k := k.comp (Primrec.fst (β := ℕ))
have n := Primrec.... | Mathlib.Computability.PartrecCode.976_0.A3c3Aev6SyIRjCJ | private theorem hG : Primrec G | Mathlib_Computability_PartrecCode |
case hrf
a : Primrec fun a => ofNat (ℕ × Code) (List.length a)
k✝¹ : Primrec fun a => (ofNat (ℕ × Code) (List.length a.1)).1
n✝¹ : Primrec Prod.snd
k✝ : Primrec fun a => (ofNat (ℕ × Code) (List.length a.1.1)).1
n✝ : Primrec fun a => a.1.2
k' : Primrec Prod.snd
c : Primrec fun a => (ofNat (ℕ × Code) (List.length a.1.1))... | /-
Copyright (c) 2018 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro
-/
import Mathlib.Computability.Partrec
#align_import computability.partrec_code from "leanprover-community/mathlib"@"6155d4351090a6fad236e3d2e4e0e4e7342668e8"
/-!
# G... | have m := m.comp (Primrec.fst (β := ℕ)) | private theorem hG : Primrec G := by
have a := (Primrec.ofNat (ℕ × Code)).comp (Primrec.list_length (α := List (Option ℕ)))
have k := Primrec.fst.comp a
refine' Primrec.option_some.comp (Primrec.list_map (Primrec.list_range.comp k) (_ : Primrec _))
replace k := k.comp (Primrec.fst (β := ℕ))
have n := Primrec.... | Mathlib.Computability.PartrecCode.976_0.A3c3Aev6SyIRjCJ | private theorem hG : Primrec G | Mathlib_Computability_PartrecCode |
case hrf
a : Primrec fun a => ofNat (ℕ × Code) (List.length a)
k✝¹ : Primrec fun a => (ofNat (ℕ × Code) (List.length a.1)).1
n✝¹ : Primrec Prod.snd
k✝ : Primrec fun a => (ofNat (ℕ × Code) (List.length a.1.1)).1
n✝ : Primrec fun a => a.1.2
k' : Primrec Prod.snd
c : Primrec fun a => (ofNat (ℕ × Code) (List.length a.1.1))... | /-
Copyright (c) 2018 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro
-/
import Mathlib.Computability.Partrec
#align_import computability.partrec_code from "leanprover-community/mathlib"@"6155d4351090a6fad236e3d2e4e0e4e7342668e8"
/-!
# G... | refine Primrec.nat_casesOn Primrec.snd (Primrec.option_some.comp m) ?_ | private theorem hG : Primrec G := by
have a := (Primrec.ofNat (ℕ × Code)).comp (Primrec.list_length (α := List (Option ℕ)))
have k := Primrec.fst.comp a
refine' Primrec.option_some.comp (Primrec.list_map (Primrec.list_range.comp k) (_ : Primrec _))
replace k := k.comp (Primrec.fst (β := ℕ))
have n := Primrec.... | Mathlib.Computability.PartrecCode.976_0.A3c3Aev6SyIRjCJ | private theorem hG : Primrec G | Mathlib_Computability_PartrecCode |
case hrf
a : Primrec fun a => ofNat (ℕ × Code) (List.length a)
k✝¹ : Primrec fun a => (ofNat (ℕ × Code) (List.length a.1)).1
n✝¹ : Primrec Prod.snd
k✝ : Primrec fun a => (ofNat (ℕ × Code) (List.length a.1.1)).1
n✝ : Primrec fun a => a.1.2
k' : Primrec Prod.snd
c : Primrec fun a => (ofNat (ℕ × Code) (List.length a.1.1))... | /-
Copyright (c) 2018 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro
-/
import Mathlib.Computability.Partrec
#align_import computability.partrec_code from "leanprover-community/mathlib"@"6155d4351090a6fad236e3d2e4e0e4e7342668e8"
/-!
# G... | unfold Primrec₂ | private theorem hG : Primrec G := by
have a := (Primrec.ofNat (ℕ × Code)).comp (Primrec.list_length (α := List (Option ℕ)))
have k := Primrec.fst.comp a
refine' Primrec.option_some.comp (Primrec.list_map (Primrec.list_range.comp k) (_ : Primrec _))
replace k := k.comp (Primrec.fst (β := ℕ))
have n := Primrec.... | Mathlib.Computability.PartrecCode.976_0.A3c3Aev6SyIRjCJ | private theorem hG : Primrec G | Mathlib_Computability_PartrecCode |
case hrf
a : Primrec fun a => ofNat (ℕ × Code) (List.length a)
k✝¹ : Primrec fun a => (ofNat (ℕ × Code) (List.length a.1)).1
n✝¹ : Primrec Prod.snd
k✝ : Primrec fun a => (ofNat (ℕ × Code) (List.length a.1.1)).1
n✝ : Primrec fun a => a.1.2
k' : Primrec Prod.snd
c : Primrec fun a => (ofNat (ℕ × Code) (List.length a.1.1))... | /-
Copyright (c) 2018 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro
-/
import Mathlib.Computability.Partrec
#align_import computability.partrec_code from "leanprover-community/mathlib"@"6155d4351090a6fad236e3d2e4e0e4e7342668e8"
/-!
# G... | exact (hlup.comp ((L.comp Primrec.fst).pair <|
((k'.pair c).comp <| Primrec.fst.comp Primrec.fst).pair
(Primrec₂.natPair.comp (z.comp Primrec.fst) (_root_.Primrec.succ.comp m)))).comp
Primrec.fst | private theorem hG : Primrec G := by
have a := (Primrec.ofNat (ℕ × Code)).comp (Primrec.list_length (α := List (Option ℕ)))
have k := Primrec.fst.comp a
refine' Primrec.option_some.comp (Primrec.list_map (Primrec.list_range.comp k) (_ : Primrec _))
replace k := k.comp (Primrec.fst (β := ℕ))
have n := Primrec.... | Mathlib.Computability.PartrecCode.976_0.A3c3Aev6SyIRjCJ | private theorem hG : Primrec G | Mathlib_Computability_PartrecCode |
k : ℕ
c : Code
n : ℕ
⊢ (Option.bind (Option.map (evaln k c) (List.get? (List.range k) n)) fun b => b) = evaln k c n | /-
Copyright (c) 2018 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro
-/
import Mathlib.Computability.Partrec
#align_import computability.partrec_code from "leanprover-community/mathlib"@"6155d4351090a6fad236e3d2e4e0e4e7342668e8"
/-!
# G... | by_cases kn : n < k | private theorem evaln_map (k c n) :
((((List.range k).get? n).map (evaln k c)).bind fun b => b) = evaln k c n := by
| Mathlib.Computability.PartrecCode.1078_0.A3c3Aev6SyIRjCJ | private theorem evaln_map (k c n) :
((((List.range k).get? n).map (evaln k c)).bind fun b => b) = evaln k c n | Mathlib_Computability_PartrecCode |
case pos
k : ℕ
c : Code
n : ℕ
kn : n < k
⊢ (Option.bind (Option.map (evaln k c) (List.get? (List.range k) n)) fun b => b) = evaln k c n | /-
Copyright (c) 2018 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro
-/
import Mathlib.Computability.Partrec
#align_import computability.partrec_code from "leanprover-community/mathlib"@"6155d4351090a6fad236e3d2e4e0e4e7342668e8"
/-!
# G... | simp [List.get?_range kn] | private theorem evaln_map (k c n) :
((((List.range k).get? n).map (evaln k c)).bind fun b => b) = evaln k c n := by
by_cases kn : n < k
· | Mathlib.Computability.PartrecCode.1078_0.A3c3Aev6SyIRjCJ | private theorem evaln_map (k c n) :
((((List.range k).get? n).map (evaln k c)).bind fun b => b) = evaln k c n | Mathlib_Computability_PartrecCode |
case neg
k : ℕ
c : Code
n : ℕ
kn : ¬n < k
⊢ (Option.bind (Option.map (evaln k c) (List.get? (List.range k) n)) fun b => b) = evaln k c n | /-
Copyright (c) 2018 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro
-/
import Mathlib.Computability.Partrec
#align_import computability.partrec_code from "leanprover-community/mathlib"@"6155d4351090a6fad236e3d2e4e0e4e7342668e8"
/-!
# G... | rw [List.get?_len_le] | private theorem evaln_map (k c n) :
((((List.range k).get? n).map (evaln k c)).bind fun b => b) = evaln k c n := by
by_cases kn : n < k
· simp [List.get?_range kn]
· | Mathlib.Computability.PartrecCode.1078_0.A3c3Aev6SyIRjCJ | private theorem evaln_map (k c n) :
((((List.range k).get? n).map (evaln k c)).bind fun b => b) = evaln k c n | Mathlib_Computability_PartrecCode |
case neg
k : ℕ
c : Code
n : ℕ
kn : ¬n < k
⊢ (Option.bind (Option.map (evaln k c) Option.none) fun b => b) = evaln k c n | /-
Copyright (c) 2018 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro
-/
import Mathlib.Computability.Partrec
#align_import computability.partrec_code from "leanprover-community/mathlib"@"6155d4351090a6fad236e3d2e4e0e4e7342668e8"
/-!
# G... | cases e : evaln k c n | private theorem evaln_map (k c n) :
((((List.range k).get? n).map (evaln k c)).bind fun b => b) = evaln k c n := by
by_cases kn : n < k
· simp [List.get?_range kn]
· rw [List.get?_len_le]
· | Mathlib.Computability.PartrecCode.1078_0.A3c3Aev6SyIRjCJ | private theorem evaln_map (k c n) :
((((List.range k).get? n).map (evaln k c)).bind fun b => b) = evaln k c n | Mathlib_Computability_PartrecCode |
case neg.none
k : ℕ
c : Code
n : ℕ
kn : ¬n < k
e : evaln k c n = Option.none
⊢ (Option.bind (Option.map (evaln k c) Option.none) fun b => b) = Option.none | /-
Copyright (c) 2018 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro
-/
import Mathlib.Computability.Partrec
#align_import computability.partrec_code from "leanprover-community/mathlib"@"6155d4351090a6fad236e3d2e4e0e4e7342668e8"
/-!
# G... | rfl | private theorem evaln_map (k c n) :
((((List.range k).get? n).map (evaln k c)).bind fun b => b) = evaln k c n := by
by_cases kn : n < k
· simp [List.get?_range kn]
· rw [List.get?_len_le]
· cases e : evaln k c n
· | Mathlib.Computability.PartrecCode.1078_0.A3c3Aev6SyIRjCJ | private theorem evaln_map (k c n) :
((((List.range k).get? n).map (evaln k c)).bind fun b => b) = evaln k c n | Mathlib_Computability_PartrecCode |
case neg.some
k : ℕ
c : Code
n : ℕ
kn : ¬n < k
val✝ : ℕ
e : evaln k c n = some val✝
⊢ (Option.bind (Option.map (evaln k c) Option.none) fun b => b) = some val✝ | /-
Copyright (c) 2018 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro
-/
import Mathlib.Computability.Partrec
#align_import computability.partrec_code from "leanprover-community/mathlib"@"6155d4351090a6fad236e3d2e4e0e4e7342668e8"
/-!
# G... | exact kn.elim (evaln_bound e) | private theorem evaln_map (k c n) :
((((List.range k).get? n).map (evaln k c)).bind fun b => b) = evaln k c n := by
by_cases kn : n < k
· simp [List.get?_range kn]
· rw [List.get?_len_le]
· cases e : evaln k c n
· rfl
| Mathlib.Computability.PartrecCode.1078_0.A3c3Aev6SyIRjCJ | private theorem evaln_map (k c n) :
((((List.range k).get? n).map (evaln k c)).bind fun b => b) = evaln k c n | Mathlib_Computability_PartrecCode |
case neg
k : ℕ
c : Code
n : ℕ
kn : ¬n < k
⊢ List.length (List.range k) ≤ n | /-
Copyright (c) 2018 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro
-/
import Mathlib.Computability.Partrec
#align_import computability.partrec_code from "leanprover-community/mathlib"@"6155d4351090a6fad236e3d2e4e0e4e7342668e8"
/-!
# G... | simpa using kn | private theorem evaln_map (k c n) :
((((List.range k).get? n).map (evaln k c)).bind fun b => b) = evaln k c n := by
by_cases kn : n < k
· simp [List.get?_range kn]
· rw [List.get?_len_le]
· cases e : evaln k c n
· rfl
exact kn.elim (evaln_bound e)
| Mathlib.Computability.PartrecCode.1078_0.A3c3Aev6SyIRjCJ | private theorem evaln_map (k c n) :
((((List.range k).get? n).map (evaln k c)).bind fun b => b) = evaln k c n | Mathlib_Computability_PartrecCode |
x✝ : Unit
p : ℕ
⊢ Nat.Partrec.Code.G
(x✝,
List.map
(fun n =>
let a := ofNat (ℕ × Code) n;
List.map (evaln a.1 a.2) (List.range a.1))
(List.range p)).2 =
some
(let a := ofNat (ℕ × Code) p;
List.map (evaln a.1 a.2) (List.range a.1)) | /-
Copyright (c) 2018 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro
-/
import Mathlib.Computability.Partrec
#align_import computability.partrec_code from "leanprover-community/mathlib"@"6155d4351090a6fad236e3d2e4e0e4e7342668e8"
/-!
# G... | simp only [G, prod_ofNat_val, ofNat_nat, List.length_map, List.length_range,
Nat.pair_unpair, Option.some_inj] | /-- The `Nat.Partrec.Code.evaln` function is primitive recursive. -/
theorem evaln_prim : Primrec fun a : (ℕ × Code) × ℕ => evaln a.1.1 a.1.2 a.2 :=
have :
Primrec₂ fun (_ : Unit) (n : ℕ) =>
let a := ofNat (ℕ × Code) n
(List.range a.1).map (evaln a.1 a.2) :=
Primrec.nat_strong_rec _ (hG.comp Primr... | Mathlib.Computability.PartrecCode.1088_0.A3c3Aev6SyIRjCJ | /-- The `Nat.Partrec.Code.evaln` function is primitive recursive. -/
theorem evaln_prim : Primrec fun a : (ℕ × Code) × ℕ => evaln a.1.1 a.1.2 a.2 | Mathlib_Computability_PartrecCode |
x✝ : Unit
p : ℕ
⊢ List.map
(fun n =>
Nat.rec Option.none
(fun n_1 n_ih =>
rec (some 0) (some (Nat.succ n)) (some (unpair n).1) (some (unpair n).2)
(fun cf cg x x => do
let x ←
Nat.Partrec.Code.lup
(List.map
... | /-
Copyright (c) 2018 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro
-/
import Mathlib.Computability.Partrec
#align_import computability.partrec_code from "leanprover-community/mathlib"@"6155d4351090a6fad236e3d2e4e0e4e7342668e8"
/-!
# G... | refine List.map_congr fun n => ?_ | /-- The `Nat.Partrec.Code.evaln` function is primitive recursive. -/
theorem evaln_prim : Primrec fun a : (ℕ × Code) × ℕ => evaln a.1.1 a.1.2 a.2 :=
have :
Primrec₂ fun (_ : Unit) (n : ℕ) =>
let a := ofNat (ℕ × Code) n
(List.range a.1).map (evaln a.1 a.2) :=
Primrec.nat_strong_rec _ (hG.comp Primr... | Mathlib.Computability.PartrecCode.1088_0.A3c3Aev6SyIRjCJ | /-- The `Nat.Partrec.Code.evaln` function is primitive recursive. -/
theorem evaln_prim : Primrec fun a : (ℕ × Code) × ℕ => evaln a.1.1 a.1.2 a.2 | Mathlib_Computability_PartrecCode |
x✝ : Unit
p n : ℕ
⊢ n ∈ List.range (unpair p).1 →
Nat.rec Option.none
(fun n_1 n_ih =>
rec (some 0) (some (Nat.succ n)) (some (unpair n).1) (some (unpair n).2)
(fun cf cg x x => do
let x ←
Nat.Partrec.Code.lup
(List.map
... | /-
Copyright (c) 2018 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro
-/
import Mathlib.Computability.Partrec
#align_import computability.partrec_code from "leanprover-community/mathlib"@"6155d4351090a6fad236e3d2e4e0e4e7342668e8"
/-!
# G... | have : List.range p = List.range (Nat.pair p.unpair.1 (encode (ofNat Code p.unpair.2))) := by
simp | /-- The `Nat.Partrec.Code.evaln` function is primitive recursive. -/
theorem evaln_prim : Primrec fun a : (ℕ × Code) × ℕ => evaln a.1.1 a.1.2 a.2 :=
have :
Primrec₂ fun (_ : Unit) (n : ℕ) =>
let a := ofNat (ℕ × Code) n
(List.range a.1).map (evaln a.1 a.2) :=
Primrec.nat_strong_rec _ (hG.comp Primr... | Mathlib.Computability.PartrecCode.1088_0.A3c3Aev6SyIRjCJ | /-- The `Nat.Partrec.Code.evaln` function is primitive recursive. -/
theorem evaln_prim : Primrec fun a : (ℕ × Code) × ℕ => evaln a.1.1 a.1.2 a.2 | Mathlib_Computability_PartrecCode |
x✝ : Unit
p n : ℕ
⊢ List.range p = List.range (Nat.pair (unpair p).1 (encode (ofNat Code (unpair p).2))) | /-
Copyright (c) 2018 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro
-/
import Mathlib.Computability.Partrec
#align_import computability.partrec_code from "leanprover-community/mathlib"@"6155d4351090a6fad236e3d2e4e0e4e7342668e8"
/-!
# G... | simp | /-- The `Nat.Partrec.Code.evaln` function is primitive recursive. -/
theorem evaln_prim : Primrec fun a : (ℕ × Code) × ℕ => evaln a.1.1 a.1.2 a.2 :=
have :
Primrec₂ fun (_ : Unit) (n : ℕ) =>
let a := ofNat (ℕ × Code) n
(List.range a.1).map (evaln a.1 a.2) :=
Primrec.nat_strong_rec _ (hG.comp Primr... | Mathlib.Computability.PartrecCode.1088_0.A3c3Aev6SyIRjCJ | /-- The `Nat.Partrec.Code.evaln` function is primitive recursive. -/
theorem evaln_prim : Primrec fun a : (ℕ × Code) × ℕ => evaln a.1.1 a.1.2 a.2 | Mathlib_Computability_PartrecCode |
x✝ : Unit
p n : ℕ
this : List.range p = List.range (Nat.pair (unpair p).1 (encode (ofNat Code (unpair p).2)))
⊢ n ∈ List.range (unpair p).1 →
Nat.rec Option.none
(fun n_1 n_ih =>
rec (some 0) (some (Nat.succ n)) (some (unpair n).1) (some (unpair n).2)
(fun cf cg x x => do
... | /-
Copyright (c) 2018 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro
-/
import Mathlib.Computability.Partrec
#align_import computability.partrec_code from "leanprover-community/mathlib"@"6155d4351090a6fad236e3d2e4e0e4e7342668e8"
/-!
# G... | rw [this] | /-- The `Nat.Partrec.Code.evaln` function is primitive recursive. -/
theorem evaln_prim : Primrec fun a : (ℕ × Code) × ℕ => evaln a.1.1 a.1.2 a.2 :=
have :
Primrec₂ fun (_ : Unit) (n : ℕ) =>
let a := ofNat (ℕ × Code) n
(List.range a.1).map (evaln a.1 a.2) :=
Primrec.nat_strong_rec _ (hG.comp Primr... | Mathlib.Computability.PartrecCode.1088_0.A3c3Aev6SyIRjCJ | /-- The `Nat.Partrec.Code.evaln` function is primitive recursive. -/
theorem evaln_prim : Primrec fun a : (ℕ × Code) × ℕ => evaln a.1.1 a.1.2 a.2 | Mathlib_Computability_PartrecCode |
x✝ : Unit
p n : ℕ
this : List.range p = List.range (Nat.pair (unpair p).1 (encode (ofNat Code (unpair p).2)))
⊢ n ∈ List.range (unpair p).1 →
Nat.rec Option.none
(fun n_1 n_ih =>
rec (some 0) (some (Nat.succ n)) (some (unpair n).1) (some (unpair n).2)
(fun cf cg x x => do
... | /-
Copyright (c) 2018 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro
-/
import Mathlib.Computability.Partrec
#align_import computability.partrec_code from "leanprover-community/mathlib"@"6155d4351090a6fad236e3d2e4e0e4e7342668e8"
/-!
# G... | generalize p.unpair.1 = k | /-- The `Nat.Partrec.Code.evaln` function is primitive recursive. -/
theorem evaln_prim : Primrec fun a : (ℕ × Code) × ℕ => evaln a.1.1 a.1.2 a.2 :=
have :
Primrec₂ fun (_ : Unit) (n : ℕ) =>
let a := ofNat (ℕ × Code) n
(List.range a.1).map (evaln a.1 a.2) :=
Primrec.nat_strong_rec _ (hG.comp Primr... | Mathlib.Computability.PartrecCode.1088_0.A3c3Aev6SyIRjCJ | /-- The `Nat.Partrec.Code.evaln` function is primitive recursive. -/
theorem evaln_prim : Primrec fun a : (ℕ × Code) × ℕ => evaln a.1.1 a.1.2 a.2 | Mathlib_Computability_PartrecCode |
x✝ : Unit
p n : ℕ
this : List.range p = List.range (Nat.pair (unpair p).1 (encode (ofNat Code (unpair p).2)))
k : ℕ
⊢ n ∈ List.range k →
Nat.rec Option.none
(fun n_1 n_ih =>
rec (some 0) (some (Nat.succ n)) (some (unpair n).1) (some (unpair n).2)
(fun cf cg x x => do
let ... | /-
Copyright (c) 2018 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro
-/
import Mathlib.Computability.Partrec
#align_import computability.partrec_code from "leanprover-community/mathlib"@"6155d4351090a6fad236e3d2e4e0e4e7342668e8"
/-!
# G... | generalize ofNat Code p.unpair.2 = c | /-- The `Nat.Partrec.Code.evaln` function is primitive recursive. -/
theorem evaln_prim : Primrec fun a : (ℕ × Code) × ℕ => evaln a.1.1 a.1.2 a.2 :=
have :
Primrec₂ fun (_ : Unit) (n : ℕ) =>
let a := ofNat (ℕ × Code) n
(List.range a.1).map (evaln a.1 a.2) :=
Primrec.nat_strong_rec _ (hG.comp Primr... | Mathlib.Computability.PartrecCode.1088_0.A3c3Aev6SyIRjCJ | /-- The `Nat.Partrec.Code.evaln` function is primitive recursive. -/
theorem evaln_prim : Primrec fun a : (ℕ × Code) × ℕ => evaln a.1.1 a.1.2 a.2 | Mathlib_Computability_PartrecCode |
x✝ : Unit
p n : ℕ
this : List.range p = List.range (Nat.pair (unpair p).1 (encode (ofNat Code (unpair p).2)))
k : ℕ
c : Code
⊢ n ∈ List.range k →
Nat.rec Option.none
(fun n_1 n_ih =>
rec (some 0) (some (Nat.succ n)) (some (unpair n).1) (some (unpair n).2)
(fun cf cg x x => do
... | /-
Copyright (c) 2018 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro
-/
import Mathlib.Computability.Partrec
#align_import computability.partrec_code from "leanprover-community/mathlib"@"6155d4351090a6fad236e3d2e4e0e4e7342668e8"
/-!
# G... | intro nk | /-- The `Nat.Partrec.Code.evaln` function is primitive recursive. -/
theorem evaln_prim : Primrec fun a : (ℕ × Code) × ℕ => evaln a.1.1 a.1.2 a.2 :=
have :
Primrec₂ fun (_ : Unit) (n : ℕ) =>
let a := ofNat (ℕ × Code) n
(List.range a.1).map (evaln a.1 a.2) :=
Primrec.nat_strong_rec _ (hG.comp Primr... | Mathlib.Computability.PartrecCode.1088_0.A3c3Aev6SyIRjCJ | /-- The `Nat.Partrec.Code.evaln` function is primitive recursive. -/
theorem evaln_prim : Primrec fun a : (ℕ × Code) × ℕ => evaln a.1.1 a.1.2 a.2 | Mathlib_Computability_PartrecCode |
x✝ : Unit
p n : ℕ
this : List.range p = List.range (Nat.pair (unpair p).1 (encode (ofNat Code (unpair p).2)))
k : ℕ
c : Code
nk : n ∈ List.range k
⊢ Nat.rec Option.none
(fun n_1 n_ih =>
rec (some 0) (some (Nat.succ n)) (some (unpair n).1) (some (unpair n).2)
(fun cf cg x x => do
let ... | /-
Copyright (c) 2018 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro
-/
import Mathlib.Computability.Partrec
#align_import computability.partrec_code from "leanprover-community/mathlib"@"6155d4351090a6fad236e3d2e4e0e4e7342668e8"
/-!
# G... | cases' k with k' | /-- The `Nat.Partrec.Code.evaln` function is primitive recursive. -/
theorem evaln_prim : Primrec fun a : (ℕ × Code) × ℕ => evaln a.1.1 a.1.2 a.2 :=
have :
Primrec₂ fun (_ : Unit) (n : ℕ) =>
let a := ofNat (ℕ × Code) n
(List.range a.1).map (evaln a.1 a.2) :=
Primrec.nat_strong_rec _ (hG.comp Primr... | Mathlib.Computability.PartrecCode.1088_0.A3c3Aev6SyIRjCJ | /-- The `Nat.Partrec.Code.evaln` function is primitive recursive. -/
theorem evaln_prim : Primrec fun a : (ℕ × Code) × ℕ => evaln a.1.1 a.1.2 a.2 | Mathlib_Computability_PartrecCode |
case zero
x✝ : Unit
p n : ℕ
this : List.range p = List.range (Nat.pair (unpair p).1 (encode (ofNat Code (unpair p).2)))
c : Code
nk : n ∈ List.range Nat.zero
⊢ Nat.rec Option.none
(fun n_1 n_ih =>
rec (some 0) (some (Nat.succ n)) (some (unpair n).1) (some (unpair n).2)
(fun cf cg x x => do
... | /-
Copyright (c) 2018 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro
-/
import Mathlib.Computability.Partrec
#align_import computability.partrec_code from "leanprover-community/mathlib"@"6155d4351090a6fad236e3d2e4e0e4e7342668e8"
/-!
# G... | simp [evaln] | /-- The `Nat.Partrec.Code.evaln` function is primitive recursive. -/
theorem evaln_prim : Primrec fun a : (ℕ × Code) × ℕ => evaln a.1.1 a.1.2 a.2 :=
have :
Primrec₂ fun (_ : Unit) (n : ℕ) =>
let a := ofNat (ℕ × Code) n
(List.range a.1).map (evaln a.1 a.2) :=
Primrec.nat_strong_rec _ (hG.comp Primr... | Mathlib.Computability.PartrecCode.1088_0.A3c3Aev6SyIRjCJ | /-- The `Nat.Partrec.Code.evaln` function is primitive recursive. -/
theorem evaln_prim : Primrec fun a : (ℕ × Code) × ℕ => evaln a.1.1 a.1.2 a.2 | Mathlib_Computability_PartrecCode |
case succ
x✝ : Unit
p n : ℕ
this : List.range p = List.range (Nat.pair (unpair p).1 (encode (ofNat Code (unpair p).2)))
c : Code
k' : ℕ
nk : n ∈ List.range (Nat.succ k')
⊢ Nat.rec Option.none
(fun n_1 n_ih =>
rec (some 0) (some (Nat.succ n)) (some (unpair n).1) (some (unpair n).2)
(fun cf cg x x... | /-
Copyright (c) 2018 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro
-/
import Mathlib.Computability.Partrec
#align_import computability.partrec_code from "leanprover-community/mathlib"@"6155d4351090a6fad236e3d2e4e0e4e7342668e8"
/-!
# G... | let k := k' + 1 | /-- The `Nat.Partrec.Code.evaln` function is primitive recursive. -/
theorem evaln_prim : Primrec fun a : (ℕ × Code) × ℕ => evaln a.1.1 a.1.2 a.2 :=
have :
Primrec₂ fun (_ : Unit) (n : ℕ) =>
let a := ofNat (ℕ × Code) n
(List.range a.1).map (evaln a.1 a.2) :=
Primrec.nat_strong_rec _ (hG.comp Primr... | Mathlib.Computability.PartrecCode.1088_0.A3c3Aev6SyIRjCJ | /-- The `Nat.Partrec.Code.evaln` function is primitive recursive. -/
theorem evaln_prim : Primrec fun a : (ℕ × Code) × ℕ => evaln a.1.1 a.1.2 a.2 | Mathlib_Computability_PartrecCode |
case succ
x✝ : Unit
p n : ℕ
this : List.range p = List.range (Nat.pair (unpair p).1 (encode (ofNat Code (unpair p).2)))
c : Code
k' : ℕ
nk : n ∈ List.range (Nat.succ k')
k : ℕ := k' + 1
⊢ Nat.rec Option.none
(fun n_1 n_ih =>
rec (some 0) (some (Nat.succ n)) (some (unpair n).1) (some (unpair n).2)
... | /-
Copyright (c) 2018 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro
-/
import Mathlib.Computability.Partrec
#align_import computability.partrec_code from "leanprover-community/mathlib"@"6155d4351090a6fad236e3d2e4e0e4e7342668e8"
/-!
# G... | simp only [show k'.succ = k from rfl] | /-- The `Nat.Partrec.Code.evaln` function is primitive recursive. -/
theorem evaln_prim : Primrec fun a : (ℕ × Code) × ℕ => evaln a.1.1 a.1.2 a.2 :=
have :
Primrec₂ fun (_ : Unit) (n : ℕ) =>
let a := ofNat (ℕ × Code) n
(List.range a.1).map (evaln a.1 a.2) :=
Primrec.nat_strong_rec _ (hG.comp Primr... | Mathlib.Computability.PartrecCode.1088_0.A3c3Aev6SyIRjCJ | /-- The `Nat.Partrec.Code.evaln` function is primitive recursive. -/
theorem evaln_prim : Primrec fun a : (ℕ × Code) × ℕ => evaln a.1.1 a.1.2 a.2 | Mathlib_Computability_PartrecCode |
case succ
x✝ : Unit
p n : ℕ
this : List.range p = List.range (Nat.pair (unpair p).1 (encode (ofNat Code (unpair p).2)))
c : Code
k' : ℕ
nk : n ∈ List.range (Nat.succ k')
k : ℕ := k' + 1
⊢ rec (some 0) (some (Nat.succ n)) (some (unpair n).1) (some (unpair n).2)
(fun cf cg x x => do
let x ←
Nat.Pa... | /-
Copyright (c) 2018 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro
-/
import Mathlib.Computability.Partrec
#align_import computability.partrec_code from "leanprover-community/mathlib"@"6155d4351090a6fad236e3d2e4e0e4e7342668e8"
/-!
# G... | simp? [Nat.lt_succ_iff] at nk says simp only [List.mem_range, lt_succ_iff] at nk | /-- The `Nat.Partrec.Code.evaln` function is primitive recursive. -/
theorem evaln_prim : Primrec fun a : (ℕ × Code) × ℕ => evaln a.1.1 a.1.2 a.2 :=
have :
Primrec₂ fun (_ : Unit) (n : ℕ) =>
let a := ofNat (ℕ × Code) n
(List.range a.1).map (evaln a.1 a.2) :=
Primrec.nat_strong_rec _ (hG.comp Primr... | Mathlib.Computability.PartrecCode.1088_0.A3c3Aev6SyIRjCJ | /-- The `Nat.Partrec.Code.evaln` function is primitive recursive. -/
theorem evaln_prim : Primrec fun a : (ℕ × Code) × ℕ => evaln a.1.1 a.1.2 a.2 | Mathlib_Computability_PartrecCode |
case succ
x✝ : Unit
p n : ℕ
this : List.range p = List.range (Nat.pair (unpair p).1 (encode (ofNat Code (unpair p).2)))
c : Code
k' : ℕ
nk : n ∈ List.range (Nat.succ k')
k : ℕ := k' + 1
⊢ rec (some 0) (some (Nat.succ n)) (some (unpair n).1) (some (unpair n).2)
(fun cf cg x x => do
let x ←
Nat.Pa... | /-
Copyright (c) 2018 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro
-/
import Mathlib.Computability.Partrec
#align_import computability.partrec_code from "leanprover-community/mathlib"@"6155d4351090a6fad236e3d2e4e0e4e7342668e8"
/-!
# G... | simp only [List.mem_range, lt_succ_iff] at nk | /-- The `Nat.Partrec.Code.evaln` function is primitive recursive. -/
theorem evaln_prim : Primrec fun a : (ℕ × Code) × ℕ => evaln a.1.1 a.1.2 a.2 :=
have :
Primrec₂ fun (_ : Unit) (n : ℕ) =>
let a := ofNat (ℕ × Code) n
(List.range a.1).map (evaln a.1 a.2) :=
Primrec.nat_strong_rec _ (hG.comp Primr... | Mathlib.Computability.PartrecCode.1088_0.A3c3Aev6SyIRjCJ | /-- The `Nat.Partrec.Code.evaln` function is primitive recursive. -/
theorem evaln_prim : Primrec fun a : (ℕ × Code) × ℕ => evaln a.1.1 a.1.2 a.2 | Mathlib_Computability_PartrecCode |
case succ
x✝ : Unit
p n : ℕ
this : List.range p = List.range (Nat.pair (unpair p).1 (encode (ofNat Code (unpair p).2)))
c : Code
k' : ℕ
k : ℕ := k' + 1
nk : n ≤ k'
⊢ rec (some 0) (some (Nat.succ n)) (some (unpair n).1) (some (unpair n).2)
(fun cf cg x x => do
let x ←
Nat.Partrec.Code.lup
... | /-
Copyright (c) 2018 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro
-/
import Mathlib.Computability.Partrec
#align_import computability.partrec_code from "leanprover-community/mathlib"@"6155d4351090a6fad236e3d2e4e0e4e7342668e8"
/-!
# G... | have hg :
∀ {k' c' n},
Nat.pair k' (encode c') < Nat.pair k (encode c) →
lup ((List.range (Nat.pair k (encode c))).map fun n =>
(List.range n.unpair.1).map (evaln n.unpair.1 (ofNat Code n.unpair.2))) (k', c') n =
evaln k' c' n := by
intro k₁ c₁ n₁ hl
... | /-- The `Nat.Partrec.Code.evaln` function is primitive recursive. -/
theorem evaln_prim : Primrec fun a : (ℕ × Code) × ℕ => evaln a.1.1 a.1.2 a.2 :=
have :
Primrec₂ fun (_ : Unit) (n : ℕ) =>
let a := ofNat (ℕ × Code) n
(List.range a.1).map (evaln a.1 a.2) :=
Primrec.nat_strong_rec _ (hG.comp Primr... | Mathlib.Computability.PartrecCode.1088_0.A3c3Aev6SyIRjCJ | /-- The `Nat.Partrec.Code.evaln` function is primitive recursive. -/
theorem evaln_prim : Primrec fun a : (ℕ × Code) × ℕ => evaln a.1.1 a.1.2 a.2 | Mathlib_Computability_PartrecCode |
x✝ : Unit
p n : ℕ
this : List.range p = List.range (Nat.pair (unpair p).1 (encode (ofNat Code (unpair p).2)))
c : Code
k' : ℕ
k : ℕ := k' + 1
nk : n ≤ k'
⊢ ∀ {k' : ℕ} {c' : Code} {n : ℕ},
Nat.pair k' (encode c') < Nat.pair k (encode c) →
Nat.Partrec.Code.lup
(List.map (fun n => List.map (evaln (unpa... | /-
Copyright (c) 2018 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro
-/
import Mathlib.Computability.Partrec
#align_import computability.partrec_code from "leanprover-community/mathlib"@"6155d4351090a6fad236e3d2e4e0e4e7342668e8"
/-!
# G... | intro k₁ c₁ n₁ hl | /-- The `Nat.Partrec.Code.evaln` function is primitive recursive. -/
theorem evaln_prim : Primrec fun a : (ℕ × Code) × ℕ => evaln a.1.1 a.1.2 a.2 :=
have :
Primrec₂ fun (_ : Unit) (n : ℕ) =>
let a := ofNat (ℕ × Code) n
(List.range a.1).map (evaln a.1 a.2) :=
Primrec.nat_strong_rec _ (hG.comp Primr... | Mathlib.Computability.PartrecCode.1088_0.A3c3Aev6SyIRjCJ | /-- The `Nat.Partrec.Code.evaln` function is primitive recursive. -/
theorem evaln_prim : Primrec fun a : (ℕ × Code) × ℕ => evaln a.1.1 a.1.2 a.2 | Mathlib_Computability_PartrecCode |
x✝ : Unit
p n : ℕ
this : List.range p = List.range (Nat.pair (unpair p).1 (encode (ofNat Code (unpair p).2)))
c : Code
k' : ℕ
k : ℕ := k' + 1
nk : n ≤ k'
k₁ : ℕ
c₁ : Code
n₁ : ℕ
hl : Nat.pair k₁ (encode c₁) < Nat.pair k (encode c)
⊢ Nat.Partrec.Code.lup
(List.map (fun n => List.map (evaln (unpair n).1 (ofNat Code... | /-
Copyright (c) 2018 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro
-/
import Mathlib.Computability.Partrec
#align_import computability.partrec_code from "leanprover-community/mathlib"@"6155d4351090a6fad236e3d2e4e0e4e7342668e8"
/-!
# G... | simp [lup, List.get?_range hl, evaln_map, Bind.bind] | /-- The `Nat.Partrec.Code.evaln` function is primitive recursive. -/
theorem evaln_prim : Primrec fun a : (ℕ × Code) × ℕ => evaln a.1.1 a.1.2 a.2 :=
have :
Primrec₂ fun (_ : Unit) (n : ℕ) =>
let a := ofNat (ℕ × Code) n
(List.range a.1).map (evaln a.1 a.2) :=
Primrec.nat_strong_rec _ (hG.comp Primr... | Mathlib.Computability.PartrecCode.1088_0.A3c3Aev6SyIRjCJ | /-- The `Nat.Partrec.Code.evaln` function is primitive recursive. -/
theorem evaln_prim : Primrec fun a : (ℕ × Code) × ℕ => evaln a.1.1 a.1.2 a.2 | Mathlib_Computability_PartrecCode |
case succ
x✝ : Unit
p n : ℕ
this : List.range p = List.range (Nat.pair (unpair p).1 (encode (ofNat Code (unpair p).2)))
c : Code
k' : ℕ
k : ℕ := k' + 1
nk : n ≤ k'
hg :
∀ {k' : ℕ} {c' : Code} {n : ℕ},
Nat.pair k' (encode c') < Nat.pair k (encode c) →
Nat.Partrec.Code.lup
(List.map (fun n => List.m... | /-
Copyright (c) 2018 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro
-/
import Mathlib.Computability.Partrec
#align_import computability.partrec_code from "leanprover-community/mathlib"@"6155d4351090a6fad236e3d2e4e0e4e7342668e8"
/-!
# G... | cases' c with cf cg cf cg cf cg cf | /-- The `Nat.Partrec.Code.evaln` function is primitive recursive. -/
theorem evaln_prim : Primrec fun a : (ℕ × Code) × ℕ => evaln a.1.1 a.1.2 a.2 :=
have :
Primrec₂ fun (_ : Unit) (n : ℕ) =>
let a := ofNat (ℕ × Code) n
(List.range a.1).map (evaln a.1 a.2) :=
Primrec.nat_strong_rec _ (hG.comp Primr... | Mathlib.Computability.PartrecCode.1088_0.A3c3Aev6SyIRjCJ | /-- The `Nat.Partrec.Code.evaln` function is primitive recursive. -/
theorem evaln_prim : Primrec fun a : (ℕ × Code) × ℕ => evaln a.1.1 a.1.2 a.2 | Mathlib_Computability_PartrecCode |
case succ.zero
x✝ : Unit
p n : ℕ
this : List.range p = List.range (Nat.pair (unpair p).1 (encode (ofNat Code (unpair p).2)))
k' : ℕ
k : ℕ := k' + 1
nk : n ≤ k'
hg :
∀ {k' : ℕ} {c' : Code} {n : ℕ},
Nat.pair k' (encode c') < Nat.pair k (encode zero) →
Nat.Partrec.Code.lup
(List.map (fun n => List.ma... | /-
Copyright (c) 2018 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro
-/
import Mathlib.Computability.Partrec
#align_import computability.partrec_code from "leanprover-community/mathlib"@"6155d4351090a6fad236e3d2e4e0e4e7342668e8"
/-!
# G... | simp [evaln, nk, Bind.bind, Functor.map, Seq.seq, pure] | /-- The `Nat.Partrec.Code.evaln` function is primitive recursive. -/
theorem evaln_prim : Primrec fun a : (ℕ × Code) × ℕ => evaln a.1.1 a.1.2 a.2 :=
have :
Primrec₂ fun (_ : Unit) (n : ℕ) =>
let a := ofNat (ℕ × Code) n
(List.range a.1).map (evaln a.1 a.2) :=
Primrec.nat_strong_rec _ (hG.comp Primr... | Mathlib.Computability.PartrecCode.1088_0.A3c3Aev6SyIRjCJ | /-- The `Nat.Partrec.Code.evaln` function is primitive recursive. -/
theorem evaln_prim : Primrec fun a : (ℕ × Code) × ℕ => evaln a.1.1 a.1.2 a.2 | Mathlib_Computability_PartrecCode |
case succ.succ
x✝ : Unit
p n : ℕ
this : List.range p = List.range (Nat.pair (unpair p).1 (encode (ofNat Code (unpair p).2)))
k' : ℕ
k : ℕ := k' + 1
nk : n ≤ k'
hg :
∀ {k' : ℕ} {c' : Code} {n : ℕ},
Nat.pair k' (encode c') < Nat.pair k (encode succ) →
Nat.Partrec.Code.lup
(List.map (fun n => List.ma... | /-
Copyright (c) 2018 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro
-/
import Mathlib.Computability.Partrec
#align_import computability.partrec_code from "leanprover-community/mathlib"@"6155d4351090a6fad236e3d2e4e0e4e7342668e8"
/-!
# G... | simp [evaln, nk, Bind.bind, Functor.map, Seq.seq, pure] | /-- The `Nat.Partrec.Code.evaln` function is primitive recursive. -/
theorem evaln_prim : Primrec fun a : (ℕ × Code) × ℕ => evaln a.1.1 a.1.2 a.2 :=
have :
Primrec₂ fun (_ : Unit) (n : ℕ) =>
let a := ofNat (ℕ × Code) n
(List.range a.1).map (evaln a.1 a.2) :=
Primrec.nat_strong_rec _ (hG.comp Primr... | Mathlib.Computability.PartrecCode.1088_0.A3c3Aev6SyIRjCJ | /-- The `Nat.Partrec.Code.evaln` function is primitive recursive. -/
theorem evaln_prim : Primrec fun a : (ℕ × Code) × ℕ => evaln a.1.1 a.1.2 a.2 | Mathlib_Computability_PartrecCode |
case succ.left
x✝ : Unit
p n : ℕ
this : List.range p = List.range (Nat.pair (unpair p).1 (encode (ofNat Code (unpair p).2)))
k' : ℕ
k : ℕ := k' + 1
nk : n ≤ k'
hg :
∀ {k' : ℕ} {c' : Code} {n : ℕ},
Nat.pair k' (encode c') < Nat.pair k (encode left) →
Nat.Partrec.Code.lup
(List.map (fun n => List.ma... | /-
Copyright (c) 2018 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro
-/
import Mathlib.Computability.Partrec
#align_import computability.partrec_code from "leanprover-community/mathlib"@"6155d4351090a6fad236e3d2e4e0e4e7342668e8"
/-!
# G... | simp [evaln, nk, Bind.bind, Functor.map, Seq.seq, pure] | /-- The `Nat.Partrec.Code.evaln` function is primitive recursive. -/
theorem evaln_prim : Primrec fun a : (ℕ × Code) × ℕ => evaln a.1.1 a.1.2 a.2 :=
have :
Primrec₂ fun (_ : Unit) (n : ℕ) =>
let a := ofNat (ℕ × Code) n
(List.range a.1).map (evaln a.1 a.2) :=
Primrec.nat_strong_rec _ (hG.comp Primr... | Mathlib.Computability.PartrecCode.1088_0.A3c3Aev6SyIRjCJ | /-- The `Nat.Partrec.Code.evaln` function is primitive recursive. -/
theorem evaln_prim : Primrec fun a : (ℕ × Code) × ℕ => evaln a.1.1 a.1.2 a.2 | Mathlib_Computability_PartrecCode |
case succ.right
x✝ : Unit
p n : ℕ
this : List.range p = List.range (Nat.pair (unpair p).1 (encode (ofNat Code (unpair p).2)))
k' : ℕ
k : ℕ := k' + 1
nk : n ≤ k'
hg :
∀ {k' : ℕ} {c' : Code} {n : ℕ},
Nat.pair k' (encode c') < Nat.pair k (encode right) →
Nat.Partrec.Code.lup
(List.map (fun n => List.... | /-
Copyright (c) 2018 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro
-/
import Mathlib.Computability.Partrec
#align_import computability.partrec_code from "leanprover-community/mathlib"@"6155d4351090a6fad236e3d2e4e0e4e7342668e8"
/-!
# G... | simp [evaln, nk, Bind.bind, Functor.map, Seq.seq, pure] | /-- The `Nat.Partrec.Code.evaln` function is primitive recursive. -/
theorem evaln_prim : Primrec fun a : (ℕ × Code) × ℕ => evaln a.1.1 a.1.2 a.2 :=
have :
Primrec₂ fun (_ : Unit) (n : ℕ) =>
let a := ofNat (ℕ × Code) n
(List.range a.1).map (evaln a.1 a.2) :=
Primrec.nat_strong_rec _ (hG.comp Primr... | Mathlib.Computability.PartrecCode.1088_0.A3c3Aev6SyIRjCJ | /-- The `Nat.Partrec.Code.evaln` function is primitive recursive. -/
theorem evaln_prim : Primrec fun a : (ℕ × Code) × ℕ => evaln a.1.1 a.1.2 a.2 | Mathlib_Computability_PartrecCode |
case succ.pair
x✝ : Unit
p n : ℕ
this : List.range p = List.range (Nat.pair (unpair p).1 (encode (ofNat Code (unpair p).2)))
k' : ℕ
k : ℕ := k' + 1
nk : n ≤ k'
cf cg : Code
hg :
∀ {k' : ℕ} {c' : Code} {n : ℕ},
Nat.pair k' (encode c') < Nat.pair k (encode (pair cf cg)) →
Nat.Partrec.Code.lup
(List.... | /-
Copyright (c) 2018 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro
-/
import Mathlib.Computability.Partrec
#align_import computability.partrec_code from "leanprover-community/mathlib"@"6155d4351090a6fad236e3d2e4e0e4e7342668e8"
/-!
# G... | simp [evaln, nk, Bind.bind, Functor.map, Seq.seq, pure] | /-- The `Nat.Partrec.Code.evaln` function is primitive recursive. -/
theorem evaln_prim : Primrec fun a : (ℕ × Code) × ℕ => evaln a.1.1 a.1.2 a.2 :=
have :
Primrec₂ fun (_ : Unit) (n : ℕ) =>
let a := ofNat (ℕ × Code) n
(List.range a.1).map (evaln a.1 a.2) :=
Primrec.nat_strong_rec _ (hG.comp Primr... | Mathlib.Computability.PartrecCode.1088_0.A3c3Aev6SyIRjCJ | /-- The `Nat.Partrec.Code.evaln` function is primitive recursive. -/
theorem evaln_prim : Primrec fun a : (ℕ × Code) × ℕ => evaln a.1.1 a.1.2 a.2 | Mathlib_Computability_PartrecCode |
case succ.comp
x✝ : Unit
p n : ℕ
this : List.range p = List.range (Nat.pair (unpair p).1 (encode (ofNat Code (unpair p).2)))
k' : ℕ
k : ℕ := k' + 1
nk : n ≤ k'
cf cg : Code
hg :
∀ {k' : ℕ} {c' : Code} {n : ℕ},
Nat.pair k' (encode c') < Nat.pair k (encode (comp cf cg)) →
Nat.Partrec.Code.lup
(List.... | /-
Copyright (c) 2018 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro
-/
import Mathlib.Computability.Partrec
#align_import computability.partrec_code from "leanprover-community/mathlib"@"6155d4351090a6fad236e3d2e4e0e4e7342668e8"
/-!
# G... | simp [evaln, nk, Bind.bind, Functor.map, Seq.seq, pure] | /-- The `Nat.Partrec.Code.evaln` function is primitive recursive. -/
theorem evaln_prim : Primrec fun a : (ℕ × Code) × ℕ => evaln a.1.1 a.1.2 a.2 :=
have :
Primrec₂ fun (_ : Unit) (n : ℕ) =>
let a := ofNat (ℕ × Code) n
(List.range a.1).map (evaln a.1 a.2) :=
Primrec.nat_strong_rec _ (hG.comp Primr... | Mathlib.Computability.PartrecCode.1088_0.A3c3Aev6SyIRjCJ | /-- The `Nat.Partrec.Code.evaln` function is primitive recursive. -/
theorem evaln_prim : Primrec fun a : (ℕ × Code) × ℕ => evaln a.1.1 a.1.2 a.2 | Mathlib_Computability_PartrecCode |
case succ.prec
x✝ : Unit
p n : ℕ
this : List.range p = List.range (Nat.pair (unpair p).1 (encode (ofNat Code (unpair p).2)))
k' : ℕ
k : ℕ := k' + 1
nk : n ≤ k'
cf cg : Code
hg :
∀ {k' : ℕ} {c' : Code} {n : ℕ},
Nat.pair k' (encode c') < Nat.pair k (encode (prec cf cg)) →
Nat.Partrec.Code.lup
(List.... | /-
Copyright (c) 2018 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro
-/
import Mathlib.Computability.Partrec
#align_import computability.partrec_code from "leanprover-community/mathlib"@"6155d4351090a6fad236e3d2e4e0e4e7342668e8"
/-!
# G... | simp [evaln, nk, Bind.bind, Functor.map, Seq.seq, pure] | /-- The `Nat.Partrec.Code.evaln` function is primitive recursive. -/
theorem evaln_prim : Primrec fun a : (ℕ × Code) × ℕ => evaln a.1.1 a.1.2 a.2 :=
have :
Primrec₂ fun (_ : Unit) (n : ℕ) =>
let a := ofNat (ℕ × Code) n
(List.range a.1).map (evaln a.1 a.2) :=
Primrec.nat_strong_rec _ (hG.comp Primr... | Mathlib.Computability.PartrecCode.1088_0.A3c3Aev6SyIRjCJ | /-- The `Nat.Partrec.Code.evaln` function is primitive recursive. -/
theorem evaln_prim : Primrec fun a : (ℕ × Code) × ℕ => evaln a.1.1 a.1.2 a.2 | Mathlib_Computability_PartrecCode |
case succ.rfind'
x✝ : Unit
p n : ℕ
this : List.range p = List.range (Nat.pair (unpair p).1 (encode (ofNat Code (unpair p).2)))
k' : ℕ
k : ℕ := k' + 1
nk : n ≤ k'
cf : Code
hg :
∀ {k' : ℕ} {c' : Code} {n : ℕ},
Nat.pair k' (encode c') < Nat.pair k (encode (rfind' cf)) →
Nat.Partrec.Code.lup
(List.ma... | /-
Copyright (c) 2018 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro
-/
import Mathlib.Computability.Partrec
#align_import computability.partrec_code from "leanprover-community/mathlib"@"6155d4351090a6fad236e3d2e4e0e4e7342668e8"
/-!
# G... | simp [evaln, nk, Bind.bind, Functor.map, Seq.seq, pure] | /-- The `Nat.Partrec.Code.evaln` function is primitive recursive. -/
theorem evaln_prim : Primrec fun a : (ℕ × Code) × ℕ => evaln a.1.1 a.1.2 a.2 :=
have :
Primrec₂ fun (_ : Unit) (n : ℕ) =>
let a := ofNat (ℕ × Code) n
(List.range a.1).map (evaln a.1 a.2) :=
Primrec.nat_strong_rec _ (hG.comp Primr... | Mathlib.Computability.PartrecCode.1088_0.A3c3Aev6SyIRjCJ | /-- The `Nat.Partrec.Code.evaln` function is primitive recursive. -/
theorem evaln_prim : Primrec fun a : (ℕ × Code) × ℕ => evaln a.1.1 a.1.2 a.2 | Mathlib_Computability_PartrecCode |
case succ.pair
x✝ : Unit
p n : ℕ
this : List.range p = List.range (Nat.pair (unpair p).1 (encode (ofNat Code (unpair p).2)))
k' : ℕ
k : ℕ := k' + 1
nk : n ≤ k'
cf cg : Code
hg :
∀ {k' : ℕ} {c' : Code} {n : ℕ},
Nat.pair k' (encode c') < Nat.pair k (encode (pair cf cg)) →
Nat.Partrec.Code.lup
(List.... | /-
Copyright (c) 2018 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro
-/
import Mathlib.Computability.Partrec
#align_import computability.partrec_code from "leanprover-community/mathlib"@"6155d4351090a6fad236e3d2e4e0e4e7342668e8"
/-!
# G... | cases' encode_lt_pair cf cg with lf lg | /-- The `Nat.Partrec.Code.evaln` function is primitive recursive. -/
theorem evaln_prim : Primrec fun a : (ℕ × Code) × ℕ => evaln a.1.1 a.1.2 a.2 :=
have :
Primrec₂ fun (_ : Unit) (n : ℕ) =>
let a := ofNat (ℕ × Code) n
(List.range a.1).map (evaln a.1 a.2) :=
Primrec.nat_strong_rec _ (hG.comp Primr... | Mathlib.Computability.PartrecCode.1088_0.A3c3Aev6SyIRjCJ | /-- The `Nat.Partrec.Code.evaln` function is primitive recursive. -/
theorem evaln_prim : Primrec fun a : (ℕ × Code) × ℕ => evaln a.1.1 a.1.2 a.2 | Mathlib_Computability_PartrecCode |
case succ.pair.intro
x✝ : Unit
p n : ℕ
this : List.range p = List.range (Nat.pair (unpair p).1 (encode (ofNat Code (unpair p).2)))
k' : ℕ
k : ℕ := k' + 1
nk : n ≤ k'
cf cg : Code
hg :
∀ {k' : ℕ} {c' : Code} {n : ℕ},
Nat.pair k' (encode c') < Nat.pair k (encode (pair cf cg)) →
Nat.Partrec.Code.lup
... | /-
Copyright (c) 2018 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro
-/
import Mathlib.Computability.Partrec
#align_import computability.partrec_code from "leanprover-community/mathlib"@"6155d4351090a6fad236e3d2e4e0e4e7342668e8"
/-!
# G... | rw [hg (Nat.pair_lt_pair_right _ lf), hg (Nat.pair_lt_pair_right _ lg)] | /-- The `Nat.Partrec.Code.evaln` function is primitive recursive. -/
theorem evaln_prim : Primrec fun a : (ℕ × Code) × ℕ => evaln a.1.1 a.1.2 a.2 :=
have :
Primrec₂ fun (_ : Unit) (n : ℕ) =>
let a := ofNat (ℕ × Code) n
(List.range a.1).map (evaln a.1 a.2) :=
Primrec.nat_strong_rec _ (hG.comp Primr... | Mathlib.Computability.PartrecCode.1088_0.A3c3Aev6SyIRjCJ | /-- The `Nat.Partrec.Code.evaln` function is primitive recursive. -/
theorem evaln_prim : Primrec fun a : (ℕ × Code) × ℕ => evaln a.1.1 a.1.2 a.2 | Mathlib_Computability_PartrecCode |
case succ.pair.intro
x✝ : Unit
p n : ℕ
this : List.range p = List.range (Nat.pair (unpair p).1 (encode (ofNat Code (unpair p).2)))
k' : ℕ
k : ℕ := k' + 1
nk : n ≤ k'
cf cg : Code
hg :
∀ {k' : ℕ} {c' : Code} {n : ℕ},
Nat.pair k' (encode c') < Nat.pair k (encode (pair cf cg)) →
Nat.Partrec.Code.lup
... | /-
Copyright (c) 2018 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro
-/
import Mathlib.Computability.Partrec
#align_import computability.partrec_code from "leanprover-community/mathlib"@"6155d4351090a6fad236e3d2e4e0e4e7342668e8"
/-!
# G... | cases evaln k cf n | /-- The `Nat.Partrec.Code.evaln` function is primitive recursive. -/
theorem evaln_prim : Primrec fun a : (ℕ × Code) × ℕ => evaln a.1.1 a.1.2 a.2 :=
have :
Primrec₂ fun (_ : Unit) (n : ℕ) =>
let a := ofNat (ℕ × Code) n
(List.range a.1).map (evaln a.1 a.2) :=
Primrec.nat_strong_rec _ (hG.comp Primr... | Mathlib.Computability.PartrecCode.1088_0.A3c3Aev6SyIRjCJ | /-- The `Nat.Partrec.Code.evaln` function is primitive recursive. -/
theorem evaln_prim : Primrec fun a : (ℕ × Code) × ℕ => evaln a.1.1 a.1.2 a.2 | Mathlib_Computability_PartrecCode |
case succ.pair.intro.none
x✝ : Unit
p n : ℕ
this : List.range p = List.range (Nat.pair (unpair p).1 (encode (ofNat Code (unpair p).2)))
k' : ℕ
k : ℕ := k' + 1
nk : n ≤ k'
cf cg : Code
hg :
∀ {k' : ℕ} {c' : Code} {n : ℕ},
Nat.pair k' (encode c') < Nat.pair k (encode (pair cf cg)) →
Nat.Partrec.Code.lup
... | /-
Copyright (c) 2018 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro
-/
import Mathlib.Computability.Partrec
#align_import computability.partrec_code from "leanprover-community/mathlib"@"6155d4351090a6fad236e3d2e4e0e4e7342668e8"
/-!
# G... | rfl | /-- The `Nat.Partrec.Code.evaln` function is primitive recursive. -/
theorem evaln_prim : Primrec fun a : (ℕ × Code) × ℕ => evaln a.1.1 a.1.2 a.2 :=
have :
Primrec₂ fun (_ : Unit) (n : ℕ) =>
let a := ofNat (ℕ × Code) n
(List.range a.1).map (evaln a.1 a.2) :=
Primrec.nat_strong_rec _ (hG.comp Primr... | Mathlib.Computability.PartrecCode.1088_0.A3c3Aev6SyIRjCJ | /-- The `Nat.Partrec.Code.evaln` function is primitive recursive. -/
theorem evaln_prim : Primrec fun a : (ℕ × Code) × ℕ => evaln a.1.1 a.1.2 a.2 | Mathlib_Computability_PartrecCode |
case succ.pair.intro.some
x✝ : Unit
p n : ℕ
this : List.range p = List.range (Nat.pair (unpair p).1 (encode (ofNat Code (unpair p).2)))
k' : ℕ
k : ℕ := k' + 1
nk : n ≤ k'
cf cg : Code
hg :
∀ {k' : ℕ} {c' : Code} {n : ℕ},
Nat.pair k' (encode c') < Nat.pair k (encode (pair cf cg)) →
Nat.Partrec.Code.lup
... | /-
Copyright (c) 2018 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro
-/
import Mathlib.Computability.Partrec
#align_import computability.partrec_code from "leanprover-community/mathlib"@"6155d4351090a6fad236e3d2e4e0e4e7342668e8"
/-!
# G... | cases evaln k cg n | /-- The `Nat.Partrec.Code.evaln` function is primitive recursive. -/
theorem evaln_prim : Primrec fun a : (ℕ × Code) × ℕ => evaln a.1.1 a.1.2 a.2 :=
have :
Primrec₂ fun (_ : Unit) (n : ℕ) =>
let a := ofNat (ℕ × Code) n
(List.range a.1).map (evaln a.1 a.2) :=
Primrec.nat_strong_rec _ (hG.comp Primr... | Mathlib.Computability.PartrecCode.1088_0.A3c3Aev6SyIRjCJ | /-- The `Nat.Partrec.Code.evaln` function is primitive recursive. -/
theorem evaln_prim : Primrec fun a : (ℕ × Code) × ℕ => evaln a.1.1 a.1.2 a.2 | Mathlib_Computability_PartrecCode |
case succ.pair.intro.some.none
x✝ : Unit
p n : ℕ
this : List.range p = List.range (Nat.pair (unpair p).1 (encode (ofNat Code (unpair p).2)))
k' : ℕ
k : ℕ := k' + 1
nk : n ≤ k'
cf cg : Code
hg :
∀ {k' : ℕ} {c' : Code} {n : ℕ},
Nat.pair k' (encode c') < Nat.pair k (encode (pair cf cg)) →
Nat.Partrec.Code.lup
... | /-
Copyright (c) 2018 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro
-/
import Mathlib.Computability.Partrec
#align_import computability.partrec_code from "leanprover-community/mathlib"@"6155d4351090a6fad236e3d2e4e0e4e7342668e8"
/-!
# G... | rfl | /-- The `Nat.Partrec.Code.evaln` function is primitive recursive. -/
theorem evaln_prim : Primrec fun a : (ℕ × Code) × ℕ => evaln a.1.1 a.1.2 a.2 :=
have :
Primrec₂ fun (_ : Unit) (n : ℕ) =>
let a := ofNat (ℕ × Code) n
(List.range a.1).map (evaln a.1 a.2) :=
Primrec.nat_strong_rec _ (hG.comp Primr... | Mathlib.Computability.PartrecCode.1088_0.A3c3Aev6SyIRjCJ | /-- The `Nat.Partrec.Code.evaln` function is primitive recursive. -/
theorem evaln_prim : Primrec fun a : (ℕ × Code) × ℕ => evaln a.1.1 a.1.2 a.2 | Mathlib_Computability_PartrecCode |
case succ.pair.intro.some.some
x✝ : Unit
p n : ℕ
this : List.range p = List.range (Nat.pair (unpair p).1 (encode (ofNat Code (unpair p).2)))
k' : ℕ
k : ℕ := k' + 1
nk : n ≤ k'
cf cg : Code
hg :
∀ {k' : ℕ} {c' : Code} {n : ℕ},
Nat.pair k' (encode c') < Nat.pair k (encode (pair cf cg)) →
Nat.Partrec.Code.lup
... | /-
Copyright (c) 2018 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro
-/
import Mathlib.Computability.Partrec
#align_import computability.partrec_code from "leanprover-community/mathlib"@"6155d4351090a6fad236e3d2e4e0e4e7342668e8"
/-!
# G... | rfl | /-- The `Nat.Partrec.Code.evaln` function is primitive recursive. -/
theorem evaln_prim : Primrec fun a : (ℕ × Code) × ℕ => evaln a.1.1 a.1.2 a.2 :=
have :
Primrec₂ fun (_ : Unit) (n : ℕ) =>
let a := ofNat (ℕ × Code) n
(List.range a.1).map (evaln a.1 a.2) :=
Primrec.nat_strong_rec _ (hG.comp Primr... | Mathlib.Computability.PartrecCode.1088_0.A3c3Aev6SyIRjCJ | /-- The `Nat.Partrec.Code.evaln` function is primitive recursive. -/
theorem evaln_prim : Primrec fun a : (ℕ × Code) × ℕ => evaln a.1.1 a.1.2 a.2 | Mathlib_Computability_PartrecCode |
case succ.comp
x✝ : Unit
p n : ℕ
this : List.range p = List.range (Nat.pair (unpair p).1 (encode (ofNat Code (unpair p).2)))
k' : ℕ
k : ℕ := k' + 1
nk : n ≤ k'
cf cg : Code
hg :
∀ {k' : ℕ} {c' : Code} {n : ℕ},
Nat.pair k' (encode c') < Nat.pair k (encode (comp cf cg)) →
Nat.Partrec.Code.lup
(List.... | /-
Copyright (c) 2018 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro
-/
import Mathlib.Computability.Partrec
#align_import computability.partrec_code from "leanprover-community/mathlib"@"6155d4351090a6fad236e3d2e4e0e4e7342668e8"
/-!
# G... | cases' encode_lt_comp cf cg with lf lg | /-- The `Nat.Partrec.Code.evaln` function is primitive recursive. -/
theorem evaln_prim : Primrec fun a : (ℕ × Code) × ℕ => evaln a.1.1 a.1.2 a.2 :=
have :
Primrec₂ fun (_ : Unit) (n : ℕ) =>
let a := ofNat (ℕ × Code) n
(List.range a.1).map (evaln a.1 a.2) :=
Primrec.nat_strong_rec _ (hG.comp Primr... | Mathlib.Computability.PartrecCode.1088_0.A3c3Aev6SyIRjCJ | /-- The `Nat.Partrec.Code.evaln` function is primitive recursive. -/
theorem evaln_prim : Primrec fun a : (ℕ × Code) × ℕ => evaln a.1.1 a.1.2 a.2 | Mathlib_Computability_PartrecCode |
case succ.comp.intro
x✝ : Unit
p n : ℕ
this : List.range p = List.range (Nat.pair (unpair p).1 (encode (ofNat Code (unpair p).2)))
k' : ℕ
k : ℕ := k' + 1
nk : n ≤ k'
cf cg : Code
hg :
∀ {k' : ℕ} {c' : Code} {n : ℕ},
Nat.pair k' (encode c') < Nat.pair k (encode (comp cf cg)) →
Nat.Partrec.Code.lup
... | /-
Copyright (c) 2018 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro
-/
import Mathlib.Computability.Partrec
#align_import computability.partrec_code from "leanprover-community/mathlib"@"6155d4351090a6fad236e3d2e4e0e4e7342668e8"
/-!
# G... | rw [hg (Nat.pair_lt_pair_right _ lg)] | /-- The `Nat.Partrec.Code.evaln` function is primitive recursive. -/
theorem evaln_prim : Primrec fun a : (ℕ × Code) × ℕ => evaln a.1.1 a.1.2 a.2 :=
have :
Primrec₂ fun (_ : Unit) (n : ℕ) =>
let a := ofNat (ℕ × Code) n
(List.range a.1).map (evaln a.1 a.2) :=
Primrec.nat_strong_rec _ (hG.comp Primr... | Mathlib.Computability.PartrecCode.1088_0.A3c3Aev6SyIRjCJ | /-- The `Nat.Partrec.Code.evaln` function is primitive recursive. -/
theorem evaln_prim : Primrec fun a : (ℕ × Code) × ℕ => evaln a.1.1 a.1.2 a.2 | Mathlib_Computability_PartrecCode |
case succ.comp.intro
x✝ : Unit
p n : ℕ
this : List.range p = List.range (Nat.pair (unpair p).1 (encode (ofNat Code (unpair p).2)))
k' : ℕ
k : ℕ := k' + 1
nk : n ≤ k'
cf cg : Code
hg :
∀ {k' : ℕ} {c' : Code} {n : ℕ},
Nat.pair k' (encode c') < Nat.pair k (encode (comp cf cg)) →
Nat.Partrec.Code.lup
... | /-
Copyright (c) 2018 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro
-/
import Mathlib.Computability.Partrec
#align_import computability.partrec_code from "leanprover-community/mathlib"@"6155d4351090a6fad236e3d2e4e0e4e7342668e8"
/-!
# G... | cases evaln k cg n | /-- The `Nat.Partrec.Code.evaln` function is primitive recursive. -/
theorem evaln_prim : Primrec fun a : (ℕ × Code) × ℕ => evaln a.1.1 a.1.2 a.2 :=
have :
Primrec₂ fun (_ : Unit) (n : ℕ) =>
let a := ofNat (ℕ × Code) n
(List.range a.1).map (evaln a.1 a.2) :=
Primrec.nat_strong_rec _ (hG.comp Primr... | Mathlib.Computability.PartrecCode.1088_0.A3c3Aev6SyIRjCJ | /-- The `Nat.Partrec.Code.evaln` function is primitive recursive. -/
theorem evaln_prim : Primrec fun a : (ℕ × Code) × ℕ => evaln a.1.1 a.1.2 a.2 | Mathlib_Computability_PartrecCode |
case succ.comp.intro.none
x✝ : Unit
p n : ℕ
this : List.range p = List.range (Nat.pair (unpair p).1 (encode (ofNat Code (unpair p).2)))
k' : ℕ
k : ℕ := k' + 1
nk : n ≤ k'
cf cg : Code
hg :
∀ {k' : ℕ} {c' : Code} {n : ℕ},
Nat.pair k' (encode c') < Nat.pair k (encode (comp cf cg)) →
Nat.Partrec.Code.lup
... | /-
Copyright (c) 2018 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro
-/
import Mathlib.Computability.Partrec
#align_import computability.partrec_code from "leanprover-community/mathlib"@"6155d4351090a6fad236e3d2e4e0e4e7342668e8"
/-!
# G... | rfl | /-- The `Nat.Partrec.Code.evaln` function is primitive recursive. -/
theorem evaln_prim : Primrec fun a : (ℕ × Code) × ℕ => evaln a.1.1 a.1.2 a.2 :=
have :
Primrec₂ fun (_ : Unit) (n : ℕ) =>
let a := ofNat (ℕ × Code) n
(List.range a.1).map (evaln a.1 a.2) :=
Primrec.nat_strong_rec _ (hG.comp Primr... | Mathlib.Computability.PartrecCode.1088_0.A3c3Aev6SyIRjCJ | /-- The `Nat.Partrec.Code.evaln` function is primitive recursive. -/
theorem evaln_prim : Primrec fun a : (ℕ × Code) × ℕ => evaln a.1.1 a.1.2 a.2 | Mathlib_Computability_PartrecCode |
case succ.comp.intro.some
x✝ : Unit
p n : ℕ
this : List.range p = List.range (Nat.pair (unpair p).1 (encode (ofNat Code (unpair p).2)))
k' : ℕ
k : ℕ := k' + 1
nk : n ≤ k'
cf cg : Code
hg :
∀ {k' : ℕ} {c' : Code} {n : ℕ},
Nat.pair k' (encode c') < Nat.pair k (encode (comp cf cg)) →
Nat.Partrec.Code.lup
... | /-
Copyright (c) 2018 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro
-/
import Mathlib.Computability.Partrec
#align_import computability.partrec_code from "leanprover-community/mathlib"@"6155d4351090a6fad236e3d2e4e0e4e7342668e8"
/-!
# G... | simp [hg (Nat.pair_lt_pair_right _ lf)] | /-- The `Nat.Partrec.Code.evaln` function is primitive recursive. -/
theorem evaln_prim : Primrec fun a : (ℕ × Code) × ℕ => evaln a.1.1 a.1.2 a.2 :=
have :
Primrec₂ fun (_ : Unit) (n : ℕ) =>
let a := ofNat (ℕ × Code) n
(List.range a.1).map (evaln a.1 a.2) :=
Primrec.nat_strong_rec _ (hG.comp Primr... | Mathlib.Computability.PartrecCode.1088_0.A3c3Aev6SyIRjCJ | /-- The `Nat.Partrec.Code.evaln` function is primitive recursive. -/
theorem evaln_prim : Primrec fun a : (ℕ × Code) × ℕ => evaln a.1.1 a.1.2 a.2 | Mathlib_Computability_PartrecCode |
case succ.prec
x✝ : Unit
p n : ℕ
this : List.range p = List.range (Nat.pair (unpair p).1 (encode (ofNat Code (unpair p).2)))
k' : ℕ
k : ℕ := k' + 1
nk : n ≤ k'
cf cg : Code
hg :
∀ {k' : ℕ} {c' : Code} {n : ℕ},
Nat.pair k' (encode c') < Nat.pair k (encode (prec cf cg)) →
Nat.Partrec.Code.lup
(List.... | /-
Copyright (c) 2018 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro
-/
import Mathlib.Computability.Partrec
#align_import computability.partrec_code from "leanprover-community/mathlib"@"6155d4351090a6fad236e3d2e4e0e4e7342668e8"
/-!
# G... | cases' encode_lt_prec cf cg with lf lg | /-- The `Nat.Partrec.Code.evaln` function is primitive recursive. -/
theorem evaln_prim : Primrec fun a : (ℕ × Code) × ℕ => evaln a.1.1 a.1.2 a.2 :=
have :
Primrec₂ fun (_ : Unit) (n : ℕ) =>
let a := ofNat (ℕ × Code) n
(List.range a.1).map (evaln a.1 a.2) :=
Primrec.nat_strong_rec _ (hG.comp Primr... | Mathlib.Computability.PartrecCode.1088_0.A3c3Aev6SyIRjCJ | /-- The `Nat.Partrec.Code.evaln` function is primitive recursive. -/
theorem evaln_prim : Primrec fun a : (ℕ × Code) × ℕ => evaln a.1.1 a.1.2 a.2 | Mathlib_Computability_PartrecCode |
case succ.prec.intro
x✝ : Unit
p n : ℕ
this : List.range p = List.range (Nat.pair (unpair p).1 (encode (ofNat Code (unpair p).2)))
k' : ℕ
k : ℕ := k' + 1
nk : n ≤ k'
cf cg : Code
hg :
∀ {k' : ℕ} {c' : Code} {n : ℕ},
Nat.pair k' (encode c') < Nat.pair k (encode (prec cf cg)) →
Nat.Partrec.Code.lup
... | /-
Copyright (c) 2018 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro
-/
import Mathlib.Computability.Partrec
#align_import computability.partrec_code from "leanprover-community/mathlib"@"6155d4351090a6fad236e3d2e4e0e4e7342668e8"
/-!
# G... | rw [hg (Nat.pair_lt_pair_right _ lf)] | /-- The `Nat.Partrec.Code.evaln` function is primitive recursive. -/
theorem evaln_prim : Primrec fun a : (ℕ × Code) × ℕ => evaln a.1.1 a.1.2 a.2 :=
have :
Primrec₂ fun (_ : Unit) (n : ℕ) =>
let a := ofNat (ℕ × Code) n
(List.range a.1).map (evaln a.1 a.2) :=
Primrec.nat_strong_rec _ (hG.comp Primr... | Mathlib.Computability.PartrecCode.1088_0.A3c3Aev6SyIRjCJ | /-- The `Nat.Partrec.Code.evaln` function is primitive recursive. -/
theorem evaln_prim : Primrec fun a : (ℕ × Code) × ℕ => evaln a.1.1 a.1.2 a.2 | Mathlib_Computability_PartrecCode |
case succ.prec.intro
x✝ : Unit
p n : ℕ
this : List.range p = List.range (Nat.pair (unpair p).1 (encode (ofNat Code (unpair p).2)))
k' : ℕ
k : ℕ := k' + 1
nk : n ≤ k'
cf cg : Code
hg :
∀ {k' : ℕ} {c' : Code} {n : ℕ},
Nat.pair k' (encode c') < Nat.pair k (encode (prec cf cg)) →
Nat.Partrec.Code.lup
... | /-
Copyright (c) 2018 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro
-/
import Mathlib.Computability.Partrec
#align_import computability.partrec_code from "leanprover-community/mathlib"@"6155d4351090a6fad236e3d2e4e0e4e7342668e8"
/-!
# G... | cases n.unpair.2 | /-- The `Nat.Partrec.Code.evaln` function is primitive recursive. -/
theorem evaln_prim : Primrec fun a : (ℕ × Code) × ℕ => evaln a.1.1 a.1.2 a.2 :=
have :
Primrec₂ fun (_ : Unit) (n : ℕ) =>
let a := ofNat (ℕ × Code) n
(List.range a.1).map (evaln a.1 a.2) :=
Primrec.nat_strong_rec _ (hG.comp Primr... | Mathlib.Computability.PartrecCode.1088_0.A3c3Aev6SyIRjCJ | /-- The `Nat.Partrec.Code.evaln` function is primitive recursive. -/
theorem evaln_prim : Primrec fun a : (ℕ × Code) × ℕ => evaln a.1.1 a.1.2 a.2 | Mathlib_Computability_PartrecCode |
case succ.prec.intro.zero
x✝ : Unit
p n : ℕ
this : List.range p = List.range (Nat.pair (unpair p).1 (encode (ofNat Code (unpair p).2)))
k' : ℕ
k : ℕ := k' + 1
nk : n ≤ k'
cf cg : Code
hg :
∀ {k' : ℕ} {c' : Code} {n : ℕ},
Nat.pair k' (encode c') < Nat.pair k (encode (prec cf cg)) →
Nat.Partrec.Code.lup
... | /-
Copyright (c) 2018 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro
-/
import Mathlib.Computability.Partrec
#align_import computability.partrec_code from "leanprover-community/mathlib"@"6155d4351090a6fad236e3d2e4e0e4e7342668e8"
/-!
# G... | rfl | /-- The `Nat.Partrec.Code.evaln` function is primitive recursive. -/
theorem evaln_prim : Primrec fun a : (ℕ × Code) × ℕ => evaln a.1.1 a.1.2 a.2 :=
have :
Primrec₂ fun (_ : Unit) (n : ℕ) =>
let a := ofNat (ℕ × Code) n
(List.range a.1).map (evaln a.1 a.2) :=
Primrec.nat_strong_rec _ (hG.comp Primr... | Mathlib.Computability.PartrecCode.1088_0.A3c3Aev6SyIRjCJ | /-- The `Nat.Partrec.Code.evaln` function is primitive recursive. -/
theorem evaln_prim : Primrec fun a : (ℕ × Code) × ℕ => evaln a.1.1 a.1.2 a.2 | Mathlib_Computability_PartrecCode |
case succ.prec.intro.succ
x✝ : Unit
p n : ℕ
this : List.range p = List.range (Nat.pair (unpair p).1 (encode (ofNat Code (unpair p).2)))
k' : ℕ
k : ℕ := k' + 1
nk : n ≤ k'
cf cg : Code
hg :
∀ {k' : ℕ} {c' : Code} {n : ℕ},
Nat.pair k' (encode c') < Nat.pair k (encode (prec cf cg)) →
Nat.Partrec.Code.lup
... | /-
Copyright (c) 2018 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro
-/
import Mathlib.Computability.Partrec
#align_import computability.partrec_code from "leanprover-community/mathlib"@"6155d4351090a6fad236e3d2e4e0e4e7342668e8"
/-!
# G... | simp only [decode_eq_ofNat, Option.some.injEq] | /-- The `Nat.Partrec.Code.evaln` function is primitive recursive. -/
theorem evaln_prim : Primrec fun a : (ℕ × Code) × ℕ => evaln a.1.1 a.1.2 a.2 :=
have :
Primrec₂ fun (_ : Unit) (n : ℕ) =>
let a := ofNat (ℕ × Code) n
(List.range a.1).map (evaln a.1 a.2) :=
Primrec.nat_strong_rec _ (hG.comp Primr... | Mathlib.Computability.PartrecCode.1088_0.A3c3Aev6SyIRjCJ | /-- The `Nat.Partrec.Code.evaln` function is primitive recursive. -/
theorem evaln_prim : Primrec fun a : (ℕ × Code) × ℕ => evaln a.1.1 a.1.2 a.2 | Mathlib_Computability_PartrecCode |
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