url stringclasses 147
values | commit stringclasses 147
values | file_path stringlengths 7 101 | full_name stringlengths 1 94 | start stringlengths 6 10 | end stringlengths 6 11 | tactic stringlengths 1 11.2k | state_before stringlengths 3 2.09M | state_after stringlengths 6 2.09M |
|---|---|---|---|---|---|---|---|---|
https://github.com/codyroux/traat-lean.git | f2babab84f81d4003446f476790022ac175d7236 | Traat/chapter1.lean | confluent_implies_church_rosser | [471, 1] | [495, 13] | case trans x y z red_x_y red_y_z joins_x_y joins_y_z =>
cases' joins_x_y with w1 h1
cases' h1 with h11 h12
cases' joins_y_z with w2 h2
cases' h2 with h21 h22
have h' : wedge R w1 w2 := by
exists y
have h := confl w1 w2 h'
cases' h with w h''
exists w; cases' h'' with h3 h4
constructor <;> apply re... | A : Type
R : A → A → Prop
inhabited_A : Nonempty A
confl : confluent R
x✝ y✝ x y z : A
red_x_y : refl_trans_sym_clos R x y
red_y_z : refl_trans_sym_clos R y z
joins_x_y : joins R x y
joins_y_z : joins R y z
⊢ joins R x z | no goals |
https://github.com/codyroux/traat-lean.git | f2babab84f81d4003446f476790022ac175d7236 | Traat/chapter1.lean | confluent_implies_church_rosser | [471, 1] | [495, 13] | case inv _ h =>
cases' h with w h'
cases' h' with h1 h2
exists w | A : Type
R : A → A → Prop
inhabited_A : Nonempty A
confl : confluent R
x y a✝¹ b✝ : A
a✝ : refl_trans_sym_clos R b✝ a✝¹
h : joins R b✝ a✝¹
⊢ joins R a✝¹ b✝ | no goals |
https://github.com/codyroux/traat-lean.git | f2babab84f81d4003446f476790022ac175d7236 | Traat/chapter1.lean | confluent_implies_church_rosser | [471, 1] | [495, 13] | exists x | A : Type
R : A → A → Prop
inhabited_A : Nonempty A
confl : confluent R
x✝ y x : A
⊢ joins R x x | A : Type
R : A → A → Prop
inhabited_A : Nonempty A
confl : confluent R
x✝ y x : A
⊢ refl_trans_clos R x x ∧ refl_trans_clos R x x |
https://github.com/codyroux/traat-lean.git | f2babab84f81d4003446f476790022ac175d7236 | Traat/chapter1.lean | confluent_implies_church_rosser | [471, 1] | [495, 13] | repeat constructor | A : Type
R : A → A → Prop
inhabited_A : Nonempty A
confl : confluent R
x✝ y x : A
⊢ refl_trans_clos R x x ∧ refl_trans_clos R x x | no goals |
https://github.com/codyroux/traat-lean.git | f2babab84f81d4003446f476790022ac175d7236 | Traat/chapter1.lean | confluent_implies_church_rosser | [471, 1] | [495, 13] | constructor | case right
A : Type
R : A → A → Prop
inhabited_A : Nonempty A
confl : confluent R
x✝ y x : A
⊢ refl_trans_clos R x x | no goals |
https://github.com/codyroux/traat-lean.git | f2babab84f81d4003446f476790022ac175d7236 | Traat/chapter1.lean | confluent_implies_church_rosser | [471, 1] | [495, 13] | exists y | A : Type
R : A → A → Prop
inhabited_A : Nonempty A
confl : confluent R
x✝ y✝ x y : A
red_x_y : R x y
⊢ joins R x y | A : Type
R : A → A → Prop
inhabited_A : Nonempty A
confl : confluent R
x✝ y✝ x y : A
red_x_y : R x y
⊢ refl_trans_clos R x y ∧ refl_trans_clos R y y |
https://github.com/codyroux/traat-lean.git | f2babab84f81d4003446f476790022ac175d7236 | Traat/chapter1.lean | confluent_implies_church_rosser | [471, 1] | [495, 13] | constructor <;> aesop | A : Type
R : A → A → Prop
inhabited_A : Nonempty A
confl : confluent R
x✝ y✝ x y : A
red_x_y : R x y
⊢ refl_trans_clos R x y ∧ refl_trans_clos R y y | no goals |
https://github.com/codyroux/traat-lean.git | f2babab84f81d4003446f476790022ac175d7236 | Traat/chapter1.lean | confluent_implies_church_rosser | [471, 1] | [495, 13] | cases' joins_x_y with w1 h1 | A : Type
R : A → A → Prop
inhabited_A : Nonempty A
confl : confluent R
x✝ y✝ x y z : A
red_x_y : refl_trans_sym_clos R x y
red_y_z : refl_trans_sym_clos R y z
joins_x_y : joins R x y
joins_y_z : joins R y z
⊢ joins R x z | case intro
A : Type
R : A → A → Prop
inhabited_A : Nonempty A
confl : confluent R
x✝ y✝ x y z : A
red_x_y : refl_trans_sym_clos R x y
red_y_z : refl_trans_sym_clos R y z
joins_y_z : joins R y z
w1 : A
h1 : refl_trans_clos R x w1 ∧ refl_trans_clos R y w1
⊢ joins R x z |
https://github.com/codyroux/traat-lean.git | f2babab84f81d4003446f476790022ac175d7236 | Traat/chapter1.lean | confluent_implies_church_rosser | [471, 1] | [495, 13] | cases' h1 with h11 h12 | case intro
A : Type
R : A → A → Prop
inhabited_A : Nonempty A
confl : confluent R
x✝ y✝ x y z : A
red_x_y : refl_trans_sym_clos R x y
red_y_z : refl_trans_sym_clos R y z
joins_y_z : joins R y z
w1 : A
h1 : refl_trans_clos R x w1 ∧ refl_trans_clos R y w1
⊢ joins R x z | case intro.intro
A : Type
R : A → A → Prop
inhabited_A : Nonempty A
confl : confluent R
x✝ y✝ x y z : A
red_x_y : refl_trans_sym_clos R x y
red_y_z : refl_trans_sym_clos R y z
joins_y_z : joins R y z
w1 : A
h11 : refl_trans_clos R x w1
h12 : refl_trans_clos R y w1
⊢ joins R x z |
https://github.com/codyroux/traat-lean.git | f2babab84f81d4003446f476790022ac175d7236 | Traat/chapter1.lean | confluent_implies_church_rosser | [471, 1] | [495, 13] | cases' joins_y_z with w2 h2 | case intro.intro
A : Type
R : A → A → Prop
inhabited_A : Nonempty A
confl : confluent R
x✝ y✝ x y z : A
red_x_y : refl_trans_sym_clos R x y
red_y_z : refl_trans_sym_clos R y z
joins_y_z : joins R y z
w1 : A
h11 : refl_trans_clos R x w1
h12 : refl_trans_clos R y w1
⊢ joins R x z | case intro.intro.intro
A : Type
R : A → A → Prop
inhabited_A : Nonempty A
confl : confluent R
x✝ y✝ x y z : A
red_x_y : refl_trans_sym_clos R x y
red_y_z : refl_trans_sym_clos R y z
w1 : A
h11 : refl_trans_clos R x w1
h12 : refl_trans_clos R y w1
w2 : A
h2 : refl_trans_clos R y w2 ∧ refl_trans_clos R z w2
⊢ joins R x z |
https://github.com/codyroux/traat-lean.git | f2babab84f81d4003446f476790022ac175d7236 | Traat/chapter1.lean | confluent_implies_church_rosser | [471, 1] | [495, 13] | cases' h2 with h21 h22 | case intro.intro.intro
A : Type
R : A → A → Prop
inhabited_A : Nonempty A
confl : confluent R
x✝ y✝ x y z : A
red_x_y : refl_trans_sym_clos R x y
red_y_z : refl_trans_sym_clos R y z
w1 : A
h11 : refl_trans_clos R x w1
h12 : refl_trans_clos R y w1
w2 : A
h2 : refl_trans_clos R y w2 ∧ refl_trans_clos R z w2
⊢ joins R x z | case intro.intro.intro.intro
A : Type
R : A → A → Prop
inhabited_A : Nonempty A
confl : confluent R
x✝ y✝ x y z : A
red_x_y : refl_trans_sym_clos R x y
red_y_z : refl_trans_sym_clos R y z
w1 : A
h11 : refl_trans_clos R x w1
h12 : refl_trans_clos R y w1
w2 : A
h21 : refl_trans_clos R y w2
h22 : refl_trans_clos R z w2
⊢ ... |
https://github.com/codyroux/traat-lean.git | f2babab84f81d4003446f476790022ac175d7236 | Traat/chapter1.lean | confluent_implies_church_rosser | [471, 1] | [495, 13] | have h' : wedge R w1 w2 := by
exists y | case intro.intro.intro.intro
A : Type
R : A → A → Prop
inhabited_A : Nonempty A
confl : confluent R
x✝ y✝ x y z : A
red_x_y : refl_trans_sym_clos R x y
red_y_z : refl_trans_sym_clos R y z
w1 : A
h11 : refl_trans_clos R x w1
h12 : refl_trans_clos R y w1
w2 : A
h21 : refl_trans_clos R y w2
h22 : refl_trans_clos R z w2
⊢ ... | case intro.intro.intro.intro
A : Type
R : A → A → Prop
inhabited_A : Nonempty A
confl : confluent R
x✝ y✝ x y z : A
red_x_y : refl_trans_sym_clos R x y
red_y_z : refl_trans_sym_clos R y z
w1 : A
h11 : refl_trans_clos R x w1
h12 : refl_trans_clos R y w1
w2 : A
h21 : refl_trans_clos R y w2
h22 : refl_trans_clos R z w2
h'... |
https://github.com/codyroux/traat-lean.git | f2babab84f81d4003446f476790022ac175d7236 | Traat/chapter1.lean | confluent_implies_church_rosser | [471, 1] | [495, 13] | have h := confl w1 w2 h' | case intro.intro.intro.intro
A : Type
R : A → A → Prop
inhabited_A : Nonempty A
confl : confluent R
x✝ y✝ x y z : A
red_x_y : refl_trans_sym_clos R x y
red_y_z : refl_trans_sym_clos R y z
w1 : A
h11 : refl_trans_clos R x w1
h12 : refl_trans_clos R y w1
w2 : A
h21 : refl_trans_clos R y w2
h22 : refl_trans_clos R z w2
h'... | case intro.intro.intro.intro
A : Type
R : A → A → Prop
inhabited_A : Nonempty A
confl : confluent R
x✝ y✝ x y z : A
red_x_y : refl_trans_sym_clos R x y
red_y_z : refl_trans_sym_clos R y z
w1 : A
h11 : refl_trans_clos R x w1
h12 : refl_trans_clos R y w1
w2 : A
h21 : refl_trans_clos R y w2
h22 : refl_trans_clos R z w2
h'... |
https://github.com/codyroux/traat-lean.git | f2babab84f81d4003446f476790022ac175d7236 | Traat/chapter1.lean | confluent_implies_church_rosser | [471, 1] | [495, 13] | cases' h with w h'' | case intro.intro.intro.intro
A : Type
R : A → A → Prop
inhabited_A : Nonempty A
confl : confluent R
x✝ y✝ x y z : A
red_x_y : refl_trans_sym_clos R x y
red_y_z : refl_trans_sym_clos R y z
w1 : A
h11 : refl_trans_clos R x w1
h12 : refl_trans_clos R y w1
w2 : A
h21 : refl_trans_clos R y w2
h22 : refl_trans_clos R z w2
h'... | case intro.intro.intro.intro.intro
A : Type
R : A → A → Prop
inhabited_A : Nonempty A
confl : confluent R
x✝ y✝ x y z : A
red_x_y : refl_trans_sym_clos R x y
red_y_z : refl_trans_sym_clos R y z
w1 : A
h11 : refl_trans_clos R x w1
h12 : refl_trans_clos R y w1
w2 : A
h21 : refl_trans_clos R y w2
h22 : refl_trans_clos R z... |
https://github.com/codyroux/traat-lean.git | f2babab84f81d4003446f476790022ac175d7236 | Traat/chapter1.lean | confluent_implies_church_rosser | [471, 1] | [495, 13] | exists w | case intro.intro.intro.intro.intro
A : Type
R : A → A → Prop
inhabited_A : Nonempty A
confl : confluent R
x✝ y✝ x y z : A
red_x_y : refl_trans_sym_clos R x y
red_y_z : refl_trans_sym_clos R y z
w1 : A
h11 : refl_trans_clos R x w1
h12 : refl_trans_clos R y w1
w2 : A
h21 : refl_trans_clos R y w2
h22 : refl_trans_clos R z... | case intro.intro.intro.intro.intro
A : Type
R : A → A → Prop
inhabited_A : Nonempty A
confl : confluent R
x✝ y✝ x y z : A
red_x_y : refl_trans_sym_clos R x y
red_y_z : refl_trans_sym_clos R y z
w1 : A
h11 : refl_trans_clos R x w1
h12 : refl_trans_clos R y w1
w2 : A
h21 : refl_trans_clos R y w2
h22 : refl_trans_clos R z... |
https://github.com/codyroux/traat-lean.git | f2babab84f81d4003446f476790022ac175d7236 | Traat/chapter1.lean | confluent_implies_church_rosser | [471, 1] | [495, 13] | cases' h'' with h3 h4 | case intro.intro.intro.intro.intro
A : Type
R : A → A → Prop
inhabited_A : Nonempty A
confl : confluent R
x✝ y✝ x y z : A
red_x_y : refl_trans_sym_clos R x y
red_y_z : refl_trans_sym_clos R y z
w1 : A
h11 : refl_trans_clos R x w1
h12 : refl_trans_clos R y w1
w2 : A
h21 : refl_trans_clos R y w2
h22 : refl_trans_clos R z... | case intro.intro.intro.intro.intro.intro
A : Type
R : A → A → Prop
inhabited_A : Nonempty A
confl : confluent R
x✝ y✝ x y z : A
red_x_y : refl_trans_sym_clos R x y
red_y_z : refl_trans_sym_clos R y z
w1 : A
h11 : refl_trans_clos R x w1
h12 : refl_trans_clos R y w1
w2 : A
h21 : refl_trans_clos R y w2
h22 : refl_trans_cl... |
https://github.com/codyroux/traat-lean.git | f2babab84f81d4003446f476790022ac175d7236 | Traat/chapter1.lean | confluent_implies_church_rosser | [471, 1] | [495, 13] | constructor <;> apply refl_trans_clos_transitive <;> trivial | case intro.intro.intro.intro.intro.intro
A : Type
R : A → A → Prop
inhabited_A : Nonempty A
confl : confluent R
x✝ y✝ x y z : A
red_x_y : refl_trans_sym_clos R x y
red_y_z : refl_trans_sym_clos R y z
w1 : A
h11 : refl_trans_clos R x w1
h12 : refl_trans_clos R y w1
w2 : A
h21 : refl_trans_clos R y w2
h22 : refl_trans_cl... | no goals |
https://github.com/codyroux/traat-lean.git | f2babab84f81d4003446f476790022ac175d7236 | Traat/chapter1.lean | confluent_implies_church_rosser | [471, 1] | [495, 13] | exists y | A : Type
R : A → A → Prop
inhabited_A : Nonempty A
confl : confluent R
x✝ y✝ x y z : A
red_x_y : refl_trans_sym_clos R x y
red_y_z : refl_trans_sym_clos R y z
w1 : A
h11 : refl_trans_clos R x w1
h12 : refl_trans_clos R y w1
w2 : A
h21 : refl_trans_clos R y w2
h22 : refl_trans_clos R z w2
⊢ wedge R w1 w2 | no goals |
https://github.com/codyroux/traat-lean.git | f2babab84f81d4003446f476790022ac175d7236 | Traat/chapter1.lean | confluent_implies_church_rosser | [471, 1] | [495, 13] | cases' h with w h' | A : Type
R : A → A → Prop
inhabited_A : Nonempty A
confl : confluent R
x y a✝¹ b✝ : A
a✝ : refl_trans_sym_clos R b✝ a✝¹
h : joins R b✝ a✝¹
⊢ joins R a✝¹ b✝ | case intro
A : Type
R : A → A → Prop
inhabited_A : Nonempty A
confl : confluent R
x y a✝¹ b✝ : A
a✝ : refl_trans_sym_clos R b✝ a✝¹
w : A
h' : refl_trans_clos R b✝ w ∧ refl_trans_clos R a✝¹ w
⊢ joins R a✝¹ b✝ |
https://github.com/codyroux/traat-lean.git | f2babab84f81d4003446f476790022ac175d7236 | Traat/chapter1.lean | confluent_implies_church_rosser | [471, 1] | [495, 13] | cases' h' with h1 h2 | case intro
A : Type
R : A → A → Prop
inhabited_A : Nonempty A
confl : confluent R
x y a✝¹ b✝ : A
a✝ : refl_trans_sym_clos R b✝ a✝¹
w : A
h' : refl_trans_clos R b✝ w ∧ refl_trans_clos R a✝¹ w
⊢ joins R a✝¹ b✝ | case intro.intro
A : Type
R : A → A → Prop
inhabited_A : Nonempty A
confl : confluent R
x y a✝¹ b✝ : A
a✝ : refl_trans_sym_clos R b✝ a✝¹
w : A
h1 : refl_trans_clos R b✝ w
h2 : refl_trans_clos R a✝¹ w
⊢ joins R a✝¹ b✝ |
https://github.com/codyroux/traat-lean.git | f2babab84f81d4003446f476790022ac175d7236 | Traat/chapter1.lean | confluent_implies_church_rosser | [471, 1] | [495, 13] | exists w | case intro.intro
A : Type
R : A → A → Prop
inhabited_A : Nonempty A
confl : confluent R
x y a✝¹ b✝ : A
a✝ : refl_trans_sym_clos R b✝ a✝¹
w : A
h1 : refl_trans_clos R b✝ w
h2 : refl_trans_clos R a✝¹ w
⊢ joins R a✝¹ b✝ | no goals |
https://github.com/codyroux/traat-lean.git | f2babab84f81d4003446f476790022ac175d7236 | Traat/chapter1.lean | not_joins_a_d | [520, 1] | [529, 24] | intros h | A : Type
R : A → A → Prop
inhabited_A : Nonempty A
⊢ ¬joins RX X.a X.d | A : Type
R : A → A → Prop
inhabited_A : Nonempty A
h : joins RX X.a X.d
⊢ False |
https://github.com/codyroux/traat-lean.git | f2babab84f81d4003446f476790022ac175d7236 | Traat/chapter1.lean | not_joins_a_d | [520, 1] | [529, 24] | cases' h with w h | A : Type
R : A → A → Prop
inhabited_A : Nonempty A
h : joins RX X.a X.d
⊢ False | case intro
A : Type
R : A → A → Prop
inhabited_A : Nonempty A
w : X
h : refl_trans_clos RX X.a w ∧ refl_trans_clos RX X.d w
⊢ False |
https://github.com/codyroux/traat-lean.git | f2babab84f81d4003446f476790022ac175d7236 | Traat/chapter1.lean | not_joins_a_d | [520, 1] | [529, 24] | cases' h with h1 h2 | case intro
A : Type
R : A → A → Prop
inhabited_A : Nonempty A
w : X
h : refl_trans_clos RX X.a w ∧ refl_trans_clos RX X.d w
⊢ False | case intro.intro
A : Type
R : A → A → Prop
inhabited_A : Nonempty A
w : X
h1 : refl_trans_clos RX X.a w
h2 : refl_trans_clos RX X.d w
⊢ False |
https://github.com/codyroux/traat-lean.git | f2babab84f81d4003446f476790022ac175d7236 | Traat/chapter1.lean | not_joins_a_d | [520, 1] | [529, 24] | have eq_a : X.a = w := by
apply normal_red RX <;> aesop | case intro.intro
A : Type
R : A → A → Prop
inhabited_A : Nonempty A
w : X
h1 : refl_trans_clos RX X.a w
h2 : refl_trans_clos RX X.d w
⊢ False | case intro.intro
A : Type
R : A → A → Prop
inhabited_A : Nonempty A
w : X
h1 : refl_trans_clos RX X.a w
h2 : refl_trans_clos RX X.d w
eq_a : X.a = w
⊢ False |
https://github.com/codyroux/traat-lean.git | f2babab84f81d4003446f476790022ac175d7236 | Traat/chapter1.lean | not_joins_a_d | [520, 1] | [529, 24] | have eq_d : X.d = w := by
apply normal_red RX <;> aesop | case intro.intro
A : Type
R : A → A → Prop
inhabited_A : Nonempty A
w : X
h1 : refl_trans_clos RX X.a w
h2 : refl_trans_clos RX X.d w
eq_a : X.a = w
⊢ False | case intro.intro
A : Type
R : A → A → Prop
inhabited_A : Nonempty A
w : X
h1 : refl_trans_clos RX X.a w
h2 : refl_trans_clos RX X.d w
eq_a : X.a = w
eq_d : X.d = w
⊢ False |
https://github.com/codyroux/traat-lean.git | f2babab84f81d4003446f476790022ac175d7236 | Traat/chapter1.lean | not_joins_a_d | [520, 1] | [529, 24] | simp [← eq_a] at eq_d | case intro.intro
A : Type
R : A → A → Prop
inhabited_A : Nonempty A
w : X
h1 : refl_trans_clos RX X.a w
h2 : refl_trans_clos RX X.d w
eq_a : X.a = w
eq_d : X.d = w
⊢ False | no goals |
https://github.com/codyroux/traat-lean.git | f2babab84f81d4003446f476790022ac175d7236 | Traat/chapter1.lean | not_joins_a_d | [520, 1] | [529, 24] | apply normal_red RX <;> aesop | A : Type
R : A → A → Prop
inhabited_A : Nonempty A
w : X
h1 : refl_trans_clos RX X.a w
h2 : refl_trans_clos RX X.d w
⊢ X.a = w | no goals |
https://github.com/codyroux/traat-lean.git | f2babab84f81d4003446f476790022ac175d7236 | Traat/chapter1.lean | not_joins_a_d | [520, 1] | [529, 24] | apply normal_red RX <;> aesop | A : Type
R : A → A → Prop
inhabited_A : Nonempty A
w : X
h1 : refl_trans_clos RX X.a w
h2 : refl_trans_clos RX X.d w
eq_a : X.a = w
⊢ X.d = w | no goals |
https://github.com/codyroux/traat-lean.git | f2babab84f81d4003446f476790022ac175d7236 | Traat/chapter1.lean | weakly_confluent_does_not_imply_confluent | [532, 1] | [582, 20] | exists X, RX | A : Type
R : A → A → Prop
inhabited_A : Nonempty A
⊢ ∃ A R, weakly_confluent R ∧ ¬confluent R | A : Type
R : A → A → Prop
inhabited_A : Nonempty A
⊢ weakly_confluent RX ∧ ¬confluent RX |
https://github.com/codyroux/traat-lean.git | f2babab84f81d4003446f476790022ac175d7236 | Traat/chapter1.lean | weakly_confluent_does_not_imply_confluent | [532, 1] | [582, 20] | constructor | A : Type
R : A → A → Prop
inhabited_A : Nonempty A
⊢ weakly_confluent RX ∧ ¬confluent RX | case left
A : Type
R : A → A → Prop
inhabited_A : Nonempty A
⊢ weakly_confluent RX
case right
A : Type
R : A → A → Prop
inhabited_A : Nonempty A
⊢ ¬confluent RX |
https://github.com/codyroux/traat-lean.git | f2babab84f81d4003446f476790022ac175d7236 | Traat/chapter1.lean | weakly_confluent_does_not_imply_confluent | [532, 1] | [582, 20] | . intros x y z r_x_y r_x_z
simp [*] at r_x_y
simp [*] at r_x_z
cases r_x_y <;> cases r_x_z <;> simp [*] at *
. exists X.a; repeat constructor
. exists X.a; try constructor
. constructor
. simp [*]; constructor; simp [RX]
. left; trivial
. constructor; simp [RX]; left; trivial; constructor
... | case left
A : Type
R : A → A → Prop
inhabited_A : Nonempty A
⊢ weakly_confluent RX
case right
A : Type
R : A → A → Prop
inhabited_A : Nonempty A
⊢ ¬confluent RX | case right
A : Type
R : A → A → Prop
inhabited_A : Nonempty A
⊢ ¬confluent RX |
https://github.com/codyroux/traat-lean.git | f2babab84f81d4003446f476790022ac175d7236 | Traat/chapter1.lean | weakly_confluent_does_not_imply_confluent | [532, 1] | [582, 20] | . intros h
apply not_joins_a_d
apply h
exists X.b; constructor
. constructor
simp [RX]
left; trivial
constructor
. constructor
simp [RX]
right; trivial
constructor
. simp [RX]; right; trivial
. constructor | case right
A : Type
R : A → A → Prop
inhabited_A : Nonempty A
⊢ ¬confluent RX | no goals |
https://github.com/codyroux/traat-lean.git | f2babab84f81d4003446f476790022ac175d7236 | Traat/chapter1.lean | weakly_confluent_does_not_imply_confluent | [532, 1] | [582, 20] | intros x y z r_x_y r_x_z | case left
A : Type
R : A → A → Prop
inhabited_A : Nonempty A
⊢ weakly_confluent RX | case left
A : Type
R : A → A → Prop
inhabited_A : Nonempty A
x y z : X
r_x_y : RX x y
r_x_z : RX x z
⊢ joins RX y z |
https://github.com/codyroux/traat-lean.git | f2babab84f81d4003446f476790022ac175d7236 | Traat/chapter1.lean | weakly_confluent_does_not_imply_confluent | [532, 1] | [582, 20] | simp [*] at r_x_y | case left
A : Type
R : A → A → Prop
inhabited_A : Nonempty A
x y z : X
r_x_y : RX x y
r_x_z : RX x z
⊢ joins RX y z | case left
A : Type
R : A → A → Prop
inhabited_A : Nonempty A
x y z : X
r_x_y : x = X.b ∧ y = X.a ∨ x = X.b ∧ y = X.c ∨ x = X.c ∧ y = X.b ∨ x = X.c ∧ y = X.d
r_x_z : RX x z
⊢ joins RX y z |
https://github.com/codyroux/traat-lean.git | f2babab84f81d4003446f476790022ac175d7236 | Traat/chapter1.lean | weakly_confluent_does_not_imply_confluent | [532, 1] | [582, 20] | simp [*] at r_x_z | case left
A : Type
R : A → A → Prop
inhabited_A : Nonempty A
x y z : X
r_x_y : x = X.b ∧ y = X.a ∨ x = X.b ∧ y = X.c ∨ x = X.c ∧ y = X.b ∨ x = X.c ∧ y = X.d
r_x_z : RX x z
⊢ joins RX y z | case left
A : Type
R : A → A → Prop
inhabited_A : Nonempty A
x y z : X
r_x_y : x = X.b ∧ y = X.a ∨ x = X.b ∧ y = X.c ∨ x = X.c ∧ y = X.b ∨ x = X.c ∧ y = X.d
r_x_z : x = X.b ∧ z = X.a ∨ x = X.b ∧ z = X.c ∨ x = X.c ∧ z = X.b ∨ x = X.c ∧ z = X.d
⊢ joins RX y z |
https://github.com/codyroux/traat-lean.git | f2babab84f81d4003446f476790022ac175d7236 | Traat/chapter1.lean | weakly_confluent_does_not_imply_confluent | [532, 1] | [582, 20] | cases r_x_y <;> cases r_x_z <;> simp [*] at * | case left
A : Type
R : A → A → Prop
inhabited_A : Nonempty A
x y z : X
r_x_y : x = X.b ∧ y = X.a ∨ x = X.b ∧ y = X.c ∨ x = X.c ∧ y = X.b ∨ x = X.c ∧ y = X.d
r_x_z : x = X.b ∧ z = X.a ∨ x = X.b ∧ z = X.c ∨ x = X.c ∧ z = X.b ∨ x = X.c ∧ z = X.d
⊢ joins RX y z | case left.inl.inl
A : Type
R : A → A → Prop
inhabited_A : Nonempty A
x y z : X
h✝¹ : y = X.a
h✝ : z = X.a
⊢ joins (fun x y => x = X.b ∧ y = X.a ∨ x = X.b ∧ y = X.c ∨ x = X.c ∧ y = X.b ∨ x = X.c ∧ y = X.d) X.a X.a
case left.inl.inr
A : Type
R : A → A → Prop
inhabited_A : Nonempty A
x y z : X
h✝¹ : x = X.b ∧ y = X.a
h✝ ... |
https://github.com/codyroux/traat-lean.git | f2babab84f81d4003446f476790022ac175d7236 | Traat/chapter1.lean | weakly_confluent_does_not_imply_confluent | [532, 1] | [582, 20] | . exists X.a; repeat constructor | case left.inl.inl
A : Type
R : A → A → Prop
inhabited_A : Nonempty A
x y z : X
h✝¹ : y = X.a
h✝ : z = X.a
⊢ joins (fun x y => x = X.b ∧ y = X.a ∨ x = X.b ∧ y = X.c ∨ x = X.c ∧ y = X.b ∨ x = X.c ∧ y = X.d) X.a X.a
case left.inl.inr
A : Type
R : A → A → Prop
inhabited_A : Nonempty A
x y z : X
h✝¹ : x = X.b ∧ y = X.a
h✝ ... | case left.inl.inr
A : Type
R : A → A → Prop
inhabited_A : Nonempty A
x y z : X
h✝¹ : x = X.b ∧ y = X.a
h✝ : z = X.c
⊢ joins (fun x y => x = X.b ∧ y = X.a ∨ x = X.b ∧ y = X.c ∨ x = X.c ∧ y = X.b ∨ x = X.c ∧ y = X.d) X.a z
case left.inr.inl
A : Type
R : A → A → Prop
inhabited_A : Nonempty A
x y z : X
h✝¹ : x = X.b ∧ z =... |
https://github.com/codyroux/traat-lean.git | f2babab84f81d4003446f476790022ac175d7236 | Traat/chapter1.lean | weakly_confluent_does_not_imply_confluent | [532, 1] | [582, 20] | . exists X.a; try constructor
. constructor
. simp [*]; constructor; simp [RX]
. left; trivial
. constructor; simp [RX]; left; trivial; constructor | case left.inl.inr
A : Type
R : A → A → Prop
inhabited_A : Nonempty A
x y z : X
h✝¹ : x = X.b ∧ y = X.a
h✝ : z = X.c
⊢ joins (fun x y => x = X.b ∧ y = X.a ∨ x = X.b ∧ y = X.c ∨ x = X.c ∧ y = X.b ∨ x = X.c ∧ y = X.d) X.a z
case left.inr.inl
A : Type
R : A → A → Prop
inhabited_A : Nonempty A
x y z : X
h✝¹ : x = X.b ∧ z =... | case left.inr.inl
A : Type
R : A → A → Prop
inhabited_A : Nonempty A
x y z : X
h✝¹ : x = X.b ∧ z = X.a
h✝ : y = X.c
⊢ joins (fun x y => x = X.b ∧ y = X.a ∨ x = X.b ∧ y = X.c ∨ x = X.c ∧ y = X.b ∨ x = X.c ∧ y = X.d) y X.a
case left.inr.inr
A : Type
R : A → A → Prop
inhabited_A : Nonempty A
x y z : X
h✝¹ : x = X.b ∧ y =... |
https://github.com/codyroux/traat-lean.git | f2babab84f81d4003446f476790022ac175d7236 | Traat/chapter1.lean | weakly_confluent_does_not_imply_confluent | [532, 1] | [582, 20] | . exists X.a; simp [*]; constructor
. repeat (constructor; simp [RX]; left; trivial)
constructor
. constructor | case left.inr.inl
A : Type
R : A → A → Prop
inhabited_A : Nonempty A
x y z : X
h✝¹ : x = X.b ∧ z = X.a
h✝ : y = X.c
⊢ joins (fun x y => x = X.b ∧ y = X.a ∨ x = X.b ∧ y = X.c ∨ x = X.c ∧ y = X.b ∨ x = X.c ∧ y = X.d) y X.a
case left.inr.inr
A : Type
R : A → A → Prop
inhabited_A : Nonempty A
x y z : X
h✝¹ : x = X.b ∧ y =... | case left.inr.inr
A : Type
R : A → A → Prop
inhabited_A : Nonempty A
x y z : X
h✝¹ : x = X.b ∧ y = X.c ∨ x = X.c ∧ y = X.b ∨ x = X.c ∧ y = X.d
h✝ : x = X.b ∧ z = X.c ∨ x = X.c ∧ z = X.b ∨ x = X.c ∧ z = X.d
⊢ joins (fun x y => x = X.b ∧ y = X.a ∨ x = X.b ∧ y = X.c ∨ x = X.c ∧ y = X.b ∨ x = X.c ∧ y = X.d) y z |
https://github.com/codyroux/traat-lean.git | f2babab84f81d4003446f476790022ac175d7236 | Traat/chapter1.lean | weakly_confluent_does_not_imply_confluent | [532, 1] | [582, 20] | . case inr h1 h2 =>
cases h1 <;> cases h2 <;> simp [*] at *
. exists X.c; repeat constructor
. case inr h1 h2 =>
cases h1 <;> cases h2 <;> simp [*] at *
. exists X.b; repeat constructor
. exists X.d; constructor
. constructor; simp [RX]; right; trivial
constructor; simp [RX]; right; triv... | case left.inr.inr
A : Type
R : A → A → Prop
inhabited_A : Nonempty A
x y z : X
h✝¹ : x = X.b ∧ y = X.c ∨ x = X.c ∧ y = X.b ∨ x = X.c ∧ y = X.d
h✝ : x = X.b ∧ z = X.c ∨ x = X.c ∧ z = X.b ∨ x = X.c ∧ z = X.d
⊢ joins (fun x y => x = X.b ∧ y = X.a ∨ x = X.b ∧ y = X.c ∨ x = X.c ∧ y = X.b ∨ x = X.c ∧ y = X.d) y z | no goals |
https://github.com/codyroux/traat-lean.git | f2babab84f81d4003446f476790022ac175d7236 | Traat/chapter1.lean | weakly_confluent_does_not_imply_confluent | [532, 1] | [582, 20] | exists X.a | case left.inl.inl
A : Type
R : A → A → Prop
inhabited_A : Nonempty A
x y z : X
h✝¹ : y = X.a
h✝ : z = X.a
⊢ joins (fun x y => x = X.b ∧ y = X.a ∨ x = X.b ∧ y = X.c ∨ x = X.c ∧ y = X.b ∨ x = X.c ∧ y = X.d) X.a X.a | case left.inl.inl
A : Type
R : A → A → Prop
inhabited_A : Nonempty A
x y z : X
h✝¹ : y = X.a
h✝ : z = X.a
⊢ refl_trans_clos (fun x y => x = X.b ∧ y = X.a ∨ x = X.b ∧ y = X.c ∨ x = X.c ∧ y = X.b ∨ x = X.c ∧ y = X.d) X.a X.a ∧
refl_trans_clos (fun x y => x = X.b ∧ y = X.a ∨ x = X.b ∧ y = X.c ∨ x = X.c ∧ y = X.b ∨ x =... |
https://github.com/codyroux/traat-lean.git | f2babab84f81d4003446f476790022ac175d7236 | Traat/chapter1.lean | weakly_confluent_does_not_imply_confluent | [532, 1] | [582, 20] | repeat constructor | case left.inl.inl
A : Type
R : A → A → Prop
inhabited_A : Nonempty A
x y z : X
h✝¹ : y = X.a
h✝ : z = X.a
⊢ refl_trans_clos (fun x y => x = X.b ∧ y = X.a ∨ x = X.b ∧ y = X.c ∨ x = X.c ∧ y = X.b ∨ x = X.c ∧ y = X.d) X.a X.a ∧
refl_trans_clos (fun x y => x = X.b ∧ y = X.a ∨ x = X.b ∧ y = X.c ∨ x = X.c ∧ y = X.b ∨ x =... | no goals |
https://github.com/codyroux/traat-lean.git | f2babab84f81d4003446f476790022ac175d7236 | Traat/chapter1.lean | weakly_confluent_does_not_imply_confluent | [532, 1] | [582, 20] | constructor | case left.inl.inl.right
A : Type
R : A → A → Prop
inhabited_A : Nonempty A
x y z : X
h✝¹ : y = X.a
h✝ : z = X.a
⊢ refl_trans_clos (fun x y => x = X.b ∧ y = X.a ∨ x = X.b ∧ y = X.c ∨ x = X.c ∧ y = X.b ∨ x = X.c ∧ y = X.d) X.a X.a | no goals |
https://github.com/codyroux/traat-lean.git | f2babab84f81d4003446f476790022ac175d7236 | Traat/chapter1.lean | weakly_confluent_does_not_imply_confluent | [532, 1] | [582, 20] | exists X.a | case left.inl.inr
A : Type
R : A → A → Prop
inhabited_A : Nonempty A
x y z : X
h✝¹ : x = X.b ∧ y = X.a
h✝ : z = X.c
⊢ joins (fun x y => x = X.b ∧ y = X.a ∨ x = X.b ∧ y = X.c ∨ x = X.c ∧ y = X.b ∨ x = X.c ∧ y = X.d) X.a z | case left.inl.inr
A : Type
R : A → A → Prop
inhabited_A : Nonempty A
x y z : X
h✝¹ : x = X.b ∧ y = X.a
h✝ : z = X.c
⊢ refl_trans_clos (fun x y => x = X.b ∧ y = X.a ∨ x = X.b ∧ y = X.c ∨ x = X.c ∧ y = X.b ∨ x = X.c ∧ y = X.d) X.a X.a ∧
refl_trans_clos (fun x y => x = X.b ∧ y = X.a ∨ x = X.b ∧ y = X.c ∨ x = X.c ∧ y =... |
https://github.com/codyroux/traat-lean.git | f2babab84f81d4003446f476790022ac175d7236 | Traat/chapter1.lean | weakly_confluent_does_not_imply_confluent | [532, 1] | [582, 20] | try constructor | case left.inl.inr
A : Type
R : A → A → Prop
inhabited_A : Nonempty A
x y z : X
h✝¹ : x = X.b ∧ y = X.a
h✝ : z = X.c
⊢ refl_trans_clos (fun x y => x = X.b ∧ y = X.a ∨ x = X.b ∧ y = X.c ∨ x = X.c ∧ y = X.b ∨ x = X.c ∧ y = X.d) X.a X.a ∧
refl_trans_clos (fun x y => x = X.b ∧ y = X.a ∨ x = X.b ∧ y = X.c ∨ x = X.c ∧ y =... | case left.inl.inr.left
A : Type
R : A → A → Prop
inhabited_A : Nonempty A
x y z : X
h✝¹ : x = X.b ∧ y = X.a
h✝ : z = X.c
⊢ refl_trans_clos (fun x y => x = X.b ∧ y = X.a ∨ x = X.b ∧ y = X.c ∨ x = X.c ∧ y = X.b ∨ x = X.c ∧ y = X.d) X.a X.a
case left.inl.inr.right
A : Type
R : A → A → Prop
inhabited_A : Nonempty A
x y z ... |
https://github.com/codyroux/traat-lean.git | f2babab84f81d4003446f476790022ac175d7236 | Traat/chapter1.lean | weakly_confluent_does_not_imply_confluent | [532, 1] | [582, 20] | . constructor | case left.inl.inr.left
A : Type
R : A → A → Prop
inhabited_A : Nonempty A
x y z : X
h✝¹ : x = X.b ∧ y = X.a
h✝ : z = X.c
⊢ refl_trans_clos (fun x y => x = X.b ∧ y = X.a ∨ x = X.b ∧ y = X.c ∨ x = X.c ∧ y = X.b ∨ x = X.c ∧ y = X.d) X.a X.a
case left.inl.inr.right
A : Type
R : A → A → Prop
inhabited_A : Nonempty A
x y z ... | case left.inl.inr.right
A : Type
R : A → A → Prop
inhabited_A : Nonempty A
x y z : X
h✝¹ : x = X.b ∧ y = X.a
h✝ : z = X.c
⊢ refl_trans_clos (fun x y => x = X.b ∧ y = X.a ∨ x = X.b ∧ y = X.c ∨ x = X.c ∧ y = X.b ∨ x = X.c ∧ y = X.d) z X.a |
https://github.com/codyroux/traat-lean.git | f2babab84f81d4003446f476790022ac175d7236 | Traat/chapter1.lean | weakly_confluent_does_not_imply_confluent | [532, 1] | [582, 20] | . simp [*]; constructor; simp [RX]
. left; trivial
. constructor; simp [RX]; left; trivial; constructor | case left.inl.inr.right
A : Type
R : A → A → Prop
inhabited_A : Nonempty A
x y z : X
h✝¹ : x = X.b ∧ y = X.a
h✝ : z = X.c
⊢ refl_trans_clos (fun x y => x = X.b ∧ y = X.a ∨ x = X.b ∧ y = X.c ∨ x = X.c ∧ y = X.b ∨ x = X.c ∧ y = X.d) z X.a | no goals |
https://github.com/codyroux/traat-lean.git | f2babab84f81d4003446f476790022ac175d7236 | Traat/chapter1.lean | weakly_confluent_does_not_imply_confluent | [532, 1] | [582, 20] | constructor | case left.inl.inr
A : Type
R : A → A → Prop
inhabited_A : Nonempty A
x y z : X
h✝¹ : x = X.b ∧ y = X.a
h✝ : z = X.c
⊢ refl_trans_clos (fun x y => x = X.b ∧ y = X.a ∨ x = X.b ∧ y = X.c ∨ x = X.c ∧ y = X.b ∨ x = X.c ∧ y = X.d) X.a X.a ∧
refl_trans_clos (fun x y => x = X.b ∧ y = X.a ∨ x = X.b ∧ y = X.c ∨ x = X.c ∧ y =... | case left.inl.inr.left
A : Type
R : A → A → Prop
inhabited_A : Nonempty A
x y z : X
h✝¹ : x = X.b ∧ y = X.a
h✝ : z = X.c
⊢ refl_trans_clos (fun x y => x = X.b ∧ y = X.a ∨ x = X.b ∧ y = X.c ∨ x = X.c ∧ y = X.b ∨ x = X.c ∧ y = X.d) X.a X.a
case left.inl.inr.right
A : Type
R : A → A → Prop
inhabited_A : Nonempty A
x y z ... |
https://github.com/codyroux/traat-lean.git | f2babab84f81d4003446f476790022ac175d7236 | Traat/chapter1.lean | weakly_confluent_does_not_imply_confluent | [532, 1] | [582, 20] | constructor | case left.inl.inr.left
A : Type
R : A → A → Prop
inhabited_A : Nonempty A
x y z : X
h✝¹ : x = X.b ∧ y = X.a
h✝ : z = X.c
⊢ refl_trans_clos (fun x y => x = X.b ∧ y = X.a ∨ x = X.b ∧ y = X.c ∨ x = X.c ∧ y = X.b ∨ x = X.c ∧ y = X.d) X.a X.a | no goals |
https://github.com/codyroux/traat-lean.git | f2babab84f81d4003446f476790022ac175d7236 | Traat/chapter1.lean | weakly_confluent_does_not_imply_confluent | [532, 1] | [582, 20] | simp [*] | case left.inl.inr.right
A : Type
R : A → A → Prop
inhabited_A : Nonempty A
x y z : X
h✝¹ : x = X.b ∧ y = X.a
h✝ : z = X.c
⊢ refl_trans_clos (fun x y => x = X.b ∧ y = X.a ∨ x = X.b ∧ y = X.c ∨ x = X.c ∧ y = X.b ∨ x = X.c ∧ y = X.d) z X.a | case left.inl.inr.right
A : Type
R : A → A → Prop
inhabited_A : Nonempty A
x y z : X
h✝¹ : x = X.b ∧ y = X.a
h✝ : z = X.c
⊢ refl_trans_clos (fun x y => x = X.b ∧ y = X.a ∨ x = X.b ∧ y = X.c ∨ x = X.c ∧ y = X.b ∨ x = X.c ∧ y = X.d) X.c X.a |
https://github.com/codyroux/traat-lean.git | f2babab84f81d4003446f476790022ac175d7236 | Traat/chapter1.lean | weakly_confluent_does_not_imply_confluent | [532, 1] | [582, 20] | constructor | case left.inl.inr.right
A : Type
R : A → A → Prop
inhabited_A : Nonempty A
x y z : X
h✝¹ : x = X.b ∧ y = X.a
h✝ : z = X.c
⊢ refl_trans_clos (fun x y => x = X.b ∧ y = X.a ∨ x = X.b ∧ y = X.c ∨ x = X.c ∧ y = X.b ∨ x = X.c ∧ y = X.d) X.c X.a | case left.inl.inr.right.a
A : Type
R : A → A → Prop
inhabited_A : Nonempty A
x y z : X
h✝¹ : x = X.b ∧ y = X.a
h✝ : z = X.c
⊢ X.c = X.b ∧ ?left.inl.inr.right.b = X.a ∨
X.c = X.b ∧ ?left.inl.inr.right.b = X.c ∨
X.c = X.c ∧ ?left.inl.inr.right.b = X.b ∨ X.c = X.c ∧ ?left.inl.inr.right.b = X.d
case left.inl.inr... |
https://github.com/codyroux/traat-lean.git | f2babab84f81d4003446f476790022ac175d7236 | Traat/chapter1.lean | weakly_confluent_does_not_imply_confluent | [532, 1] | [582, 20] | simp [RX] | case left.inl.inr.right.a
A : Type
R : A → A → Prop
inhabited_A : Nonempty A
x y z : X
h✝¹ : x = X.b ∧ y = X.a
h✝ : z = X.c
⊢ X.c = X.b ∧ ?left.inl.inr.right.b = X.a ∨
X.c = X.b ∧ ?left.inl.inr.right.b = X.c ∨
X.c = X.c ∧ ?left.inl.inr.right.b = X.b ∨ X.c = X.c ∧ ?left.inl.inr.right.b = X.d
case left.inl.inr... | case left.inl.inr.right.a
A : Type
R : A → A → Prop
inhabited_A : Nonempty A
x y z : X
h✝¹ : x = X.b ∧ y = X.a
h✝ : z = X.c
⊢ ?left.inl.inr.right.b = X.b ∨ ?left.inl.inr.right.b = X.d
case left.inl.inr.right.a
A : Type
R : A → A → Prop
inhabited_A : Nonempty A
x y z : X
h✝¹ : x = X.b ∧ y = X.a
h✝ : z = X.c
⊢ refl_tran... |
https://github.com/codyroux/traat-lean.git | f2babab84f81d4003446f476790022ac175d7236 | Traat/chapter1.lean | weakly_confluent_does_not_imply_confluent | [532, 1] | [582, 20] | . left; trivial | case left.inl.inr.right.a
A : Type
R : A → A → Prop
inhabited_A : Nonempty A
x y z : X
h✝¹ : x = X.b ∧ y = X.a
h✝ : z = X.c
⊢ ?left.inl.inr.right.b = X.b ∨ ?left.inl.inr.right.b = X.d
case left.inl.inr.right.a
A : Type
R : A → A → Prop
inhabited_A : Nonempty A
x y z : X
h✝¹ : x = X.b ∧ y = X.a
h✝ : z = X.c
⊢ refl_tran... | case left.inl.inr.right.a
A : Type
R : A → A → Prop
inhabited_A : Nonempty A
x y z : X
h✝¹ : x = X.b ∧ y = X.a
h✝ : z = X.c
⊢ refl_trans_clos (fun x y => x = X.b ∧ y = X.a ∨ x = X.b ∧ y = X.c ∨ x = X.c ∧ y = X.b ∨ x = X.c ∧ y = X.d) X.b X.a |
https://github.com/codyroux/traat-lean.git | f2babab84f81d4003446f476790022ac175d7236 | Traat/chapter1.lean | weakly_confluent_does_not_imply_confluent | [532, 1] | [582, 20] | . constructor; simp [RX]; left; trivial; constructor | case left.inl.inr.right.a
A : Type
R : A → A → Prop
inhabited_A : Nonempty A
x y z : X
h✝¹ : x = X.b ∧ y = X.a
h✝ : z = X.c
⊢ refl_trans_clos (fun x y => x = X.b ∧ y = X.a ∨ x = X.b ∧ y = X.c ∨ x = X.c ∧ y = X.b ∨ x = X.c ∧ y = X.d) X.b X.a | no goals |
https://github.com/codyroux/traat-lean.git | f2babab84f81d4003446f476790022ac175d7236 | Traat/chapter1.lean | weakly_confluent_does_not_imply_confluent | [532, 1] | [582, 20] | left | case left.inl.inr.right.a
A : Type
R : A → A → Prop
inhabited_A : Nonempty A
x y z : X
h✝¹ : x = X.b ∧ y = X.a
h✝ : z = X.c
⊢ ?left.inl.inr.right.b = X.b ∨ ?left.inl.inr.right.b = X.d | case left.inl.inr.right.a.h
A : Type
R : A → A → Prop
inhabited_A : Nonempty A
x y z : X
h✝¹ : x = X.b ∧ y = X.a
h✝ : z = X.c
⊢ ?left.inl.inr.right.b = X.b |
https://github.com/codyroux/traat-lean.git | f2babab84f81d4003446f476790022ac175d7236 | Traat/chapter1.lean | weakly_confluent_does_not_imply_confluent | [532, 1] | [582, 20] | trivial | case left.inl.inr.right.a.h
A : Type
R : A → A → Prop
inhabited_A : Nonempty A
x y z : X
h✝¹ : x = X.b ∧ y = X.a
h✝ : z = X.c
⊢ ?left.inl.inr.right.b = X.b | no goals |
https://github.com/codyroux/traat-lean.git | f2babab84f81d4003446f476790022ac175d7236 | Traat/chapter1.lean | weakly_confluent_does_not_imply_confluent | [532, 1] | [582, 20] | constructor | case left.inl.inr.right.a
A : Type
R : A → A → Prop
inhabited_A : Nonempty A
x y z : X
h✝¹ : x = X.b ∧ y = X.a
h✝ : z = X.c
⊢ refl_trans_clos (fun x y => x = X.b ∧ y = X.a ∨ x = X.b ∧ y = X.c ∨ x = X.c ∧ y = X.b ∨ x = X.c ∧ y = X.d) X.b X.a | case left.inl.inr.right.a.a
A : Type
R : A → A → Prop
inhabited_A : Nonempty A
x y z : X
h✝¹ : x = X.b ∧ y = X.a
h✝ : z = X.c
⊢ X.b = X.b ∧ ?left.inl.inr.right.a.b = X.a ∨
X.b = X.b ∧ ?left.inl.inr.right.a.b = X.c ∨
X.b = X.c ∧ ?left.inl.inr.right.a.b = X.b ∨ X.b = X.c ∧ ?left.inl.inr.right.a.b = X.d
case le... |
https://github.com/codyroux/traat-lean.git | f2babab84f81d4003446f476790022ac175d7236 | Traat/chapter1.lean | weakly_confluent_does_not_imply_confluent | [532, 1] | [582, 20] | simp [RX] | case left.inl.inr.right.a.a
A : Type
R : A → A → Prop
inhabited_A : Nonempty A
x y z : X
h✝¹ : x = X.b ∧ y = X.a
h✝ : z = X.c
⊢ X.b = X.b ∧ ?left.inl.inr.right.a.b = X.a ∨
X.b = X.b ∧ ?left.inl.inr.right.a.b = X.c ∨
X.b = X.c ∧ ?left.inl.inr.right.a.b = X.b ∨ X.b = X.c ∧ ?left.inl.inr.right.a.b = X.d
case le... | case left.inl.inr.right.a.a
A : Type
R : A → A → Prop
inhabited_A : Nonempty A
x y z : X
h✝¹ : x = X.b ∧ y = X.a
h✝ : z = X.c
⊢ ?left.inl.inr.right.a.b = X.a ∨ ?left.inl.inr.right.a.b = X.c
case left.inl.inr.right.a.a
A : Type
R : A → A → Prop
inhabited_A : Nonempty A
x y z : X
h✝¹ : x = X.b ∧ y = X.a
h✝ : z = X.c
⊢ r... |
https://github.com/codyroux/traat-lean.git | f2babab84f81d4003446f476790022ac175d7236 | Traat/chapter1.lean | weakly_confluent_does_not_imply_confluent | [532, 1] | [582, 20] | left | case left.inl.inr.right.a.a
A : Type
R : A → A → Prop
inhabited_A : Nonempty A
x y z : X
h✝¹ : x = X.b ∧ y = X.a
h✝ : z = X.c
⊢ ?left.inl.inr.right.a.b = X.a ∨ ?left.inl.inr.right.a.b = X.c
case left.inl.inr.right.a.a
A : Type
R : A → A → Prop
inhabited_A : Nonempty A
x y z : X
h✝¹ : x = X.b ∧ y = X.a
h✝ : z = X.c
⊢ r... | case left.inl.inr.right.a.a.h
A : Type
R : A → A → Prop
inhabited_A : Nonempty A
x y z : X
h✝¹ : x = X.b ∧ y = X.a
h✝ : z = X.c
⊢ ?left.inl.inr.right.a.b = X.a
case left.inl.inr.right.a.a
A : Type
R : A → A → Prop
inhabited_A : Nonempty A
x y z : X
h✝¹ : x = X.b ∧ y = X.a
h✝ : z = X.c
⊢ refl_trans_clos (fun x y => x =... |
https://github.com/codyroux/traat-lean.git | f2babab84f81d4003446f476790022ac175d7236 | Traat/chapter1.lean | weakly_confluent_does_not_imply_confluent | [532, 1] | [582, 20] | trivial | case left.inl.inr.right.a.a.h
A : Type
R : A → A → Prop
inhabited_A : Nonempty A
x y z : X
h✝¹ : x = X.b ∧ y = X.a
h✝ : z = X.c
⊢ ?left.inl.inr.right.a.b = X.a
case left.inl.inr.right.a.a
A : Type
R : A → A → Prop
inhabited_A : Nonempty A
x y z : X
h✝¹ : x = X.b ∧ y = X.a
h✝ : z = X.c
⊢ refl_trans_clos (fun x y => x =... | case left.inl.inr.right.a.a
A : Type
R : A → A → Prop
inhabited_A : Nonempty A
x y z : X
h✝¹ : x = X.b ∧ y = X.a
h✝ : z = X.c
⊢ refl_trans_clos (fun x y => x = X.b ∧ y = X.a ∨ x = X.b ∧ y = X.c ∨ x = X.c ∧ y = X.b ∨ x = X.c ∧ y = X.d) X.a X.a |
https://github.com/codyroux/traat-lean.git | f2babab84f81d4003446f476790022ac175d7236 | Traat/chapter1.lean | weakly_confluent_does_not_imply_confluent | [532, 1] | [582, 20] | constructor | case left.inl.inr.right.a.a
A : Type
R : A → A → Prop
inhabited_A : Nonempty A
x y z : X
h✝¹ : x = X.b ∧ y = X.a
h✝ : z = X.c
⊢ refl_trans_clos (fun x y => x = X.b ∧ y = X.a ∨ x = X.b ∧ y = X.c ∨ x = X.c ∧ y = X.b ∨ x = X.c ∧ y = X.d) X.a X.a | no goals |
https://github.com/codyroux/traat-lean.git | f2babab84f81d4003446f476790022ac175d7236 | Traat/chapter1.lean | weakly_confluent_does_not_imply_confluent | [532, 1] | [582, 20] | exists X.a | case left.inr.inl
A : Type
R : A → A → Prop
inhabited_A : Nonempty A
x y z : X
h✝¹ : x = X.b ∧ z = X.a
h✝ : y = X.c
⊢ joins (fun x y => x = X.b ∧ y = X.a ∨ x = X.b ∧ y = X.c ∨ x = X.c ∧ y = X.b ∨ x = X.c ∧ y = X.d) y X.a | case left.inr.inl
A : Type
R : A → A → Prop
inhabited_A : Nonempty A
x y z : X
h✝¹ : x = X.b ∧ z = X.a
h✝ : y = X.c
⊢ refl_trans_clos (fun x y => x = X.b ∧ y = X.a ∨ x = X.b ∧ y = X.c ∨ x = X.c ∧ y = X.b ∨ x = X.c ∧ y = X.d) y X.a ∧
refl_trans_clos (fun x y => x = X.b ∧ y = X.a ∨ x = X.b ∧ y = X.c ∨ x = X.c ∧ y = X... |
https://github.com/codyroux/traat-lean.git | f2babab84f81d4003446f476790022ac175d7236 | Traat/chapter1.lean | weakly_confluent_does_not_imply_confluent | [532, 1] | [582, 20] | simp [*] | case left.inr.inl
A : Type
R : A → A → Prop
inhabited_A : Nonempty A
x y z : X
h✝¹ : x = X.b ∧ z = X.a
h✝ : y = X.c
⊢ refl_trans_clos (fun x y => x = X.b ∧ y = X.a ∨ x = X.b ∧ y = X.c ∨ x = X.c ∧ y = X.b ∨ x = X.c ∧ y = X.d) y X.a ∧
refl_trans_clos (fun x y => x = X.b ∧ y = X.a ∨ x = X.b ∧ y = X.c ∨ x = X.c ∧ y = X... | case left.inr.inl
A : Type
R : A → A → Prop
inhabited_A : Nonempty A
x y z : X
h✝¹ : x = X.b ∧ z = X.a
h✝ : y = X.c
⊢ refl_trans_clos (fun x y => x = X.b ∧ y = X.a ∨ x = X.b ∧ y = X.c ∨ x = X.c ∧ y = X.b ∨ x = X.c ∧ y = X.d) X.c X.a ∧
refl_trans_clos (fun x y => x = X.b ∧ y = X.a ∨ x = X.b ∧ y = X.c ∨ x = X.c ∧ y =... |
https://github.com/codyroux/traat-lean.git | f2babab84f81d4003446f476790022ac175d7236 | Traat/chapter1.lean | weakly_confluent_does_not_imply_confluent | [532, 1] | [582, 20] | constructor | case left.inr.inl
A : Type
R : A → A → Prop
inhabited_A : Nonempty A
x y z : X
h✝¹ : x = X.b ∧ z = X.a
h✝ : y = X.c
⊢ refl_trans_clos (fun x y => x = X.b ∧ y = X.a ∨ x = X.b ∧ y = X.c ∨ x = X.c ∧ y = X.b ∨ x = X.c ∧ y = X.d) X.c X.a ∧
refl_trans_clos (fun x y => x = X.b ∧ y = X.a ∨ x = X.b ∧ y = X.c ∨ x = X.c ∧ y =... | case left.inr.inl.left
A : Type
R : A → A → Prop
inhabited_A : Nonempty A
x y z : X
h✝¹ : x = X.b ∧ z = X.a
h✝ : y = X.c
⊢ refl_trans_clos (fun x y => x = X.b ∧ y = X.a ∨ x = X.b ∧ y = X.c ∨ x = X.c ∧ y = X.b ∨ x = X.c ∧ y = X.d) X.c X.a
case left.inr.inl.right
A : Type
R : A → A → Prop
inhabited_A : Nonempty A
x y z ... |
https://github.com/codyroux/traat-lean.git | f2babab84f81d4003446f476790022ac175d7236 | Traat/chapter1.lean | weakly_confluent_does_not_imply_confluent | [532, 1] | [582, 20] | . repeat (constructor; simp [RX]; left; trivial)
constructor | case left.inr.inl.left
A : Type
R : A → A → Prop
inhabited_A : Nonempty A
x y z : X
h✝¹ : x = X.b ∧ z = X.a
h✝ : y = X.c
⊢ refl_trans_clos (fun x y => x = X.b ∧ y = X.a ∨ x = X.b ∧ y = X.c ∨ x = X.c ∧ y = X.b ∨ x = X.c ∧ y = X.d) X.c X.a
case left.inr.inl.right
A : Type
R : A → A → Prop
inhabited_A : Nonempty A
x y z ... | case left.inr.inl.right
A : Type
R : A → A → Prop
inhabited_A : Nonempty A
x y z : X
h✝¹ : x = X.b ∧ z = X.a
h✝ : y = X.c
⊢ refl_trans_clos (fun x y => x = X.b ∧ y = X.a ∨ x = X.b ∧ y = X.c ∨ x = X.c ∧ y = X.b ∨ x = X.c ∧ y = X.d) X.a X.a |
https://github.com/codyroux/traat-lean.git | f2babab84f81d4003446f476790022ac175d7236 | Traat/chapter1.lean | weakly_confluent_does_not_imply_confluent | [532, 1] | [582, 20] | . constructor | case left.inr.inl.right
A : Type
R : A → A → Prop
inhabited_A : Nonempty A
x y z : X
h✝¹ : x = X.b ∧ z = X.a
h✝ : y = X.c
⊢ refl_trans_clos (fun x y => x = X.b ∧ y = X.a ∨ x = X.b ∧ y = X.c ∨ x = X.c ∧ y = X.b ∨ x = X.c ∧ y = X.d) X.a X.a | no goals |
https://github.com/codyroux/traat-lean.git | f2babab84f81d4003446f476790022ac175d7236 | Traat/chapter1.lean | weakly_confluent_does_not_imply_confluent | [532, 1] | [582, 20] | repeat (constructor; simp [RX]; left; trivial) | case left.inr.inl.left
A : Type
R : A → A → Prop
inhabited_A : Nonempty A
x y z : X
h✝¹ : x = X.b ∧ z = X.a
h✝ : y = X.c
⊢ refl_trans_clos (fun x y => x = X.b ∧ y = X.a ∨ x = X.b ∧ y = X.c ∨ x = X.c ∧ y = X.b ∨ x = X.c ∧ y = X.d) X.c X.a | case left.inr.inl.left.a.a
A : Type
R : A → A → Prop
inhabited_A : Nonempty A
x y z : X
h✝¹ : x = X.b ∧ z = X.a
h✝ : y = X.c
⊢ refl_trans_clos (fun x y => x = X.b ∧ y = X.a ∨ x = X.b ∧ y = X.c ∨ x = X.c ∧ y = X.b ∨ x = X.c ∧ y = X.d) X.a X.a |
https://github.com/codyroux/traat-lean.git | f2babab84f81d4003446f476790022ac175d7236 | Traat/chapter1.lean | weakly_confluent_does_not_imply_confluent | [532, 1] | [582, 20] | constructor | case left.inr.inl.left.a.a
A : Type
R : A → A → Prop
inhabited_A : Nonempty A
x y z : X
h✝¹ : x = X.b ∧ z = X.a
h✝ : y = X.c
⊢ refl_trans_clos (fun x y => x = X.b ∧ y = X.a ∨ x = X.b ∧ y = X.c ∨ x = X.c ∧ y = X.b ∨ x = X.c ∧ y = X.d) X.a X.a | no goals |
https://github.com/codyroux/traat-lean.git | f2babab84f81d4003446f476790022ac175d7236 | Traat/chapter1.lean | weakly_confluent_does_not_imply_confluent | [532, 1] | [582, 20] | (constructor; simp [RX]; left; trivial) | case left.inr.inl.left.a.a
A : Type
R : A → A → Prop
inhabited_A : Nonempty A
x y z : X
h✝¹ : x = X.b ∧ z = X.a
h✝ : y = X.c
⊢ refl_trans_clos (fun x y => x = X.b ∧ y = X.a ∨ x = X.b ∧ y = X.c ∨ x = X.c ∧ y = X.b ∨ x = X.c ∧ y = X.d) X.a X.a | no goals |
https://github.com/codyroux/traat-lean.git | f2babab84f81d4003446f476790022ac175d7236 | Traat/chapter1.lean | weakly_confluent_does_not_imply_confluent | [532, 1] | [582, 20] | simp [RX] | case left.inr.inl.left.a.a
A : Type
R : A → A → Prop
inhabited_A : Nonempty A
x y z : X
h✝¹ : x = X.b ∧ z = X.a
h✝ : y = X.c
⊢ X.b = X.b ∧ ?left.inr.inl.left.a.b = X.a ∨
X.b = X.b ∧ ?left.inr.inl.left.a.b = X.c ∨
X.b = X.c ∧ ?left.inr.inl.left.a.b = X.b ∨ X.b = X.c ∧ ?left.inr.inl.left.a.b = X.d
case left.in... | case left.inr.inl.left.a.a
A : Type
R : A → A → Prop
inhabited_A : Nonempty A
x y z : X
h✝¹ : x = X.b ∧ z = X.a
h✝ : y = X.c
⊢ ?left.inr.inl.left.a.b = X.a ∨ ?left.inr.inl.left.a.b = X.c
case left.inr.inl.left.a.a
A : Type
R : A → A → Prop
inhabited_A : Nonempty A
x y z : X
h✝¹ : x = X.b ∧ z = X.a
h✝ : y = X.c
⊢ refl_... |
https://github.com/codyroux/traat-lean.git | f2babab84f81d4003446f476790022ac175d7236 | Traat/chapter1.lean | weakly_confluent_does_not_imply_confluent | [532, 1] | [582, 20] | left | case left.inr.inl.left.a.a
A : Type
R : A → A → Prop
inhabited_A : Nonempty A
x y z : X
h✝¹ : x = X.b ∧ z = X.a
h✝ : y = X.c
⊢ ?left.inr.inl.left.a.b = X.a ∨ ?left.inr.inl.left.a.b = X.c
case left.inr.inl.left.a.a
A : Type
R : A → A → Prop
inhabited_A : Nonempty A
x y z : X
h✝¹ : x = X.b ∧ z = X.a
h✝ : y = X.c
⊢ refl_... | case left.inr.inl.left.a.a.h
A : Type
R : A → A → Prop
inhabited_A : Nonempty A
x y z : X
h✝¹ : x = X.b ∧ z = X.a
h✝ : y = X.c
⊢ ?left.inr.inl.left.a.b = X.a
case left.inr.inl.left.a.a
A : Type
R : A → A → Prop
inhabited_A : Nonempty A
x y z : X
h✝¹ : x = X.b ∧ z = X.a
h✝ : y = X.c
⊢ refl_trans_clos (fun x y => x = X.... |
https://github.com/codyroux/traat-lean.git | f2babab84f81d4003446f476790022ac175d7236 | Traat/chapter1.lean | weakly_confluent_does_not_imply_confluent | [532, 1] | [582, 20] | trivial | case left.inr.inl.left.a.a.h
A : Type
R : A → A → Prop
inhabited_A : Nonempty A
x y z : X
h✝¹ : x = X.b ∧ z = X.a
h✝ : y = X.c
⊢ ?left.inr.inl.left.a.b = X.a
case left.inr.inl.left.a.a
A : Type
R : A → A → Prop
inhabited_A : Nonempty A
x y z : X
h✝¹ : x = X.b ∧ z = X.a
h✝ : y = X.c
⊢ refl_trans_clos (fun x y => x = X.... | case left.inr.inl.left.a.a
A : Type
R : A → A → Prop
inhabited_A : Nonempty A
x y z : X
h✝¹ : x = X.b ∧ z = X.a
h✝ : y = X.c
⊢ refl_trans_clos (fun x y => x = X.b ∧ y = X.a ∨ x = X.b ∧ y = X.c ∨ x = X.c ∧ y = X.b ∨ x = X.c ∧ y = X.d) X.a X.a |
https://github.com/codyroux/traat-lean.git | f2babab84f81d4003446f476790022ac175d7236 | Traat/chapter1.lean | weakly_confluent_does_not_imply_confluent | [532, 1] | [582, 20] | constructor | case left.inr.inl.right
A : Type
R : A → A → Prop
inhabited_A : Nonempty A
x y z : X
h✝¹ : x = X.b ∧ z = X.a
h✝ : y = X.c
⊢ refl_trans_clos (fun x y => x = X.b ∧ y = X.a ∨ x = X.b ∧ y = X.c ∨ x = X.c ∧ y = X.b ∨ x = X.c ∧ y = X.d) X.a X.a | no goals |
https://github.com/codyroux/traat-lean.git | f2babab84f81d4003446f476790022ac175d7236 | Traat/chapter1.lean | weakly_confluent_does_not_imply_confluent | [532, 1] | [582, 20] | case inr h1 h2 =>
cases h1 <;> cases h2 <;> simp [*] at *
. exists X.c; repeat constructor
. case inr h1 h2 =>
cases h1 <;> cases h2 <;> simp [*] at *
. exists X.b; repeat constructor
. exists X.d; constructor
. constructor; simp [RX]; right; trivial
constructor; simp [RX]; right; trivial
construc... | A : Type
R : A → A → Prop
inhabited_A : Nonempty A
x y z : X
h1 : x = X.b ∧ y = X.c ∨ x = X.c ∧ y = X.b ∨ x = X.c ∧ y = X.d
h2 : x = X.b ∧ z = X.c ∨ x = X.c ∧ z = X.b ∨ x = X.c ∧ z = X.d
⊢ joins (fun x y => x = X.b ∧ y = X.a ∨ x = X.b ∧ y = X.c ∨ x = X.c ∧ y = X.b ∨ x = X.c ∧ y = X.d) y z | no goals |
https://github.com/codyroux/traat-lean.git | f2babab84f81d4003446f476790022ac175d7236 | Traat/chapter1.lean | weakly_confluent_does_not_imply_confluent | [532, 1] | [582, 20] | cases h1 <;> cases h2 <;> simp [*] at * | A : Type
R : A → A → Prop
inhabited_A : Nonempty A
x y z : X
h1 : x = X.b ∧ y = X.c ∨ x = X.c ∧ y = X.b ∨ x = X.c ∧ y = X.d
h2 : x = X.b ∧ z = X.c ∨ x = X.c ∧ z = X.b ∨ x = X.c ∧ z = X.d
⊢ joins (fun x y => x = X.b ∧ y = X.a ∨ x = X.b ∧ y = X.c ∨ x = X.c ∧ y = X.b ∨ x = X.c ∧ y = X.d) y z | case inl.inl
A : Type
R : A → A → Prop
inhabited_A : Nonempty A
x y z : X
h✝¹ : y = X.c
h✝ : z = X.c
⊢ joins (fun x y => x = X.b ∧ y = X.a ∨ x = X.b ∧ y = X.c ∨ x = X.c ∧ y = X.b ∨ x = X.c ∧ y = X.d) X.c X.c
case inr.inr
A : Type
R : A → A → Prop
inhabited_A : Nonempty A
x y z : X
h✝¹ : x = X.c ∧ y = X.b ∨ x = X.c ∧ y... |
https://github.com/codyroux/traat-lean.git | f2babab84f81d4003446f476790022ac175d7236 | Traat/chapter1.lean | weakly_confluent_does_not_imply_confluent | [532, 1] | [582, 20] | . exists X.c; repeat constructor | case inl.inl
A : Type
R : A → A → Prop
inhabited_A : Nonempty A
x y z : X
h✝¹ : y = X.c
h✝ : z = X.c
⊢ joins (fun x y => x = X.b ∧ y = X.a ∨ x = X.b ∧ y = X.c ∨ x = X.c ∧ y = X.b ∨ x = X.c ∧ y = X.d) X.c X.c
case inr.inr
A : Type
R : A → A → Prop
inhabited_A : Nonempty A
x y z : X
h✝¹ : x = X.c ∧ y = X.b ∨ x = X.c ∧ y... | case inr.inr
A : Type
R : A → A → Prop
inhabited_A : Nonempty A
x y z : X
h✝¹ : x = X.c ∧ y = X.b ∨ x = X.c ∧ y = X.d
h✝ : x = X.c ∧ z = X.b ∨ x = X.c ∧ z = X.d
⊢ joins (fun x y => x = X.b ∧ y = X.a ∨ x = X.b ∧ y = X.c ∨ x = X.c ∧ y = X.b ∨ x = X.c ∧ y = X.d) y z |
https://github.com/codyroux/traat-lean.git | f2babab84f81d4003446f476790022ac175d7236 | Traat/chapter1.lean | weakly_confluent_does_not_imply_confluent | [532, 1] | [582, 20] | . case inr h1 h2 =>
cases h1 <;> cases h2 <;> simp [*] at *
. exists X.b; repeat constructor
. exists X.d; constructor
. constructor; simp [RX]; right; trivial
constructor; simp [RX]; right; trivial
constructor
. constructor
. exists X.d; constructor
. constructor
. constructor; simp... | case inr.inr
A : Type
R : A → A → Prop
inhabited_A : Nonempty A
x y z : X
h✝¹ : x = X.c ∧ y = X.b ∨ x = X.c ∧ y = X.d
h✝ : x = X.c ∧ z = X.b ∨ x = X.c ∧ z = X.d
⊢ joins (fun x y => x = X.b ∧ y = X.a ∨ x = X.b ∧ y = X.c ∨ x = X.c ∧ y = X.b ∨ x = X.c ∧ y = X.d) y z | no goals |
https://github.com/codyroux/traat-lean.git | f2babab84f81d4003446f476790022ac175d7236 | Traat/chapter1.lean | weakly_confluent_does_not_imply_confluent | [532, 1] | [582, 20] | exists X.c | case inl.inl
A : Type
R : A → A → Prop
inhabited_A : Nonempty A
x y z : X
h✝¹ : y = X.c
h✝ : z = X.c
⊢ joins (fun x y => x = X.b ∧ y = X.a ∨ x = X.b ∧ y = X.c ∨ x = X.c ∧ y = X.b ∨ x = X.c ∧ y = X.d) X.c X.c | case inl.inl
A : Type
R : A → A → Prop
inhabited_A : Nonempty A
x y z : X
h✝¹ : y = X.c
h✝ : z = X.c
⊢ refl_trans_clos (fun x y => x = X.b ∧ y = X.a ∨ x = X.b ∧ y = X.c ∨ x = X.c ∧ y = X.b ∨ x = X.c ∧ y = X.d) X.c X.c ∧
refl_trans_clos (fun x y => x = X.b ∧ y = X.a ∨ x = X.b ∧ y = X.c ∨ x = X.c ∧ y = X.b ∨ x = X.c ... |
https://github.com/codyroux/traat-lean.git | f2babab84f81d4003446f476790022ac175d7236 | Traat/chapter1.lean | weakly_confluent_does_not_imply_confluent | [532, 1] | [582, 20] | repeat constructor | case inl.inl
A : Type
R : A → A → Prop
inhabited_A : Nonempty A
x y z : X
h✝¹ : y = X.c
h✝ : z = X.c
⊢ refl_trans_clos (fun x y => x = X.b ∧ y = X.a ∨ x = X.b ∧ y = X.c ∨ x = X.c ∧ y = X.b ∨ x = X.c ∧ y = X.d) X.c X.c ∧
refl_trans_clos (fun x y => x = X.b ∧ y = X.a ∨ x = X.b ∧ y = X.c ∨ x = X.c ∧ y = X.b ∨ x = X.c ... | no goals |
https://github.com/codyroux/traat-lean.git | f2babab84f81d4003446f476790022ac175d7236 | Traat/chapter1.lean | weakly_confluent_does_not_imply_confluent | [532, 1] | [582, 20] | constructor | case inl.inl.right
A : Type
R : A → A → Prop
inhabited_A : Nonempty A
x y z : X
h✝¹ : y = X.c
h✝ : z = X.c
⊢ refl_trans_clos (fun x y => x = X.b ∧ y = X.a ∨ x = X.b ∧ y = X.c ∨ x = X.c ∧ y = X.b ∨ x = X.c ∧ y = X.d) X.c X.c | no goals |
https://github.com/codyroux/traat-lean.git | f2babab84f81d4003446f476790022ac175d7236 | Traat/chapter1.lean | weakly_confluent_does_not_imply_confluent | [532, 1] | [582, 20] | case inr h1 h2 =>
cases h1 <;> cases h2 <;> simp [*] at *
. exists X.b; repeat constructor
. exists X.d; constructor
. constructor; simp [RX]; right; trivial
constructor; simp [RX]; right; trivial
constructor
. constructor
. exists X.d; constructor
. constructor
. constructor; simp [RX]; right; trivial
... | A : Type
R : A → A → Prop
inhabited_A : Nonempty A
x y z : X
h1 : x = X.c ∧ y = X.b ∨ x = X.c ∧ y = X.d
h2 : x = X.c ∧ z = X.b ∨ x = X.c ∧ z = X.d
⊢ joins (fun x y => x = X.b ∧ y = X.a ∨ x = X.b ∧ y = X.c ∨ x = X.c ∧ y = X.b ∨ x = X.c ∧ y = X.d) y z | no goals |
https://github.com/codyroux/traat-lean.git | f2babab84f81d4003446f476790022ac175d7236 | Traat/chapter1.lean | weakly_confluent_does_not_imply_confluent | [532, 1] | [582, 20] | cases h1 <;> cases h2 <;> simp [*] at * | A : Type
R : A → A → Prop
inhabited_A : Nonempty A
x y z : X
h1 : x = X.c ∧ y = X.b ∨ x = X.c ∧ y = X.d
h2 : x = X.c ∧ z = X.b ∨ x = X.c ∧ z = X.d
⊢ joins (fun x y => x = X.b ∧ y = X.a ∨ x = X.b ∧ y = X.c ∨ x = X.c ∧ y = X.b ∨ x = X.c ∧ y = X.d) y z | case inl.inl
A : Type
R : A → A → Prop
inhabited_A : Nonempty A
x y z : X
h✝¹ : y = X.b
h✝ : z = X.b
⊢ joins (fun x y => x = X.b ∧ y = X.a ∨ x = X.b ∧ y = X.c ∨ x = X.c ∧ y = X.b ∨ x = X.c ∧ y = X.d) X.b X.b
case inl.inr
A : Type
R : A → A → Prop
inhabited_A : Nonempty A
x y z : X
h✝¹ : y = X.b
h✝ : z = X.d
⊢ joins (f... |
https://github.com/codyroux/traat-lean.git | f2babab84f81d4003446f476790022ac175d7236 | Traat/chapter1.lean | weakly_confluent_does_not_imply_confluent | [532, 1] | [582, 20] | . exists X.b; repeat constructor | case inl.inl
A : Type
R : A → A → Prop
inhabited_A : Nonempty A
x y z : X
h✝¹ : y = X.b
h✝ : z = X.b
⊢ joins (fun x y => x = X.b ∧ y = X.a ∨ x = X.b ∧ y = X.c ∨ x = X.c ∧ y = X.b ∨ x = X.c ∧ y = X.d) X.b X.b
case inl.inr
A : Type
R : A → A → Prop
inhabited_A : Nonempty A
x y z : X
h✝¹ : y = X.b
h✝ : z = X.d
⊢ joins (f... | case inl.inr
A : Type
R : A → A → Prop
inhabited_A : Nonempty A
x y z : X
h✝¹ : y = X.b
h✝ : z = X.d
⊢ joins (fun x y => x = X.b ∧ y = X.a ∨ x = X.b ∧ y = X.c ∨ x = X.c ∧ y = X.b ∨ x = X.c ∧ y = X.d) X.b X.d
case inr.inl
A : Type
R : A → A → Prop
inhabited_A : Nonempty A
x y z : X
h✝¹ : y = X.d
h✝ : z = X.b
⊢ joins (f... |
https://github.com/codyroux/traat-lean.git | f2babab84f81d4003446f476790022ac175d7236 | Traat/chapter1.lean | weakly_confluent_does_not_imply_confluent | [532, 1] | [582, 20] | . exists X.d; constructor
. constructor; simp [RX]; right; trivial
constructor; simp [RX]; right; trivial
constructor
. constructor | case inl.inr
A : Type
R : A → A → Prop
inhabited_A : Nonempty A
x y z : X
h✝¹ : y = X.b
h✝ : z = X.d
⊢ joins (fun x y => x = X.b ∧ y = X.a ∨ x = X.b ∧ y = X.c ∨ x = X.c ∧ y = X.b ∨ x = X.c ∧ y = X.d) X.b X.d
case inr.inl
A : Type
R : A → A → Prop
inhabited_A : Nonempty A
x y z : X
h✝¹ : y = X.d
h✝ : z = X.b
⊢ joins (f... | case inr.inl
A : Type
R : A → A → Prop
inhabited_A : Nonempty A
x y z : X
h✝¹ : y = X.d
h✝ : z = X.b
⊢ joins (fun x y => x = X.b ∧ y = X.a ∨ x = X.b ∧ y = X.c ∨ x = X.c ∧ y = X.b ∨ x = X.c ∧ y = X.d) X.d X.b
case inr.inr
A : Type
R : A → A → Prop
inhabited_A : Nonempty A
x y z : X
h✝¹ : y = X.d
h✝ : z = X.d
⊢ joins (f... |
https://github.com/codyroux/traat-lean.git | f2babab84f81d4003446f476790022ac175d7236 | Traat/chapter1.lean | weakly_confluent_does_not_imply_confluent | [532, 1] | [582, 20] | . exists X.d; constructor
. constructor
. constructor; simp [RX]; right; trivial
constructor; simp [RX]; right; trivial
constructor | case inr.inl
A : Type
R : A → A → Prop
inhabited_A : Nonempty A
x y z : X
h✝¹ : y = X.d
h✝ : z = X.b
⊢ joins (fun x y => x = X.b ∧ y = X.a ∨ x = X.b ∧ y = X.c ∨ x = X.c ∧ y = X.b ∨ x = X.c ∧ y = X.d) X.d X.b
case inr.inr
A : Type
R : A → A → Prop
inhabited_A : Nonempty A
x y z : X
h✝¹ : y = X.d
h✝ : z = X.d
⊢ joins (f... | case inr.inr
A : Type
R : A → A → Prop
inhabited_A : Nonempty A
x y z : X
h✝¹ : y = X.d
h✝ : z = X.d
⊢ joins (fun x y => x = X.b ∧ y = X.a ∨ x = X.b ∧ y = X.c ∨ x = X.c ∧ y = X.b ∨ x = X.c ∧ y = X.d) X.d X.d |
https://github.com/codyroux/traat-lean.git | f2babab84f81d4003446f476790022ac175d7236 | Traat/chapter1.lean | weakly_confluent_does_not_imply_confluent | [532, 1] | [582, 20] | . exists X.d; repeat constructor | case inr.inr
A : Type
R : A → A → Prop
inhabited_A : Nonempty A
x y z : X
h✝¹ : y = X.d
h✝ : z = X.d
⊢ joins (fun x y => x = X.b ∧ y = X.a ∨ x = X.b ∧ y = X.c ∨ x = X.c ∧ y = X.b ∨ x = X.c ∧ y = X.d) X.d X.d | no goals |
https://github.com/codyroux/traat-lean.git | f2babab84f81d4003446f476790022ac175d7236 | Traat/chapter1.lean | weakly_confluent_does_not_imply_confluent | [532, 1] | [582, 20] | exists X.b | case inl.inl
A : Type
R : A → A → Prop
inhabited_A : Nonempty A
x y z : X
h✝¹ : y = X.b
h✝ : z = X.b
⊢ joins (fun x y => x = X.b ∧ y = X.a ∨ x = X.b ∧ y = X.c ∨ x = X.c ∧ y = X.b ∨ x = X.c ∧ y = X.d) X.b X.b | case inl.inl
A : Type
R : A → A → Prop
inhabited_A : Nonempty A
x y z : X
h✝¹ : y = X.b
h✝ : z = X.b
⊢ refl_trans_clos (fun x y => x = X.b ∧ y = X.a ∨ x = X.b ∧ y = X.c ∨ x = X.c ∧ y = X.b ∨ x = X.c ∧ y = X.d) X.b X.b ∧
refl_trans_clos (fun x y => x = X.b ∧ y = X.a ∨ x = X.b ∧ y = X.c ∨ x = X.c ∧ y = X.b ∨ x = X.c ... |
https://github.com/codyroux/traat-lean.git | f2babab84f81d4003446f476790022ac175d7236 | Traat/chapter1.lean | weakly_confluent_does_not_imply_confluent | [532, 1] | [582, 20] | repeat constructor | case inl.inl
A : Type
R : A → A → Prop
inhabited_A : Nonempty A
x y z : X
h✝¹ : y = X.b
h✝ : z = X.b
⊢ refl_trans_clos (fun x y => x = X.b ∧ y = X.a ∨ x = X.b ∧ y = X.c ∨ x = X.c ∧ y = X.b ∨ x = X.c ∧ y = X.d) X.b X.b ∧
refl_trans_clos (fun x y => x = X.b ∧ y = X.a ∨ x = X.b ∧ y = X.c ∨ x = X.c ∧ y = X.b ∨ x = X.c ... | no goals |
https://github.com/codyroux/traat-lean.git | f2babab84f81d4003446f476790022ac175d7236 | Traat/chapter1.lean | weakly_confluent_does_not_imply_confluent | [532, 1] | [582, 20] | constructor | case inl.inl.right
A : Type
R : A → A → Prop
inhabited_A : Nonempty A
x y z : X
h✝¹ : y = X.b
h✝ : z = X.b
⊢ refl_trans_clos (fun x y => x = X.b ∧ y = X.a ∨ x = X.b ∧ y = X.c ∨ x = X.c ∧ y = X.b ∨ x = X.c ∧ y = X.d) X.b X.b | no goals |
https://github.com/codyroux/traat-lean.git | f2babab84f81d4003446f476790022ac175d7236 | Traat/chapter1.lean | weakly_confluent_does_not_imply_confluent | [532, 1] | [582, 20] | exists X.d | case inl.inr
A : Type
R : A → A → Prop
inhabited_A : Nonempty A
x y z : X
h✝¹ : y = X.b
h✝ : z = X.d
⊢ joins (fun x y => x = X.b ∧ y = X.a ∨ x = X.b ∧ y = X.c ∨ x = X.c ∧ y = X.b ∨ x = X.c ∧ y = X.d) X.b X.d | case inl.inr
A : Type
R : A → A → Prop
inhabited_A : Nonempty A
x y z : X
h✝¹ : y = X.b
h✝ : z = X.d
⊢ refl_trans_clos (fun x y => x = X.b ∧ y = X.a ∨ x = X.b ∧ y = X.c ∨ x = X.c ∧ y = X.b ∨ x = X.c ∧ y = X.d) X.b X.d ∧
refl_trans_clos (fun x y => x = X.b ∧ y = X.a ∨ x = X.b ∧ y = X.c ∨ x = X.c ∧ y = X.b ∨ x = X.c ... |
https://github.com/codyroux/traat-lean.git | f2babab84f81d4003446f476790022ac175d7236 | Traat/chapter1.lean | weakly_confluent_does_not_imply_confluent | [532, 1] | [582, 20] | constructor | case inl.inr
A : Type
R : A → A → Prop
inhabited_A : Nonempty A
x y z : X
h✝¹ : y = X.b
h✝ : z = X.d
⊢ refl_trans_clos (fun x y => x = X.b ∧ y = X.a ∨ x = X.b ∧ y = X.c ∨ x = X.c ∧ y = X.b ∨ x = X.c ∧ y = X.d) X.b X.d ∧
refl_trans_clos (fun x y => x = X.b ∧ y = X.a ∨ x = X.b ∧ y = X.c ∨ x = X.c ∧ y = X.b ∨ x = X.c ... | case inl.inr.left
A : Type
R : A → A → Prop
inhabited_A : Nonempty A
x y z : X
h✝¹ : y = X.b
h✝ : z = X.d
⊢ refl_trans_clos (fun x y => x = X.b ∧ y = X.a ∨ x = X.b ∧ y = X.c ∨ x = X.c ∧ y = X.b ∨ x = X.c ∧ y = X.d) X.b X.d
case inl.inr.right
A : Type
R : A → A → Prop
inhabited_A : Nonempty A
x y z : X
h✝¹ : y = X.b
h✝... |
https://github.com/codyroux/traat-lean.git | f2babab84f81d4003446f476790022ac175d7236 | Traat/chapter1.lean | weakly_confluent_does_not_imply_confluent | [532, 1] | [582, 20] | . constructor; simp [RX]; right; trivial
constructor; simp [RX]; right; trivial
constructor | case inl.inr.left
A : Type
R : A → A → Prop
inhabited_A : Nonempty A
x y z : X
h✝¹ : y = X.b
h✝ : z = X.d
⊢ refl_trans_clos (fun x y => x = X.b ∧ y = X.a ∨ x = X.b ∧ y = X.c ∨ x = X.c ∧ y = X.b ∨ x = X.c ∧ y = X.d) X.b X.d
case inl.inr.right
A : Type
R : A → A → Prop
inhabited_A : Nonempty A
x y z : X
h✝¹ : y = X.b
h✝... | case inl.inr.right
A : Type
R : A → A → Prop
inhabited_A : Nonempty A
x y z : X
h✝¹ : y = X.b
h✝ : z = X.d
⊢ refl_trans_clos (fun x y => x = X.b ∧ y = X.a ∨ x = X.b ∧ y = X.c ∨ x = X.c ∧ y = X.b ∨ x = X.c ∧ y = X.d) X.d X.d |
https://github.com/codyroux/traat-lean.git | f2babab84f81d4003446f476790022ac175d7236 | Traat/chapter1.lean | weakly_confluent_does_not_imply_confluent | [532, 1] | [582, 20] | . constructor | case inl.inr.right
A : Type
R : A → A → Prop
inhabited_A : Nonempty A
x y z : X
h✝¹ : y = X.b
h✝ : z = X.d
⊢ refl_trans_clos (fun x y => x = X.b ∧ y = X.a ∨ x = X.b ∧ y = X.c ∨ x = X.c ∧ y = X.b ∨ x = X.c ∧ y = X.d) X.d X.d | no goals |
https://github.com/codyroux/traat-lean.git | f2babab84f81d4003446f476790022ac175d7236 | Traat/chapter1.lean | weakly_confluent_does_not_imply_confluent | [532, 1] | [582, 20] | constructor | case inl.inr.left
A : Type
R : A → A → Prop
inhabited_A : Nonempty A
x y z : X
h✝¹ : y = X.b
h✝ : z = X.d
⊢ refl_trans_clos (fun x y => x = X.b ∧ y = X.a ∨ x = X.b ∧ y = X.c ∨ x = X.c ∧ y = X.b ∨ x = X.c ∧ y = X.d) X.b X.d | case inl.inr.left.a
A : Type
R : A → A → Prop
inhabited_A : Nonempty A
x y z : X
h✝¹ : y = X.b
h✝ : z = X.d
⊢ X.b = X.b ∧ ?inl.inr.left.b = X.a ∨
X.b = X.b ∧ ?inl.inr.left.b = X.c ∨ X.b = X.c ∧ ?inl.inr.left.b = X.b ∨ X.b = X.c ∧ ?inl.inr.left.b = X.d
case inl.inr.left.a
A : Type
R : A → A → Prop
inhabited_A : Non... |
https://github.com/codyroux/traat-lean.git | f2babab84f81d4003446f476790022ac175d7236 | Traat/chapter1.lean | weakly_confluent_does_not_imply_confluent | [532, 1] | [582, 20] | simp [RX] | case inl.inr.left.a
A : Type
R : A → A → Prop
inhabited_A : Nonempty A
x y z : X
h✝¹ : y = X.b
h✝ : z = X.d
⊢ X.b = X.b ∧ ?inl.inr.left.b = X.a ∨
X.b = X.b ∧ ?inl.inr.left.b = X.c ∨ X.b = X.c ∧ ?inl.inr.left.b = X.b ∨ X.b = X.c ∧ ?inl.inr.left.b = X.d
case inl.inr.left.a
A : Type
R : A → A → Prop
inhabited_A : Non... | case inl.inr.left.a
A : Type
R : A → A → Prop
inhabited_A : Nonempty A
x y z : X
h✝¹ : y = X.b
h✝ : z = X.d
⊢ ?inl.inr.left.b = X.a ∨ ?inl.inr.left.b = X.c
case inl.inr.left.a
A : Type
R : A → A → Prop
inhabited_A : Nonempty A
x y z : X
h✝¹ : y = X.b
h✝ : z = X.d
⊢ refl_trans_clos (fun x y => x = X.b ∧ y = X.a ∨ x = X... |
https://github.com/codyroux/traat-lean.git | f2babab84f81d4003446f476790022ac175d7236 | Traat/chapter1.lean | weakly_confluent_does_not_imply_confluent | [532, 1] | [582, 20] | right | case inl.inr.left.a
A : Type
R : A → A → Prop
inhabited_A : Nonempty A
x y z : X
h✝¹ : y = X.b
h✝ : z = X.d
⊢ ?inl.inr.left.b = X.a ∨ ?inl.inr.left.b = X.c
case inl.inr.left.a
A : Type
R : A → A → Prop
inhabited_A : Nonempty A
x y z : X
h✝¹ : y = X.b
h✝ : z = X.d
⊢ refl_trans_clos (fun x y => x = X.b ∧ y = X.a ∨ x = X... | case inl.inr.left.a.h
A : Type
R : A → A → Prop
inhabited_A : Nonempty A
x y z : X
h✝¹ : y = X.b
h✝ : z = X.d
⊢ ?inl.inr.left.b = X.c
case inl.inr.left.a
A : Type
R : A → A → Prop
inhabited_A : Nonempty A
x y z : X
h✝¹ : y = X.b
h✝ : z = X.d
⊢ refl_trans_clos (fun x y => x = X.b ∧ y = X.a ∨ x = X.b ∧ y = X.c ∨ x = X.c... |
https://github.com/codyroux/traat-lean.git | f2babab84f81d4003446f476790022ac175d7236 | Traat/chapter1.lean | weakly_confluent_does_not_imply_confluent | [532, 1] | [582, 20] | trivial | case inl.inr.left.a.h
A : Type
R : A → A → Prop
inhabited_A : Nonempty A
x y z : X
h✝¹ : y = X.b
h✝ : z = X.d
⊢ ?inl.inr.left.b = X.c
case inl.inr.left.a
A : Type
R : A → A → Prop
inhabited_A : Nonempty A
x y z : X
h✝¹ : y = X.b
h✝ : z = X.d
⊢ refl_trans_clos (fun x y => x = X.b ∧ y = X.a ∨ x = X.b ∧ y = X.c ∨ x = X.c... | case inl.inr.left.a
A : Type
R : A → A → Prop
inhabited_A : Nonempty A
x y z : X
h✝¹ : y = X.b
h✝ : z = X.d
⊢ refl_trans_clos (fun x y => x = X.b ∧ y = X.a ∨ x = X.b ∧ y = X.c ∨ x = X.c ∧ y = X.b ∨ x = X.c ∧ y = X.d) X.c X.d |
https://github.com/codyroux/traat-lean.git | f2babab84f81d4003446f476790022ac175d7236 | Traat/chapter1.lean | weakly_confluent_does_not_imply_confluent | [532, 1] | [582, 20] | constructor | case inl.inr.left.a
A : Type
R : A → A → Prop
inhabited_A : Nonempty A
x y z : X
h✝¹ : y = X.b
h✝ : z = X.d
⊢ refl_trans_clos (fun x y => x = X.b ∧ y = X.a ∨ x = X.b ∧ y = X.c ∨ x = X.c ∧ y = X.b ∨ x = X.c ∧ y = X.d) X.c X.d | case inl.inr.left.a.a
A : Type
R : A → A → Prop
inhabited_A : Nonempty A
x y z : X
h✝¹ : y = X.b
h✝ : z = X.d
⊢ X.c = X.b ∧ ?inl.inr.left.a.b = X.a ∨
X.c = X.b ∧ ?inl.inr.left.a.b = X.c ∨ X.c = X.c ∧ ?inl.inr.left.a.b = X.b ∨ X.c = X.c ∧ ?inl.inr.left.a.b = X.d
case inl.inr.left.a.a
A : Type
R : A → A → Prop
inhab... |
https://github.com/codyroux/traat-lean.git | f2babab84f81d4003446f476790022ac175d7236 | Traat/chapter1.lean | weakly_confluent_does_not_imply_confluent | [532, 1] | [582, 20] | simp [RX] | case inl.inr.left.a.a
A : Type
R : A → A → Prop
inhabited_A : Nonempty A
x y z : X
h✝¹ : y = X.b
h✝ : z = X.d
⊢ X.c = X.b ∧ ?inl.inr.left.a.b = X.a ∨
X.c = X.b ∧ ?inl.inr.left.a.b = X.c ∨ X.c = X.c ∧ ?inl.inr.left.a.b = X.b ∨ X.c = X.c ∧ ?inl.inr.left.a.b = X.d
case inl.inr.left.a.a
A : Type
R : A → A → Prop
inhab... | case inl.inr.left.a.a
A : Type
R : A → A → Prop
inhabited_A : Nonempty A
x y z : X
h✝¹ : y = X.b
h✝ : z = X.d
⊢ ?inl.inr.left.a.b = X.b ∨ ?inl.inr.left.a.b = X.d
case inl.inr.left.a.a
A : Type
R : A → A → Prop
inhabited_A : Nonempty A
x y z : X
h✝¹ : y = X.b
h✝ : z = X.d
⊢ refl_trans_clos (fun x y => x = X.b ∧ y = X.a... |
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