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 | input stringlengths 73 2.09M |
|---|---|---|---|---|---|---|---|---|---|
https://github.com/djvelleman/HTPILeanPackage.git | 4d23e94fff351c65b5e1345c43451f2aa9908c27 | HTPILib/Chap8Part2.lean | HTPI.Cantor's_theorem | [1480, 1] | [1508, 7] | define at h7 | case pos
h1 : β R, fcnl_onto_from_nat R (π« Univ β)
R : Rel β (Set β)
h2 : unique_val_on_N R β§ nat_rel_onto R (π« Univ β)
h3 : unique_val_on_N R
h4 : β β¦x : Set ββ¦, x β π« Univ β β β n, R n x
D : Set β := {n | β X, R n X β§ n β X}
h5 : D β π« Univ β
n : β
h6 : R n D
h7 : n β D
β’ n β D | case pos
h1 : β R, fcnl_onto_from_nat R (π« Univ β)
R : Rel β (Set β)
h2 : unique_val_on_N R β§ nat_rel_onto R (π« Univ β)
h3 : unique_val_on_N R
h4 : β β¦x : Set ββ¦, x β π« Univ β β β n, R n x
D : Set β := {n | β X, R n X β§ n β X}
h5 : D β π« Univ β
n : β
h6 : R n D
h7 : β X, R n X β§ n β X
β’ n β D | Please generate a tactic in lean4 to solve the state.
STATE:
case pos
h1 : β R, fcnl_onto_from_nat R (π« Univ β)
R : Rel β (Set β)
h2 : unique_val_on_N R β§ nat_rel_onto R (π« Univ β)
h3 : unique_val_on_N R
h4 : β β¦x : Set ββ¦, x β π« Univ β β β n, R n x
D : Set β := {n | β X, R n X β§ n β X}
h5 : D β π« Univ β
n : β
h6 :... |
https://github.com/djvelleman/HTPILeanPackage.git | 4d23e94fff351c65b5e1345c43451f2aa9908c27 | HTPILib/Chap8Part2.lean | HTPI.Cantor's_theorem | [1480, 1] | [1508, 7] | obtain (X : Set Nat) (h8 : R n X β§ n β X) from h7 | case pos
h1 : β R, fcnl_onto_from_nat R (π« Univ β)
R : Rel β (Set β)
h2 : unique_val_on_N R β§ nat_rel_onto R (π« Univ β)
h3 : unique_val_on_N R
h4 : β β¦x : Set ββ¦, x β π« Univ β β β n, R n x
D : Set β := {n | β X, R n X β§ n β X}
h5 : D β π« Univ β
n : β
h6 : R n D
h7 : β X, R n X β§ n β X
β’ n β D | case pos
h1 : β R, fcnl_onto_from_nat R (π« Univ β)
R : Rel β (Set β)
h2 : unique_val_on_N R β§ nat_rel_onto R (π« Univ β)
h3 : unique_val_on_N R
h4 : β β¦x : Set ββ¦, x β π« Univ β β β n, R n x
D : Set β := {n | β X, R n X β§ n β X}
h5 : D β π« Univ β
n : β
h6 : R n D
h7 : β X, R n X β§ n β X
X : Set β
h8 : R n X β§ n β X
β’... | Please generate a tactic in lean4 to solve the state.
STATE:
case pos
h1 : β R, fcnl_onto_from_nat R (π« Univ β)
R : Rel β (Set β)
h2 : unique_val_on_N R β§ nat_rel_onto R (π« Univ β)
h3 : unique_val_on_N R
h4 : β β¦x : Set ββ¦, x β π« Univ β β β n, R n x
D : Set β := {n | β X, R n X β§ n β X}
h5 : D β π« Univ β
n : β
h6 :... |
https://github.com/djvelleman/HTPILeanPackage.git | 4d23e94fff351c65b5e1345c43451f2aa9908c27 | HTPILib/Chap8Part2.lean | HTPI.Cantor's_theorem | [1480, 1] | [1508, 7] | define at h3 | case pos
h1 : β R, fcnl_onto_from_nat R (π« Univ β)
R : Rel β (Set β)
h2 : unique_val_on_N R β§ nat_rel_onto R (π« Univ β)
h3 : unique_val_on_N R
h4 : β β¦x : Set ββ¦, x β π« Univ β β β n, R n x
D : Set β := {n | β X, R n X β§ n β X}
h5 : D β π« Univ β
n : β
h6 : R n D
h7 : β X, R n X β§ n β X
X : Set β
h8 : R n X β§ n β X
β’... | case pos
h1 : β R, fcnl_onto_from_nat R (π« Univ β)
R : Rel β (Set β)
h2 : unique_val_on_N R β§ nat_rel_onto R (π« Univ β)
h3 : β β¦n : ββ¦ β¦x1 x2 : Set ββ¦, R n x1 β R n x2 β x1 = x2
h4 : β β¦x : Set ββ¦, x β π« Univ β β β n, R n x
D : Set β := {n | β X, R n X β§ n β X}
h5 : D β π« Univ β
n : β
h6 : R n D
h7 : β X, R n X β§ n... | Please generate a tactic in lean4 to solve the state.
STATE:
case pos
h1 : β R, fcnl_onto_from_nat R (π« Univ β)
R : Rel β (Set β)
h2 : unique_val_on_N R β§ nat_rel_onto R (π« Univ β)
h3 : unique_val_on_N R
h4 : β β¦x : Set ββ¦, x β π« Univ β β β n, R n x
D : Set β := {n | β X, R n X β§ n β X}
h5 : D β π« Univ β
n : β
h6 :... |
https://github.com/djvelleman/HTPILeanPackage.git | 4d23e94fff351c65b5e1345c43451f2aa9908c27 | HTPILib/Chap8Part2.lean | HTPI.Cantor's_theorem | [1480, 1] | [1508, 7] | have h9 : D = X := h3 h6 h8.left | case pos
h1 : β R, fcnl_onto_from_nat R (π« Univ β)
R : Rel β (Set β)
h2 : unique_val_on_N R β§ nat_rel_onto R (π« Univ β)
h3 : β β¦n : ββ¦ β¦x1 x2 : Set ββ¦, R n x1 β R n x2 β x1 = x2
h4 : β β¦x : Set ββ¦, x β π« Univ β β β n, R n x
D : Set β := {n | β X, R n X β§ n β X}
h5 : D β π« Univ β
n : β
h6 : R n D
h7 : β X, R n X β§ n... | case pos
h1 : β R, fcnl_onto_from_nat R (π« Univ β)
R : Rel β (Set β)
h2 : unique_val_on_N R β§ nat_rel_onto R (π« Univ β)
h3 : β β¦n : ββ¦ β¦x1 x2 : Set ββ¦, R n x1 β R n x2 β x1 = x2
h4 : β β¦x : Set ββ¦, x β π« Univ β β β n, R n x
D : Set β := {n | β X, R n X β§ n β X}
h5 : D β π« Univ β
n : β
h6 : R n D
h7 : β X, R n X β§ n... | Please generate a tactic in lean4 to solve the state.
STATE:
case pos
h1 : β R, fcnl_onto_from_nat R (π« Univ β)
R : Rel β (Set β)
h2 : unique_val_on_N R β§ nat_rel_onto R (π« Univ β)
h3 : β β¦n : ββ¦ β¦x1 x2 : Set ββ¦, R n x1 β R n x2 β x1 = x2
h4 : β β¦x : Set ββ¦, x β π« Univ β β β n, R n x
D : Set β := {n | β X, R n X β§ n... |
https://github.com/djvelleman/HTPILeanPackage.git | 4d23e94fff351c65b5e1345c43451f2aa9908c27 | HTPILib/Chap8Part2.lean | HTPI.Cantor's_theorem | [1480, 1] | [1508, 7] | rewrite [h9] | case pos
h1 : β R, fcnl_onto_from_nat R (π« Univ β)
R : Rel β (Set β)
h2 : unique_val_on_N R β§ nat_rel_onto R (π« Univ β)
h3 : β β¦n : ββ¦ β¦x1 x2 : Set ββ¦, R n x1 β R n x2 β x1 = x2
h4 : β β¦x : Set ββ¦, x β π« Univ β β β n, R n x
D : Set β := {n | β X, R n X β§ n β X}
h5 : D β π« Univ β
n : β
h6 : R n D
h7 : β X, R n X β§ n... | case pos
h1 : β R, fcnl_onto_from_nat R (π« Univ β)
R : Rel β (Set β)
h2 : unique_val_on_N R β§ nat_rel_onto R (π« Univ β)
h3 : β β¦n : ββ¦ β¦x1 x2 : Set ββ¦, R n x1 β R n x2 β x1 = x2
h4 : β β¦x : Set ββ¦, x β π« Univ β β β n, R n x
D : Set β := {n | β X, R n X β§ n β X}
h5 : D β π« Univ β
n : β
h6 : R n D
h7 : β X, R n X β§ n... | Please generate a tactic in lean4 to solve the state.
STATE:
case pos
h1 : β R, fcnl_onto_from_nat R (π« Univ β)
R : Rel β (Set β)
h2 : unique_val_on_N R β§ nat_rel_onto R (π« Univ β)
h3 : β β¦n : ββ¦ β¦x1 x2 : Set ββ¦, R n x1 β R n x2 β x1 = x2
h4 : β β¦x : Set ββ¦, x β π« Univ β β β n, R n x
D : Set β := {n | β X, R n X β§ n... |
https://github.com/djvelleman/HTPILeanPackage.git | 4d23e94fff351c65b5e1345c43451f2aa9908c27 | HTPILib/Chap8Part2.lean | HTPI.Cantor's_theorem | [1480, 1] | [1508, 7] | show n β X from h8.right | case pos
h1 : β R, fcnl_onto_from_nat R (π« Univ β)
R : Rel β (Set β)
h2 : unique_val_on_N R β§ nat_rel_onto R (π« Univ β)
h3 : β β¦n : ββ¦ β¦x1 x2 : Set ββ¦, R n x1 β R n x2 β x1 = x2
h4 : β β¦x : Set ββ¦, x β π« Univ β β β n, R n x
D : Set β := {n | β X, R n X β§ n β X}
h5 : D β π« Univ β
n : β
h6 : R n D
h7 : β X, R n X β§ n... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case pos
h1 : β R, fcnl_onto_from_nat R (π« Univ β)
R : Rel β (Set β)
h2 : unique_val_on_N R β§ nat_rel_onto R (π« Univ β)
h3 : β β¦n : ββ¦ β¦x1 x2 : Set ββ¦, R n x1 β R n x2 β x1 = x2
h4 : β β¦x : Set ββ¦, x β π« Univ β β β n, R n x
D : Set β := {n | β X, R n X β§ n... |
https://github.com/djvelleman/HTPILeanPackage.git | 4d23e94fff351c65b5e1345c43451f2aa9908c27 | HTPILib/Chap8Part2.lean | HTPI.Cantor's_theorem | [1480, 1] | [1508, 7] | contradict h7 | case neg
h1 : β R, fcnl_onto_from_nat R (π« Univ β)
R : Rel β (Set β)
h2 : unique_val_on_N R β§ nat_rel_onto R (π« Univ β)
h3 : unique_val_on_N R
h4 : β β¦x : Set ββ¦, x β π« Univ β β β n, R n x
D : Set β := {n | β X, R n X β§ n β X}
h5 : D β π« Univ β
n : β
h6 : R n D
h7 : n β D
β’ False | case neg
h1 : β R, fcnl_onto_from_nat R (π« Univ β)
R : Rel β (Set β)
h2 : unique_val_on_N R β§ nat_rel_onto R (π« Univ β)
h3 : unique_val_on_N R
h4 : β β¦x : Set ββ¦, x β π« Univ β β β n, R n x
D : Set β := {n | β X, R n X β§ n β X}
h5 : D β π« Univ β
n : β
h6 : R n D
h7 : n β D
β’ n β D | Please generate a tactic in lean4 to solve the state.
STATE:
case neg
h1 : β R, fcnl_onto_from_nat R (π« Univ β)
R : Rel β (Set β)
h2 : unique_val_on_N R β§ nat_rel_onto R (π« Univ β)
h3 : unique_val_on_N R
h4 : β β¦x : Set ββ¦, x β π« Univ β β β n, R n x
D : Set β := {n | β X, R n X β§ n β X}
h5 : D β π« Univ β
n : β
h6 :... |
https://github.com/djvelleman/HTPILeanPackage.git | 4d23e94fff351c65b5e1345c43451f2aa9908c27 | HTPILib/Chap8Part2.lean | HTPI.Cantor's_theorem | [1480, 1] | [1508, 7] | define | case neg
h1 : β R, fcnl_onto_from_nat R (π« Univ β)
R : Rel β (Set β)
h2 : unique_val_on_N R β§ nat_rel_onto R (π« Univ β)
h3 : unique_val_on_N R
h4 : β β¦x : Set ββ¦, x β π« Univ β β β n, R n x
D : Set β := {n | β X, R n X β§ n β X}
h5 : D β π« Univ β
n : β
h6 : R n D
h7 : n β D
β’ n β D | case neg
h1 : β R, fcnl_onto_from_nat R (π« Univ β)
R : Rel β (Set β)
h2 : unique_val_on_N R β§ nat_rel_onto R (π« Univ β)
h3 : unique_val_on_N R
h4 : β β¦x : Set ββ¦, x β π« Univ β β β n, R n x
D : Set β := {n | β X, R n X β§ n β X}
h5 : D β π« Univ β
n : β
h6 : R n D
h7 : n β D
β’ β X, R n X β§ n β X | Please generate a tactic in lean4 to solve the state.
STATE:
case neg
h1 : β R, fcnl_onto_from_nat R (π« Univ β)
R : Rel β (Set β)
h2 : unique_val_on_N R β§ nat_rel_onto R (π« Univ β)
h3 : unique_val_on_N R
h4 : β β¦x : Set ββ¦, x β π« Univ β β β n, R n x
D : Set β := {n | β X, R n X β§ n β X}
h5 : D β π« Univ β
n : β
h6 :... |
https://github.com/djvelleman/HTPILeanPackage.git | 4d23e94fff351c65b5e1345c43451f2aa9908c27 | HTPILib/Chap8Part2.lean | HTPI.Cantor's_theorem | [1480, 1] | [1508, 7] | show β (X : Set Nat), R n X β§ n β X from
Exists.intro D (And.intro h6 h7) | case neg
h1 : β R, fcnl_onto_from_nat R (π« Univ β)
R : Rel β (Set β)
h2 : unique_val_on_N R β§ nat_rel_onto R (π« Univ β)
h3 : unique_val_on_N R
h4 : β β¦x : Set ββ¦, x β π« Univ β β β n, R n x
D : Set β := {n | β X, R n X β§ n β X}
h5 : D β π« Univ β
n : β
h6 : R n D
h7 : n β D
β’ β X, R n X β§ n β X | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case neg
h1 : β R, fcnl_onto_from_nat R (π« Univ β)
R : Rel β (Set β)
h2 : unique_val_on_N R β§ nat_rel_onto R (π« Univ β)
h3 : unique_val_on_N R
h4 : β β¦x : Set ββ¦, x β π« Univ β β β n, R n x
D : Set β := {n | β X, R n X β§ n β X}
h5 : D β π« Univ β
n : β
h6 :... |
https://github.com/djvelleman/HTPILeanPackage.git | 4d23e94fff351c65b5e1345c43451f2aa9908c27 | HTPILib/Chap8Part2.lean | HTPI.rep_common_image_step | [1511, 1] | [1514, 72] | rfl | U V : Type
R S : Rel U V
X0 : Set U
m : β
a : U
β’ a β rep_common_image R S X0 (m + 1) β β x β rep_common_image R S X0 m, β y, R x y β§ S a y | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
U V : Type
R S : Rel U V
X0 : Set U
m : β
a : U
β’ a β rep_common_image R S X0 (m + 1) β β x β rep_common_image R S X0 m, β y, R x y β§ S a y
TACTIC:
|
https://github.com/djvelleman/HTPILeanPackage.git | 4d23e94fff351c65b5e1345c43451f2aa9908c27 | HTPILib/Chap8Part2.lean | HTPI.csb_match_cri | [1516, 1] | [1526, 7] | by_cases on h1 | U V : Type
R S : Rel U V
X0 : Set U
x : U
y : V
h1 : csb_match R S X0 x y
h2 : x β cum_rep_image R S X0
β’ R x y | case Case_1
U V : Type
R S : Rel U V
X0 : Set U
x : U
y : V
h2 : x β cum_rep_image R S X0
h1 : x β cum_rep_image R S X0 β§ R x y
β’ R x y
case Case_2
U V : Type
R S : Rel U V
X0 : Set U
x : U
y : V
h2 : x β cum_rep_image R S X0
h1 : x β cum_rep_image R S X0 β§ S x y
β’ R x y | Please generate a tactic in lean4 to solve the state.
STATE:
U V : Type
R S : Rel U V
X0 : Set U
x : U
y : V
h1 : csb_match R S X0 x y
h2 : x β cum_rep_image R S X0
β’ R x y
TACTIC:
|
https://github.com/djvelleman/HTPILeanPackage.git | 4d23e94fff351c65b5e1345c43451f2aa9908c27 | HTPILib/Chap8Part2.lean | HTPI.csb_match_cri | [1516, 1] | [1526, 7] | show R x y from h1.right | case Case_1
U V : Type
R S : Rel U V
X0 : Set U
x : U
y : V
h2 : x β cum_rep_image R S X0
h1 : x β cum_rep_image R S X0 β§ R x y
β’ R x y | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case Case_1
U V : Type
R S : Rel U V
X0 : Set U
x : U
y : V
h2 : x β cum_rep_image R S X0
h1 : x β cum_rep_image R S X0 β§ R x y
β’ R x y
TACTIC:
|
https://github.com/djvelleman/HTPILeanPackage.git | 4d23e94fff351c65b5e1345c43451f2aa9908c27 | HTPILib/Chap8Part2.lean | HTPI.csb_match_cri | [1516, 1] | [1526, 7] | show R x y from absurd h2 h1.left | case Case_2
U V : Type
R S : Rel U V
X0 : Set U
x : U
y : V
h2 : x β cum_rep_image R S X0
h1 : x β cum_rep_image R S X0 β§ S x y
β’ R x y | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case Case_2
U V : Type
R S : Rel U V
X0 : Set U
x : U
y : V
h2 : x β cum_rep_image R S X0
h1 : x β cum_rep_image R S X0 β§ S x y
β’ R x y
TACTIC:
|
https://github.com/djvelleman/HTPILeanPackage.git | 4d23e94fff351c65b5e1345c43451f2aa9908c27 | HTPILib/Chap8Part2.lean | HTPI.csb_match_not_cri | [1528, 1] | [1538, 7] | by_cases on h1 | U V : Type
R S : Rel U V
X0 : Set U
x : U
y : V
h1 : csb_match R S X0 x y
h2 : x β cum_rep_image R S X0
β’ S x y | case Case_1
U V : Type
R S : Rel U V
X0 : Set U
x : U
y : V
h2 : x β cum_rep_image R S X0
h1 : x β cum_rep_image R S X0 β§ R x y
β’ S x y
case Case_2
U V : Type
R S : Rel U V
X0 : Set U
x : U
y : V
h2 : x β cum_rep_image R S X0
h1 : x β cum_rep_image R S X0 β§ S x y
β’ S x y | Please generate a tactic in lean4 to solve the state.
STATE:
U V : Type
R S : Rel U V
X0 : Set U
x : U
y : V
h1 : csb_match R S X0 x y
h2 : x β cum_rep_image R S X0
β’ S x y
TACTIC:
|
https://github.com/djvelleman/HTPILeanPackage.git | 4d23e94fff351c65b5e1345c43451f2aa9908c27 | HTPILib/Chap8Part2.lean | HTPI.csb_match_not_cri | [1528, 1] | [1538, 7] | show S x y from absurd h1.left h2 | case Case_1
U V : Type
R S : Rel U V
X0 : Set U
x : U
y : V
h2 : x β cum_rep_image R S X0
h1 : x β cum_rep_image R S X0 β§ R x y
β’ S x y | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case Case_1
U V : Type
R S : Rel U V
X0 : Set U
x : U
y : V
h2 : x β cum_rep_image R S X0
h1 : x β cum_rep_image R S X0 β§ R x y
β’ S x y
TACTIC:
|
https://github.com/djvelleman/HTPILeanPackage.git | 4d23e94fff351c65b5e1345c43451f2aa9908c27 | HTPILib/Chap8Part2.lean | HTPI.csb_match_not_cri | [1528, 1] | [1538, 7] | show S x y from h1.right | case Case_2
U V : Type
R S : Rel U V
X0 : Set U
x : U
y : V
h2 : x β cum_rep_image R S X0
h1 : x β cum_rep_image R S X0 β§ S x y
β’ S x y | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case Case_2
U V : Type
R S : Rel U V
X0 : Set U
x : U
y : V
h2 : x β cum_rep_image R S X0
h1 : x β cum_rep_image R S X0 β§ S x y
β’ S x y
TACTIC:
|
https://github.com/djvelleman/HTPILeanPackage.git | 4d23e94fff351c65b5e1345c43451f2aa9908c27 | HTPILib/Chap8Part2.lean | HTPI.csb_cri_of_cri | [1540, 1] | [1557, 7] | have h4 : R x1 y := csb_match_cri h1 h3 | U V : Type
R S : Rel U V
X0 : Set U
x1 x2 : U
y : V
h1 : csb_match R S X0 x1 y
h2 : csb_match R S X0 x2 y
h3 : x1 β cum_rep_image R S X0
β’ x2 β cum_rep_image R S X0 | U V : Type
R S : Rel U V
X0 : Set U
x1 x2 : U
y : V
h1 : csb_match R S X0 x1 y
h2 : csb_match R S X0 x2 y
h3 : x1 β cum_rep_image R S X0
h4 : R x1 y
β’ x2 β cum_rep_image R S X0 | Please generate a tactic in lean4 to solve the state.
STATE:
U V : Type
R S : Rel U V
X0 : Set U
x1 x2 : U
y : V
h1 : csb_match R S X0 x1 y
h2 : csb_match R S X0 x2 y
h3 : x1 β cum_rep_image R S X0
β’ x2 β cum_rep_image R S X0
TACTIC:
|
https://github.com/djvelleman/HTPILeanPackage.git | 4d23e94fff351c65b5e1345c43451f2aa9908c27 | HTPILib/Chap8Part2.lean | HTPI.csb_cri_of_cri | [1540, 1] | [1557, 7] | by_contra h5 | U V : Type
R S : Rel U V
X0 : Set U
x1 x2 : U
y : V
h1 : csb_match R S X0 x1 y
h2 : csb_match R S X0 x2 y
h3 : x1 β cum_rep_image R S X0
h4 : R x1 y
β’ x2 β cum_rep_image R S X0 | U V : Type
R S : Rel U V
X0 : Set U
x1 x2 : U
y : V
h1 : csb_match R S X0 x1 y
h2 : csb_match R S X0 x2 y
h3 : x1 β cum_rep_image R S X0
h4 : R x1 y
h5 : Β¬x2 β cum_rep_image R S X0
β’ False | Please generate a tactic in lean4 to solve the state.
STATE:
U V : Type
R S : Rel U V
X0 : Set U
x1 x2 : U
y : V
h1 : csb_match R S X0 x1 y
h2 : csb_match R S X0 x2 y
h3 : x1 β cum_rep_image R S X0
h4 : R x1 y
β’ x2 β cum_rep_image R S X0
TACTIC:
|
https://github.com/djvelleman/HTPILeanPackage.git | 4d23e94fff351c65b5e1345c43451f2aa9908c27 | HTPILib/Chap8Part2.lean | HTPI.csb_cri_of_cri | [1540, 1] | [1557, 7] | have h6 : S x2 y := csb_match_not_cri h2 h5 | U V : Type
R S : Rel U V
X0 : Set U
x1 x2 : U
y : V
h1 : csb_match R S X0 x1 y
h2 : csb_match R S X0 x2 y
h3 : x1 β cum_rep_image R S X0
h4 : R x1 y
h5 : Β¬x2 β cum_rep_image R S X0
β’ False | U V : Type
R S : Rel U V
X0 : Set U
x1 x2 : U
y : V
h1 : csb_match R S X0 x1 y
h2 : csb_match R S X0 x2 y
h3 : x1 β cum_rep_image R S X0
h4 : R x1 y
h5 : Β¬x2 β cum_rep_image R S X0
h6 : S x2 y
β’ False | Please generate a tactic in lean4 to solve the state.
STATE:
U V : Type
R S : Rel U V
X0 : Set U
x1 x2 : U
y : V
h1 : csb_match R S X0 x1 y
h2 : csb_match R S X0 x2 y
h3 : x1 β cum_rep_image R S X0
h4 : R x1 y
h5 : Β¬x2 β cum_rep_image R S X0
β’ False
TACTIC:
|
https://github.com/djvelleman/HTPILeanPackage.git | 4d23e94fff351c65b5e1345c43451f2aa9908c27 | HTPILib/Chap8Part2.lean | HTPI.csb_cri_of_cri | [1540, 1] | [1557, 7] | contradict h5 | U V : Type
R S : Rel U V
X0 : Set U
x1 x2 : U
y : V
h1 : csb_match R S X0 x1 y
h2 : csb_match R S X0 x2 y
h3 : x1 β cum_rep_image R S X0
h4 : R x1 y
h5 : Β¬x2 β cum_rep_image R S X0
h6 : S x2 y
β’ False | U V : Type
R S : Rel U V
X0 : Set U
x1 x2 : U
y : V
h1 : csb_match R S X0 x1 y
h2 : csb_match R S X0 x2 y
h3 : x1 β cum_rep_image R S X0
h4 : R x1 y
h5 : Β¬x2 β cum_rep_image R S X0
h6 : S x2 y
β’ x2 β cum_rep_image R S X0 | Please generate a tactic in lean4 to solve the state.
STATE:
U V : Type
R S : Rel U V
X0 : Set U
x1 x2 : U
y : V
h1 : csb_match R S X0 x1 y
h2 : csb_match R S X0 x2 y
h3 : x1 β cum_rep_image R S X0
h4 : R x1 y
h5 : Β¬x2 β cum_rep_image R S X0
h6 : S x2 y
β’ False
TACTIC:
|
https://github.com/djvelleman/HTPILeanPackage.git | 4d23e94fff351c65b5e1345c43451f2aa9908c27 | HTPILib/Chap8Part2.lean | HTPI.csb_cri_of_cri | [1540, 1] | [1557, 7] | define at h3 | U V : Type
R S : Rel U V
X0 : Set U
x1 x2 : U
y : V
h1 : csb_match R S X0 x1 y
h2 : csb_match R S X0 x2 y
h3 : x1 β cum_rep_image R S X0
h4 : R x1 y
h5 : Β¬x2 β cum_rep_image R S X0
h6 : S x2 y
β’ x2 β cum_rep_image R S X0 | U V : Type
R S : Rel U V
X0 : Set U
x1 x2 : U
y : V
h1 : csb_match R S X0 x1 y
h2 : csb_match R S X0 x2 y
h3 : β n, x1 β rep_common_image R S X0 n
h4 : R x1 y
h5 : Β¬x2 β cum_rep_image R S X0
h6 : S x2 y
β’ x2 β cum_rep_image R S X0 | Please generate a tactic in lean4 to solve the state.
STATE:
U V : Type
R S : Rel U V
X0 : Set U
x1 x2 : U
y : V
h1 : csb_match R S X0 x1 y
h2 : csb_match R S X0 x2 y
h3 : x1 β cum_rep_image R S X0
h4 : R x1 y
h5 : Β¬x2 β cum_rep_image R S X0
h6 : S x2 y
β’ x2 β cum_rep_image R S X0
TACTIC:
|
https://github.com/djvelleman/HTPILeanPackage.git | 4d23e94fff351c65b5e1345c43451f2aa9908c27 | HTPILib/Chap8Part2.lean | HTPI.csb_cri_of_cri | [1540, 1] | [1557, 7] | define | U V : Type
R S : Rel U V
X0 : Set U
x1 x2 : U
y : V
h1 : csb_match R S X0 x1 y
h2 : csb_match R S X0 x2 y
h3 : β n, x1 β rep_common_image R S X0 n
h4 : R x1 y
h5 : Β¬x2 β cum_rep_image R S X0
h6 : S x2 y
β’ x2 β cum_rep_image R S X0 | U V : Type
R S : Rel U V
X0 : Set U
x1 x2 : U
y : V
h1 : csb_match R S X0 x1 y
h2 : csb_match R S X0 x2 y
h3 : β n, x1 β rep_common_image R S X0 n
h4 : R x1 y
h5 : Β¬x2 β cum_rep_image R S X0
h6 : S x2 y
β’ β n, x2 β rep_common_image R S X0 n | Please generate a tactic in lean4 to solve the state.
STATE:
U V : Type
R S : Rel U V
X0 : Set U
x1 x2 : U
y : V
h1 : csb_match R S X0 x1 y
h2 : csb_match R S X0 x2 y
h3 : β n, x1 β rep_common_image R S X0 n
h4 : R x1 y
h5 : Β¬x2 β cum_rep_image R S X0
h6 : S x2 y
β’ x2 β cum_rep_image R S X0
TACTIC:
|
https://github.com/djvelleman/HTPILeanPackage.git | 4d23e94fff351c65b5e1345c43451f2aa9908c27 | HTPILib/Chap8Part2.lean | HTPI.csb_cri_of_cri | [1540, 1] | [1557, 7] | obtain (n : Nat) (h7 : x1 β rep_common_image R S X0 n) from h3 | U V : Type
R S : Rel U V
X0 : Set U
x1 x2 : U
y : V
h1 : csb_match R S X0 x1 y
h2 : csb_match R S X0 x2 y
h3 : β n, x1 β rep_common_image R S X0 n
h4 : R x1 y
h5 : Β¬x2 β cum_rep_image R S X0
h6 : S x2 y
β’ β n, x2 β rep_common_image R S X0 n | U V : Type
R S : Rel U V
X0 : Set U
x1 x2 : U
y : V
h1 : csb_match R S X0 x1 y
h2 : csb_match R S X0 x2 y
h3 : β n, x1 β rep_common_image R S X0 n
h4 : R x1 y
h5 : Β¬x2 β cum_rep_image R S X0
h6 : S x2 y
n : β
h7 : x1 β rep_common_image R S X0 n
β’ β n, x2 β rep_common_image R S X0 n | Please generate a tactic in lean4 to solve the state.
STATE:
U V : Type
R S : Rel U V
X0 : Set U
x1 x2 : U
y : V
h1 : csb_match R S X0 x1 y
h2 : csb_match R S X0 x2 y
h3 : β n, x1 β rep_common_image R S X0 n
h4 : R x1 y
h5 : Β¬x2 β cum_rep_image R S X0
h6 : S x2 y
β’ β n, x2 β rep_common_image R S X0 n
TACTIC:
|
https://github.com/djvelleman/HTPILeanPackage.git | 4d23e94fff351c65b5e1345c43451f2aa9908c27 | HTPILib/Chap8Part2.lean | HTPI.csb_cri_of_cri | [1540, 1] | [1557, 7] | apply Exists.intro (n + 1) | U V : Type
R S : Rel U V
X0 : Set U
x1 x2 : U
y : V
h1 : csb_match R S X0 x1 y
h2 : csb_match R S X0 x2 y
h3 : β n, x1 β rep_common_image R S X0 n
h4 : R x1 y
h5 : Β¬x2 β cum_rep_image R S X0
h6 : S x2 y
n : β
h7 : x1 β rep_common_image R S X0 n
β’ β n, x2 β rep_common_image R S X0 n | U V : Type
R S : Rel U V
X0 : Set U
x1 x2 : U
y : V
h1 : csb_match R S X0 x1 y
h2 : csb_match R S X0 x2 y
h3 : β n, x1 β rep_common_image R S X0 n
h4 : R x1 y
h5 : Β¬x2 β cum_rep_image R S X0
h6 : S x2 y
n : β
h7 : x1 β rep_common_image R S X0 n
β’ x2 β rep_common_image R S X0 (n + 1) | Please generate a tactic in lean4 to solve the state.
STATE:
U V : Type
R S : Rel U V
X0 : Set U
x1 x2 : U
y : V
h1 : csb_match R S X0 x1 y
h2 : csb_match R S X0 x2 y
h3 : β n, x1 β rep_common_image R S X0 n
h4 : R x1 y
h5 : Β¬x2 β cum_rep_image R S X0
h6 : S x2 y
n : β
h7 : x1 β rep_common_image R S X0 n
β’ β n, x2 β re... |
https://github.com/djvelleman/HTPILeanPackage.git | 4d23e94fff351c65b5e1345c43451f2aa9908c27 | HTPILib/Chap8Part2.lean | HTPI.csb_cri_of_cri | [1540, 1] | [1557, 7] | rewrite [rep_common_image_step] | U V : Type
R S : Rel U V
X0 : Set U
x1 x2 : U
y : V
h1 : csb_match R S X0 x1 y
h2 : csb_match R S X0 x2 y
h3 : β n, x1 β rep_common_image R S X0 n
h4 : R x1 y
h5 : Β¬x2 β cum_rep_image R S X0
h6 : S x2 y
n : β
h7 : x1 β rep_common_image R S X0 n
β’ x2 β rep_common_image R S X0 (n + 1) | U V : Type
R S : Rel U V
X0 : Set U
x1 x2 : U
y : V
h1 : csb_match R S X0 x1 y
h2 : csb_match R S X0 x2 y
h3 : β n, x1 β rep_common_image R S X0 n
h4 : R x1 y
h5 : Β¬x2 β cum_rep_image R S X0
h6 : S x2 y
n : β
h7 : x1 β rep_common_image R S X0 n
β’ β x β rep_common_image R S X0 n, β y, R x y β§ S x2 y | Please generate a tactic in lean4 to solve the state.
STATE:
U V : Type
R S : Rel U V
X0 : Set U
x1 x2 : U
y : V
h1 : csb_match R S X0 x1 y
h2 : csb_match R S X0 x2 y
h3 : β n, x1 β rep_common_image R S X0 n
h4 : R x1 y
h5 : Β¬x2 β cum_rep_image R S X0
h6 : S x2 y
n : β
h7 : x1 β rep_common_image R S X0 n
β’ x2 β rep_com... |
https://github.com/djvelleman/HTPILeanPackage.git | 4d23e94fff351c65b5e1345c43451f2aa9908c27 | HTPILib/Chap8Part2.lean | HTPI.csb_cri_of_cri | [1540, 1] | [1557, 7] | apply Exists.intro x1 | U V : Type
R S : Rel U V
X0 : Set U
x1 x2 : U
y : V
h1 : csb_match R S X0 x1 y
h2 : csb_match R S X0 x2 y
h3 : β n, x1 β rep_common_image R S X0 n
h4 : R x1 y
h5 : Β¬x2 β cum_rep_image R S X0
h6 : S x2 y
n : β
h7 : x1 β rep_common_image R S X0 n
β’ β x β rep_common_image R S X0 n, β y, R x y β§ S x2 y | U V : Type
R S : Rel U V
X0 : Set U
x1 x2 : U
y : V
h1 : csb_match R S X0 x1 y
h2 : csb_match R S X0 x2 y
h3 : β n, x1 β rep_common_image R S X0 n
h4 : R x1 y
h5 : Β¬x2 β cum_rep_image R S X0
h6 : S x2 y
n : β
h7 : x1 β rep_common_image R S X0 n
β’ x1 β rep_common_image R S X0 n β§ β y, R x1 y β§ S x2 y | Please generate a tactic in lean4 to solve the state.
STATE:
U V : Type
R S : Rel U V
X0 : Set U
x1 x2 : U
y : V
h1 : csb_match R S X0 x1 y
h2 : csb_match R S X0 x2 y
h3 : β n, x1 β rep_common_image R S X0 n
h4 : R x1 y
h5 : Β¬x2 β cum_rep_image R S X0
h6 : S x2 y
n : β
h7 : x1 β rep_common_image R S X0 n
β’ β x β rep_co... |
https://github.com/djvelleman/HTPILeanPackage.git | 4d23e94fff351c65b5e1345c43451f2aa9908c27 | HTPILib/Chap8Part2.lean | HTPI.csb_cri_of_cri | [1540, 1] | [1557, 7] | apply And.intro h7 | U V : Type
R S : Rel U V
X0 : Set U
x1 x2 : U
y : V
h1 : csb_match R S X0 x1 y
h2 : csb_match R S X0 x2 y
h3 : β n, x1 β rep_common_image R S X0 n
h4 : R x1 y
h5 : Β¬x2 β cum_rep_image R S X0
h6 : S x2 y
n : β
h7 : x1 β rep_common_image R S X0 n
β’ x1 β rep_common_image R S X0 n β§ β y, R x1 y β§ S x2 y | U V : Type
R S : Rel U V
X0 : Set U
x1 x2 : U
y : V
h1 : csb_match R S X0 x1 y
h2 : csb_match R S X0 x2 y
h3 : β n, x1 β rep_common_image R S X0 n
h4 : R x1 y
h5 : Β¬x2 β cum_rep_image R S X0
h6 : S x2 y
n : β
h7 : x1 β rep_common_image R S X0 n
β’ β y, R x1 y β§ S x2 y | Please generate a tactic in lean4 to solve the state.
STATE:
U V : Type
R S : Rel U V
X0 : Set U
x1 x2 : U
y : V
h1 : csb_match R S X0 x1 y
h2 : csb_match R S X0 x2 y
h3 : β n, x1 β rep_common_image R S X0 n
h4 : R x1 y
h5 : Β¬x2 β cum_rep_image R S X0
h6 : S x2 y
n : β
h7 : x1 β rep_common_image R S X0 n
β’ x1 β rep_com... |
https://github.com/djvelleman/HTPILeanPackage.git | 4d23e94fff351c65b5e1345c43451f2aa9908c27 | HTPILib/Chap8Part2.lean | HTPI.csb_cri_of_cri | [1540, 1] | [1557, 7] | show β (y : V), R x1 y β§ S x2 y from Exists.intro y (And.intro h4 h6) | U V : Type
R S : Rel U V
X0 : Set U
x1 x2 : U
y : V
h1 : csb_match R S X0 x1 y
h2 : csb_match R S X0 x2 y
h3 : β n, x1 β rep_common_image R S X0 n
h4 : R x1 y
h5 : Β¬x2 β cum_rep_image R S X0
h6 : S x2 y
n : β
h7 : x1 β rep_common_image R S X0 n
β’ β y, R x1 y β§ S x2 y | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
U V : Type
R S : Rel U V
X0 : Set U
x1 x2 : U
y : V
h1 : csb_match R S X0 x1 y
h2 : csb_match R S X0 x2 y
h3 : β n, x1 β rep_common_image R S X0 n
h4 : R x1 y
h5 : Β¬x2 β cum_rep_image R S X0
h6 : S x2 y
n : β
h7 : x1 β rep_common_image R S X0 n
β’ β y, R x1 y ... |
https://github.com/djvelleman/HTPILeanPackage.git | 4d23e94fff351c65b5e1345c43451f2aa9908c27 | HTPILib/Chap8Part2.lean | HTPI.Cantor_Schroeder_Bernstein_theorem | [1559, 1] | [1718, 7] | obtain (R : Rel U V) (R_match_AD : matching R A D) from h3 | U V : Type
A C : Set U
B D : Set V
h1 : C β A
h2 : D β B
h3 : A βΌ D
h4 : C βΌ B
β’ A βΌ B | U V : Type
A C : Set U
B D : Set V
h1 : C β A
h2 : D β B
h3 : A βΌ D
h4 : C βΌ B
R : Rel U V
R_match_AD : matching R A D
β’ A βΌ B | Please generate a tactic in lean4 to solve the state.
STATE:
U V : Type
A C : Set U
B D : Set V
h1 : C β A
h2 : D β B
h3 : A βΌ D
h4 : C βΌ B
β’ A βΌ B
TACTIC:
|
https://github.com/djvelleman/HTPILeanPackage.git | 4d23e94fff351c65b5e1345c43451f2aa9908c27 | HTPILib/Chap8Part2.lean | HTPI.Cantor_Schroeder_Bernstein_theorem | [1559, 1] | [1718, 7] | obtain (S : Rel U V) (S_match_CB : matching S C B) from h4 | U V : Type
A C : Set U
B D : Set V
h1 : C β A
h2 : D β B
h3 : A βΌ D
h4 : C βΌ B
R : Rel U V
R_match_AD : matching R A D
β’ A βΌ B | U V : Type
A C : Set U
B D : Set V
h1 : C β A
h2 : D β B
h3 : A βΌ D
h4 : C βΌ B
R : Rel U V
R_match_AD : matching R A D
S : Rel U V
S_match_CB : matching S C B
β’ A βΌ B | Please generate a tactic in lean4 to solve the state.
STATE:
U V : Type
A C : Set U
B D : Set V
h1 : C β A
h2 : D β B
h3 : A βΌ D
h4 : C βΌ B
R : Rel U V
R_match_AD : matching R A D
β’ A βΌ B
TACTIC:
|
https://github.com/djvelleman/HTPILeanPackage.git | 4d23e94fff351c65b5e1345c43451f2aa9908c27 | HTPILib/Chap8Part2.lean | HTPI.Cantor_Schroeder_Bernstein_theorem | [1559, 1] | [1718, 7] | define at R_match_AD | U V : Type
A C : Set U
B D : Set V
h1 : C β A
h2 : D β B
h3 : A βΌ D
h4 : C βΌ B
R : Rel U V
R_match_AD : matching R A D
S : Rel U V
S_match_CB : matching S C B
β’ A βΌ B | U V : Type
A C : Set U
B D : Set V
h1 : C β A
h2 : D β B
h3 : A βΌ D
h4 : C βΌ B
R : Rel U V
R_match_AD : rel_within R A D β§ fcnl_on R A β§ fcnl_on (invRel R) D
S : Rel U V
S_match_CB : matching S C B
β’ A βΌ B | Please generate a tactic in lean4 to solve the state.
STATE:
U V : Type
A C : Set U
B D : Set V
h1 : C β A
h2 : D β B
h3 : A βΌ D
h4 : C βΌ B
R : Rel U V
R_match_AD : matching R A D
S : Rel U V
S_match_CB : matching S C B
β’ A βΌ B
TACTIC:
|
https://github.com/djvelleman/HTPILeanPackage.git | 4d23e94fff351c65b5e1345c43451f2aa9908c27 | HTPILib/Chap8Part2.lean | HTPI.Cantor_Schroeder_Bernstein_theorem | [1559, 1] | [1718, 7] | define at S_match_CB | U V : Type
A C : Set U
B D : Set V
h1 : C β A
h2 : D β B
h3 : A βΌ D
h4 : C βΌ B
R : Rel U V
R_match_AD : rel_within R A D β§ fcnl_on R A β§ fcnl_on (invRel R) D
S : Rel U V
S_match_CB : matching S C B
β’ A βΌ B | U V : Type
A C : Set U
B D : Set V
h1 : C β A
h2 : D β B
h3 : A βΌ D
h4 : C βΌ B
R : Rel U V
R_match_AD : rel_within R A D β§ fcnl_on R A β§ fcnl_on (invRel R) D
S : Rel U V
S_match_CB : rel_within S C B β§ fcnl_on S C β§ fcnl_on (invRel S) B
β’ A βΌ B | Please generate a tactic in lean4 to solve the state.
STATE:
U V : Type
A C : Set U
B D : Set V
h1 : C β A
h2 : D β B
h3 : A βΌ D
h4 : C βΌ B
R : Rel U V
R_match_AD : rel_within R A D β§ fcnl_on R A β§ fcnl_on (invRel R) D
S : Rel U V
S_match_CB : matching S C B
β’ A βΌ B
TACTIC:
|
https://github.com/djvelleman/HTPILeanPackage.git | 4d23e94fff351c65b5e1345c43451f2aa9908c27 | HTPILib/Chap8Part2.lean | HTPI.Cantor_Schroeder_Bernstein_theorem | [1559, 1] | [1718, 7] | set X0 : Set U := A \ C | U V : Type
A C : Set U
B D : Set V
h1 : C β A
h2 : D β B
h3 : A βΌ D
h4 : C βΌ B
R : Rel U V
R_match_AD : rel_within R A D β§ fcnl_on R A β§ fcnl_on (invRel R) D
S : Rel U V
S_match_CB : rel_within S C B β§ fcnl_on S C β§ fcnl_on (invRel S) B
β’ A βΌ B | U V : Type
A C : Set U
B D : Set V
h1 : C β A
h2 : D β B
h3 : A βΌ D
h4 : C βΌ B
R : Rel U V
R_match_AD : rel_within R A D β§ fcnl_on R A β§ fcnl_on (invRel R) D
S : Rel U V
S_match_CB : rel_within S C B β§ fcnl_on S C β§ fcnl_on (invRel S) B
X0 : Set U := A \ C
β’ A βΌ B | Please generate a tactic in lean4 to solve the state.
STATE:
U V : Type
A C : Set U
B D : Set V
h1 : C β A
h2 : D β B
h3 : A βΌ D
h4 : C βΌ B
R : Rel U V
R_match_AD : rel_within R A D β§ fcnl_on R A β§ fcnl_on (invRel R) D
S : Rel U V
S_match_CB : rel_within S C B β§ fcnl_on S C β§ fcnl_on (invRel S) B
β’ A βΌ B
TACTIC:
|
https://github.com/djvelleman/HTPILeanPackage.git | 4d23e94fff351c65b5e1345c43451f2aa9908c27 | HTPILib/Chap8Part2.lean | HTPI.Cantor_Schroeder_Bernstein_theorem | [1559, 1] | [1718, 7] | set X : Set U := cum_rep_image R S X0 | U V : Type
A C : Set U
B D : Set V
h1 : C β A
h2 : D β B
h3 : A βΌ D
h4 : C βΌ B
R : Rel U V
R_match_AD : rel_within R A D β§ fcnl_on R A β§ fcnl_on (invRel R) D
S : Rel U V
S_match_CB : rel_within S C B β§ fcnl_on S C β§ fcnl_on (invRel S) B
X0 : Set U := A \ C
β’ A βΌ B | U V : Type
A C : Set U
B D : Set V
h1 : C β A
h2 : D β B
h3 : A βΌ D
h4 : C βΌ B
R : Rel U V
R_match_AD : rel_within R A D β§ fcnl_on R A β§ fcnl_on (invRel R) D
S : Rel U V
S_match_CB : rel_within S C B β§ fcnl_on S C β§ fcnl_on (invRel S) B
X0 : Set U := A \ C
X : Set U := cum_rep_image R S X0
β’ A βΌ B | Please generate a tactic in lean4 to solve the state.
STATE:
U V : Type
A C : Set U
B D : Set V
h1 : C β A
h2 : D β B
h3 : A βΌ D
h4 : C βΌ B
R : Rel U V
R_match_AD : rel_within R A D β§ fcnl_on R A β§ fcnl_on (invRel R) D
S : Rel U V
S_match_CB : rel_within S C B β§ fcnl_on S C β§ fcnl_on (invRel S) B
X0 : Set U := A \ C
β’ ... |
https://github.com/djvelleman/HTPILeanPackage.git | 4d23e94fff351c65b5e1345c43451f2aa9908c27 | HTPILib/Chap8Part2.lean | HTPI.Cantor_Schroeder_Bernstein_theorem | [1559, 1] | [1718, 7] | set T : Rel U V := csb_match R S X0 | U V : Type
A C : Set U
B D : Set V
h1 : C β A
h2 : D β B
h3 : A βΌ D
h4 : C βΌ B
R : Rel U V
R_match_AD : rel_within R A D β§ fcnl_on R A β§ fcnl_on (invRel R) D
S : Rel U V
S_match_CB : rel_within S C B β§ fcnl_on S C β§ fcnl_on (invRel S) B
X0 : Set U := A \ C
X : Set U := cum_rep_image R S X0
β’ A βΌ B | U V : Type
A C : Set U
B D : Set V
h1 : C β A
h2 : D β B
h3 : A βΌ D
h4 : C βΌ B
R : Rel U V
R_match_AD : rel_within R A D β§ fcnl_on R A β§ fcnl_on (invRel R) D
S : Rel U V
S_match_CB : rel_within S C B β§ fcnl_on S C β§ fcnl_on (invRel S) B
X0 : Set U := A \ C
X : Set U := cum_rep_image R S X0
T : Rel U V := csb_match R S ... | Please generate a tactic in lean4 to solve the state.
STATE:
U V : Type
A C : Set U
B D : Set V
h1 : C β A
h2 : D β B
h3 : A βΌ D
h4 : C βΌ B
R : Rel U V
R_match_AD : rel_within R A D β§ fcnl_on R A β§ fcnl_on (invRel R) D
S : Rel U V
S_match_CB : rel_within S C B β§ fcnl_on S C β§ fcnl_on (invRel S) B
X0 : Set U := A \ C
X ... |
https://github.com/djvelleman/HTPILeanPackage.git | 4d23e94fff351c65b5e1345c43451f2aa9908c27 | HTPILib/Chap8Part2.lean | HTPI.Cantor_Schroeder_Bernstein_theorem | [1559, 1] | [1718, 7] | have Tdef : β (x : U) (y : V),
T x y β (x β X β§ R x y) β¨ (x β X β§ S x y) := by
fix x : U; fix y : V
rfl
done | U V : Type
A C : Set U
B D : Set V
h1 : C β A
h2 : D β B
h3 : A βΌ D
h4 : C βΌ B
R : Rel U V
R_match_AD : rel_within R A D β§ fcnl_on R A β§ fcnl_on (invRel R) D
S : Rel U V
S_match_CB : rel_within S C B β§ fcnl_on S C β§ fcnl_on (invRel S) B
X0 : Set U := A \ C
X : Set U := cum_rep_image R S X0
T : Rel U V := csb_match R S ... | U V : Type
A C : Set U
B D : Set V
h1 : C β A
h2 : D β B
h3 : A βΌ D
h4 : C βΌ B
R : Rel U V
R_match_AD : rel_within R A D β§ fcnl_on R A β§ fcnl_on (invRel R) D
S : Rel U V
S_match_CB : rel_within S C B β§ fcnl_on S C β§ fcnl_on (invRel S) B
X0 : Set U := A \ C
X : Set U := cum_rep_image R S X0
T : Rel U V := csb_match R S ... | Please generate a tactic in lean4 to solve the state.
STATE:
U V : Type
A C : Set U
B D : Set V
h1 : C β A
h2 : D β B
h3 : A βΌ D
h4 : C βΌ B
R : Rel U V
R_match_AD : rel_within R A D β§ fcnl_on R A β§ fcnl_on (invRel R) D
S : Rel U V
S_match_CB : rel_within S C B β§ fcnl_on S C β§ fcnl_on (invRel S) B
X0 : Set U := A \ C
X ... |
https://github.com/djvelleman/HTPILeanPackage.git | 4d23e94fff351c65b5e1345c43451f2aa9908c27 | HTPILib/Chap8Part2.lean | HTPI.Cantor_Schroeder_Bernstein_theorem | [1559, 1] | [1718, 7] | have A_not_X_in_C : A \ X β C := by
fix a : U
assume h5 : a β A \ X
contradict h5.right with h6 define apply Exists.intro 0
define
show a β A β§ a β C from And.intro h5.left h6
done | U V : Type
A C : Set U
B D : Set V
h1 : C β A
h2 : D β B
h3 : A βΌ D
h4 : C βΌ B
R : Rel U V
R_match_AD : rel_within R A D β§ fcnl_on R A β§ fcnl_on (invRel R) D
S : Rel U V
S_match_CB : rel_within S C B β§ fcnl_on S C β§ fcnl_on (invRel S) B
X0 : Set U := A \ C
X : Set U := cum_rep_image R S X0
T : Rel U V := csb_match R S ... | U V : Type
A C : Set U
B D : Set V
h1 : C β A
h2 : D β B
h3 : A βΌ D
h4 : C βΌ B
R : Rel U V
R_match_AD : rel_within R A D β§ fcnl_on R A β§ fcnl_on (invRel R) D
S : Rel U V
S_match_CB : rel_within S C B β§ fcnl_on S C β§ fcnl_on (invRel S) B
X0 : Set U := A \ C
X : Set U := cum_rep_image R S X0
T : Rel U V := csb_match R S ... | Please generate a tactic in lean4 to solve the state.
STATE:
U V : Type
A C : Set U
B D : Set V
h1 : C β A
h2 : D β B
h3 : A βΌ D
h4 : C βΌ B
R : Rel U V
R_match_AD : rel_within R A D β§ fcnl_on R A β§ fcnl_on (invRel R) D
S : Rel U V
S_match_CB : rel_within S C B β§ fcnl_on S C β§ fcnl_on (invRel S) B
X0 : Set U := A \ C
X ... |
https://github.com/djvelleman/HTPILeanPackage.git | 4d23e94fff351c65b5e1345c43451f2aa9908c27 | HTPILib/Chap8Part2.lean | HTPI.Cantor_Schroeder_Bernstein_theorem | [1559, 1] | [1718, 7] | define | U V : Type
A C : Set U
B D : Set V
h1 : C β A
h2 : D β B
h3 : A βΌ D
h4 : C βΌ B
R : Rel U V
R_match_AD : rel_within R A D β§ fcnl_on R A β§ fcnl_on (invRel R) D
S : Rel U V
S_match_CB : rel_within S C B β§ fcnl_on S C β§ fcnl_on (invRel S) B
X0 : Set U := A \ C
X : Set U := cum_rep_image R S X0
T : Rel U V := csb_match R S ... | U V : Type
A C : Set U
B D : Set V
h1 : C β A
h2 : D β B
h3 : A βΌ D
h4 : C βΌ B
R : Rel U V
R_match_AD : rel_within R A D β§ fcnl_on R A β§ fcnl_on (invRel R) D
S : Rel U V
S_match_CB : rel_within S C B β§ fcnl_on S C β§ fcnl_on (invRel S) B
X0 : Set U := A \ C
X : Set U := cum_rep_image R S X0
T : Rel U V := csb_match R S ... | Please generate a tactic in lean4 to solve the state.
STATE:
U V : Type
A C : Set U
B D : Set V
h1 : C β A
h2 : D β B
h3 : A βΌ D
h4 : C βΌ B
R : Rel U V
R_match_AD : rel_within R A D β§ fcnl_on R A β§ fcnl_on (invRel R) D
S : Rel U V
S_match_CB : rel_within S C B β§ fcnl_on S C β§ fcnl_on (invRel S) B
X0 : Set U := A \ C
X ... |
https://github.com/djvelleman/HTPILeanPackage.git | 4d23e94fff351c65b5e1345c43451f2aa9908c27 | HTPILib/Chap8Part2.lean | HTPI.Cantor_Schroeder_Bernstein_theorem | [1559, 1] | [1718, 7] | apply Exists.intro T | U V : Type
A C : Set U
B D : Set V
h1 : C β A
h2 : D β B
h3 : A βΌ D
h4 : C βΌ B
R : Rel U V
R_match_AD : rel_within R A D β§ fcnl_on R A β§ fcnl_on (invRel R) D
S : Rel U V
S_match_CB : rel_within S C B β§ fcnl_on S C β§ fcnl_on (invRel S) B
X0 : Set U := A \ C
X : Set U := cum_rep_image R S X0
T : Rel U V := csb_match R S ... | U V : Type
A C : Set U
B D : Set V
h1 : C β A
h2 : D β B
h3 : A βΌ D
h4 : C βΌ B
R : Rel U V
R_match_AD : rel_within R A D β§ fcnl_on R A β§ fcnl_on (invRel R) D
S : Rel U V
S_match_CB : rel_within S C B β§ fcnl_on S C β§ fcnl_on (invRel S) B
X0 : Set U := A \ C
X : Set U := cum_rep_image R S X0
T : Rel U V := csb_match R S ... | Please generate a tactic in lean4 to solve the state.
STATE:
U V : Type
A C : Set U
B D : Set V
h1 : C β A
h2 : D β B
h3 : A βΌ D
h4 : C βΌ B
R : Rel U V
R_match_AD : rel_within R A D β§ fcnl_on R A β§ fcnl_on (invRel R) D
S : Rel U V
S_match_CB : rel_within S C B β§ fcnl_on S C β§ fcnl_on (invRel S) B
X0 : Set U := A \ C
X ... |
https://github.com/djvelleman/HTPILeanPackage.git | 4d23e94fff351c65b5e1345c43451f2aa9908c27 | HTPILib/Chap8Part2.lean | HTPI.Cantor_Schroeder_Bernstein_theorem | [1559, 1] | [1718, 7] | define | U V : Type
A C : Set U
B D : Set V
h1 : C β A
h2 : D β B
h3 : A βΌ D
h4 : C βΌ B
R : Rel U V
R_match_AD : rel_within R A D β§ fcnl_on R A β§ fcnl_on (invRel R) D
S : Rel U V
S_match_CB : rel_within S C B β§ fcnl_on S C β§ fcnl_on (invRel S) B
X0 : Set U := A \ C
X : Set U := cum_rep_image R S X0
T : Rel U V := csb_match R S ... | U V : Type
A C : Set U
B D : Set V
h1 : C β A
h2 : D β B
h3 : A βΌ D
h4 : C βΌ B
R : Rel U V
R_match_AD : rel_within R A D β§ fcnl_on R A β§ fcnl_on (invRel R) D
S : Rel U V
S_match_CB : rel_within S C B β§ fcnl_on S C β§ fcnl_on (invRel S) B
X0 : Set U := A \ C
X : Set U := cum_rep_image R S X0
T : Rel U V := csb_match R S ... | Please generate a tactic in lean4 to solve the state.
STATE:
U V : Type
A C : Set U
B D : Set V
h1 : C β A
h2 : D β B
h3 : A βΌ D
h4 : C βΌ B
R : Rel U V
R_match_AD : rel_within R A D β§ fcnl_on R A β§ fcnl_on (invRel R) D
S : Rel U V
S_match_CB : rel_within S C B β§ fcnl_on S C β§ fcnl_on (invRel S) B
X0 : Set U := A \ C
X ... |
https://github.com/djvelleman/HTPILeanPackage.git | 4d23e94fff351c65b5e1345c43451f2aa9908c27 | HTPILib/Chap8Part2.lean | HTPI.Cantor_Schroeder_Bernstein_theorem | [1559, 1] | [1718, 7] | apply And.intro | U V : Type
A C : Set U
B D : Set V
h1 : C β A
h2 : D β B
h3 : A βΌ D
h4 : C βΌ B
R : Rel U V
R_match_AD : rel_within R A D β§ fcnl_on R A β§ fcnl_on (invRel R) D
S : Rel U V
S_match_CB : rel_within S C B β§ fcnl_on S C β§ fcnl_on (invRel S) B
X0 : Set U := A \ C
X : Set U := cum_rep_image R S X0
T : Rel U V := csb_match R S ... | case left
U V : Type
A C : Set U
B D : Set V
h1 : C β A
h2 : D β B
h3 : A βΌ D
h4 : C βΌ B
R : Rel U V
R_match_AD : rel_within R A D β§ fcnl_on R A β§ fcnl_on (invRel R) D
S : Rel U V
S_match_CB : rel_within S C B β§ fcnl_on S C β§ fcnl_on (invRel S) B
X0 : Set U := A \ C
X : Set U := cum_rep_image R S X0
T : Rel U V := csb_... | Please generate a tactic in lean4 to solve the state.
STATE:
U V : Type
A C : Set U
B D : Set V
h1 : C β A
h2 : D β B
h3 : A βΌ D
h4 : C βΌ B
R : Rel U V
R_match_AD : rel_within R A D β§ fcnl_on R A β§ fcnl_on (invRel R) D
S : Rel U V
S_match_CB : rel_within S C B β§ fcnl_on S C β§ fcnl_on (invRel S) B
X0 : Set U := A \ C
X ... |
https://github.com/djvelleman/HTPILeanPackage.git | 4d23e94fff351c65b5e1345c43451f2aa9908c27 | HTPILib/Chap8Part2.lean | HTPI.Cantor_Schroeder_Bernstein_theorem | [1559, 1] | [1718, 7] | fix x : U | U V : Type
A C : Set U
B D : Set V
h1 : C β A
h2 : D β B
h3 : A βΌ D
h4 : C βΌ B
R : Rel U V
R_match_AD : rel_within R A D β§ fcnl_on R A β§ fcnl_on (invRel R) D
S : Rel U V
S_match_CB : rel_within S C B β§ fcnl_on S C β§ fcnl_on (invRel S) B
X0 : Set U := A \ C
X : Set U := cum_rep_image R S X0
T : Rel U V := csb_match R S ... | U V : Type
A C : Set U
B D : Set V
h1 : C β A
h2 : D β B
h3 : A βΌ D
h4 : C βΌ B
R : Rel U V
R_match_AD : rel_within R A D β§ fcnl_on R A β§ fcnl_on (invRel R) D
S : Rel U V
S_match_CB : rel_within S C B β§ fcnl_on S C β§ fcnl_on (invRel S) B
X0 : Set U := A \ C
X : Set U := cum_rep_image R S X0
T : Rel U V := csb_match R S ... | Please generate a tactic in lean4 to solve the state.
STATE:
U V : Type
A C : Set U
B D : Set V
h1 : C β A
h2 : D β B
h3 : A βΌ D
h4 : C βΌ B
R : Rel U V
R_match_AD : rel_within R A D β§ fcnl_on R A β§ fcnl_on (invRel R) D
S : Rel U V
S_match_CB : rel_within S C B β§ fcnl_on S C β§ fcnl_on (invRel S) B
X0 : Set U := A \ C
X ... |
https://github.com/djvelleman/HTPILeanPackage.git | 4d23e94fff351c65b5e1345c43451f2aa9908c27 | HTPILib/Chap8Part2.lean | HTPI.Cantor_Schroeder_Bernstein_theorem | [1559, 1] | [1718, 7] | fix y : V | U V : Type
A C : Set U
B D : Set V
h1 : C β A
h2 : D β B
h3 : A βΌ D
h4 : C βΌ B
R : Rel U V
R_match_AD : rel_within R A D β§ fcnl_on R A β§ fcnl_on (invRel R) D
S : Rel U V
S_match_CB : rel_within S C B β§ fcnl_on S C β§ fcnl_on (invRel S) B
X0 : Set U := A \ C
X : Set U := cum_rep_image R S X0
T : Rel U V := csb_match R S ... | U V : Type
A C : Set U
B D : Set V
h1 : C β A
h2 : D β B
h3 : A βΌ D
h4 : C βΌ B
R : Rel U V
R_match_AD : rel_within R A D β§ fcnl_on R A β§ fcnl_on (invRel R) D
S : Rel U V
S_match_CB : rel_within S C B β§ fcnl_on S C β§ fcnl_on (invRel S) B
X0 : Set U := A \ C
X : Set U := cum_rep_image R S X0
T : Rel U V := csb_match R S ... | Please generate a tactic in lean4 to solve the state.
STATE:
U V : Type
A C : Set U
B D : Set V
h1 : C β A
h2 : D β B
h3 : A βΌ D
h4 : C βΌ B
R : Rel U V
R_match_AD : rel_within R A D β§ fcnl_on R A β§ fcnl_on (invRel R) D
S : Rel U V
S_match_CB : rel_within S C B β§ fcnl_on S C β§ fcnl_on (invRel S) B
X0 : Set U := A \ C
X ... |
https://github.com/djvelleman/HTPILeanPackage.git | 4d23e94fff351c65b5e1345c43451f2aa9908c27 | HTPILib/Chap8Part2.lean | HTPI.Cantor_Schroeder_Bernstein_theorem | [1559, 1] | [1718, 7] | rfl | U V : Type
A C : Set U
B D : Set V
h1 : C β A
h2 : D β B
h3 : A βΌ D
h4 : C βΌ B
R : Rel U V
R_match_AD : rel_within R A D β§ fcnl_on R A β§ fcnl_on (invRel R) D
S : Rel U V
S_match_CB : rel_within S C B β§ fcnl_on S C β§ fcnl_on (invRel S) B
X0 : Set U := A \ C
X : Set U := cum_rep_image R S X0
T : Rel U V := csb_match R S ... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
U V : Type
A C : Set U
B D : Set V
h1 : C β A
h2 : D β B
h3 : A βΌ D
h4 : C βΌ B
R : Rel U V
R_match_AD : rel_within R A D β§ fcnl_on R A β§ fcnl_on (invRel R) D
S : Rel U V
S_match_CB : rel_within S C B β§ fcnl_on S C β§ fcnl_on (invRel S) B
X0 : Set U := A \ C
X ... |
https://github.com/djvelleman/HTPILeanPackage.git | 4d23e94fff351c65b5e1345c43451f2aa9908c27 | HTPILib/Chap8Part2.lean | HTPI.Cantor_Schroeder_Bernstein_theorem | [1559, 1] | [1718, 7] | fix a : U | U V : Type
A C : Set U
B D : Set V
h1 : C β A
h2 : D β B
h3 : A βΌ D
h4 : C βΌ B
R : Rel U V
R_match_AD : rel_within R A D β§ fcnl_on R A β§ fcnl_on (invRel R) D
S : Rel U V
S_match_CB : rel_within S C B β§ fcnl_on S C β§ fcnl_on (invRel S) B
X0 : Set U := A \ C
X : Set U := cum_rep_image R S X0
T : Rel U V := csb_match R S ... | U V : Type
A C : Set U
B D : Set V
h1 : C β A
h2 : D β B
h3 : A βΌ D
h4 : C βΌ B
R : Rel U V
R_match_AD : rel_within R A D β§ fcnl_on R A β§ fcnl_on (invRel R) D
S : Rel U V
S_match_CB : rel_within S C B β§ fcnl_on S C β§ fcnl_on (invRel S) B
X0 : Set U := A \ C
X : Set U := cum_rep_image R S X0
T : Rel U V := csb_match R S ... | Please generate a tactic in lean4 to solve the state.
STATE:
U V : Type
A C : Set U
B D : Set V
h1 : C β A
h2 : D β B
h3 : A βΌ D
h4 : C βΌ B
R : Rel U V
R_match_AD : rel_within R A D β§ fcnl_on R A β§ fcnl_on (invRel R) D
S : Rel U V
S_match_CB : rel_within S C B β§ fcnl_on S C β§ fcnl_on (invRel S) B
X0 : Set U := A \ C
X ... |
https://github.com/djvelleman/HTPILeanPackage.git | 4d23e94fff351c65b5e1345c43451f2aa9908c27 | HTPILib/Chap8Part2.lean | HTPI.Cantor_Schroeder_Bernstein_theorem | [1559, 1] | [1718, 7] | assume h5 : a β A \ X | U V : Type
A C : Set U
B D : Set V
h1 : C β A
h2 : D β B
h3 : A βΌ D
h4 : C βΌ B
R : Rel U V
R_match_AD : rel_within R A D β§ fcnl_on R A β§ fcnl_on (invRel R) D
S : Rel U V
S_match_CB : rel_within S C B β§ fcnl_on S C β§ fcnl_on (invRel S) B
X0 : Set U := A \ C
X : Set U := cum_rep_image R S X0
T : Rel U V := csb_match R S ... | U V : Type
A C : Set U
B D : Set V
h1 : C β A
h2 : D β B
h3 : A βΌ D
h4 : C βΌ B
R : Rel U V
R_match_AD : rel_within R A D β§ fcnl_on R A β§ fcnl_on (invRel R) D
S : Rel U V
S_match_CB : rel_within S C B β§ fcnl_on S C β§ fcnl_on (invRel S) B
X0 : Set U := A \ C
X : Set U := cum_rep_image R S X0
T : Rel U V := csb_match R S ... | Please generate a tactic in lean4 to solve the state.
STATE:
U V : Type
A C : Set U
B D : Set V
h1 : C β A
h2 : D β B
h3 : A βΌ D
h4 : C βΌ B
R : Rel U V
R_match_AD : rel_within R A D β§ fcnl_on R A β§ fcnl_on (invRel R) D
S : Rel U V
S_match_CB : rel_within S C B β§ fcnl_on S C β§ fcnl_on (invRel S) B
X0 : Set U := A \ C
X ... |
https://github.com/djvelleman/HTPILeanPackage.git | 4d23e94fff351c65b5e1345c43451f2aa9908c27 | HTPILib/Chap8Part2.lean | HTPI.Cantor_Schroeder_Bernstein_theorem | [1559, 1] | [1718, 7] | contradict h5.right with h6 | U V : Type
A C : Set U
B D : Set V
h1 : C β A
h2 : D β B
h3 : A βΌ D
h4 : C βΌ B
R : Rel U V
R_match_AD : rel_within R A D β§ fcnl_on R A β§ fcnl_on (invRel R) D
S : Rel U V
S_match_CB : rel_within S C B β§ fcnl_on S C β§ fcnl_on (invRel S) B
X0 : Set U := A \ C
X : Set U := cum_rep_image R S X0
T : Rel U V := csb_match R S ... | U V : Type
A C : Set U
B D : Set V
h1 : C β A
h2 : D β B
h3 : A βΌ D
h4 : C βΌ B
R : Rel U V
R_match_AD : rel_within R A D β§ fcnl_on R A β§ fcnl_on (invRel R) D
S : Rel U V
S_match_CB : rel_within S C B β§ fcnl_on S C β§ fcnl_on (invRel S) B
X0 : Set U := A \ C
X : Set U := cum_rep_image R S X0
T : Rel U V := csb_match R S ... | Please generate a tactic in lean4 to solve the state.
STATE:
U V : Type
A C : Set U
B D : Set V
h1 : C β A
h2 : D β B
h3 : A βΌ D
h4 : C βΌ B
R : Rel U V
R_match_AD : rel_within R A D β§ fcnl_on R A β§ fcnl_on (invRel R) D
S : Rel U V
S_match_CB : rel_within S C B β§ fcnl_on S C β§ fcnl_on (invRel S) B
X0 : Set U := A \ C
X ... |
https://github.com/djvelleman/HTPILeanPackage.git | 4d23e94fff351c65b5e1345c43451f2aa9908c27 | HTPILib/Chap8Part2.lean | HTPI.Cantor_Schroeder_Bernstein_theorem | [1559, 1] | [1718, 7] | define | U V : Type
A C : Set U
B D : Set V
h1 : C β A
h2 : D β B
h3 : A βΌ D
h4 : C βΌ B
R : Rel U V
R_match_AD : rel_within R A D β§ fcnl_on R A β§ fcnl_on (invRel R) D
S : Rel U V
S_match_CB : rel_within S C B β§ fcnl_on S C β§ fcnl_on (invRel S) B
X0 : Set U := A \ C
X : Set U := cum_rep_image R S X0
T : Rel U V := csb_match R S ... | U V : Type
A C : Set U
B D : Set V
h1 : C β A
h2 : D β B
h3 : A βΌ D
h4 : C βΌ B
R : Rel U V
R_match_AD : rel_within R A D β§ fcnl_on R A β§ fcnl_on (invRel R) D
S : Rel U V
S_match_CB : rel_within S C B β§ fcnl_on S C β§ fcnl_on (invRel S) B
X0 : Set U := A \ C
X : Set U := cum_rep_image R S X0
T : Rel U V := csb_match R S ... | Please generate a tactic in lean4 to solve the state.
STATE:
U V : Type
A C : Set U
B D : Set V
h1 : C β A
h2 : D β B
h3 : A βΌ D
h4 : C βΌ B
R : Rel U V
R_match_AD : rel_within R A D β§ fcnl_on R A β§ fcnl_on (invRel R) D
S : Rel U V
S_match_CB : rel_within S C B β§ fcnl_on S C β§ fcnl_on (invRel S) B
X0 : Set U := A \ C
X ... |
https://github.com/djvelleman/HTPILeanPackage.git | 4d23e94fff351c65b5e1345c43451f2aa9908c27 | HTPILib/Chap8Part2.lean | HTPI.Cantor_Schroeder_Bernstein_theorem | [1559, 1] | [1718, 7] | apply Exists.intro 0 | U V : Type
A C : Set U
B D : Set V
h1 : C β A
h2 : D β B
h3 : A βΌ D
h4 : C βΌ B
R : Rel U V
R_match_AD : rel_within R A D β§ fcnl_on R A β§ fcnl_on (invRel R) D
S : Rel U V
S_match_CB : rel_within S C B β§ fcnl_on S C β§ fcnl_on (invRel S) B
X0 : Set U := A \ C
X : Set U := cum_rep_image R S X0
T : Rel U V := csb_match R S ... | U V : Type
A C : Set U
B D : Set V
h1 : C β A
h2 : D β B
h3 : A βΌ D
h4 : C βΌ B
R : Rel U V
R_match_AD : rel_within R A D β§ fcnl_on R A β§ fcnl_on (invRel R) D
S : Rel U V
S_match_CB : rel_within S C B β§ fcnl_on S C β§ fcnl_on (invRel S) B
X0 : Set U := A \ C
X : Set U := cum_rep_image R S X0
T : Rel U V := csb_match R S ... | Please generate a tactic in lean4 to solve the state.
STATE:
U V : Type
A C : Set U
B D : Set V
h1 : C β A
h2 : D β B
h3 : A βΌ D
h4 : C βΌ B
R : Rel U V
R_match_AD : rel_within R A D β§ fcnl_on R A β§ fcnl_on (invRel R) D
S : Rel U V
S_match_CB : rel_within S C B β§ fcnl_on S C β§ fcnl_on (invRel S) B
X0 : Set U := A \ C
X ... |
https://github.com/djvelleman/HTPILeanPackage.git | 4d23e94fff351c65b5e1345c43451f2aa9908c27 | HTPILib/Chap8Part2.lean | HTPI.Cantor_Schroeder_Bernstein_theorem | [1559, 1] | [1718, 7] | define | U V : Type
A C : Set U
B D : Set V
h1 : C β A
h2 : D β B
h3 : A βΌ D
h4 : C βΌ B
R : Rel U V
R_match_AD : rel_within R A D β§ fcnl_on R A β§ fcnl_on (invRel R) D
S : Rel U V
S_match_CB : rel_within S C B β§ fcnl_on S C β§ fcnl_on (invRel S) B
X0 : Set U := A \ C
X : Set U := cum_rep_image R S X0
T : Rel U V := csb_match R S ... | U V : Type
A C : Set U
B D : Set V
h1 : C β A
h2 : D β B
h3 : A βΌ D
h4 : C βΌ B
R : Rel U V
R_match_AD : rel_within R A D β§ fcnl_on R A β§ fcnl_on (invRel R) D
S : Rel U V
S_match_CB : rel_within S C B β§ fcnl_on S C β§ fcnl_on (invRel S) B
X0 : Set U := A \ C
X : Set U := cum_rep_image R S X0
T : Rel U V := csb_match R S ... | Please generate a tactic in lean4 to solve the state.
STATE:
U V : Type
A C : Set U
B D : Set V
h1 : C β A
h2 : D β B
h3 : A βΌ D
h4 : C βΌ B
R : Rel U V
R_match_AD : rel_within R A D β§ fcnl_on R A β§ fcnl_on (invRel R) D
S : Rel U V
S_match_CB : rel_within S C B β§ fcnl_on S C β§ fcnl_on (invRel S) B
X0 : Set U := A \ C
X ... |
https://github.com/djvelleman/HTPILeanPackage.git | 4d23e94fff351c65b5e1345c43451f2aa9908c27 | HTPILib/Chap8Part2.lean | HTPI.Cantor_Schroeder_Bernstein_theorem | [1559, 1] | [1718, 7] | show a β A β§ a β C from And.intro h5.left h6 | U V : Type
A C : Set U
B D : Set V
h1 : C β A
h2 : D β B
h3 : A βΌ D
h4 : C βΌ B
R : Rel U V
R_match_AD : rel_within R A D β§ fcnl_on R A β§ fcnl_on (invRel R) D
S : Rel U V
S_match_CB : rel_within S C B β§ fcnl_on S C β§ fcnl_on (invRel S) B
X0 : Set U := A \ C
X : Set U := cum_rep_image R S X0
T : Rel U V := csb_match R S ... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
U V : Type
A C : Set U
B D : Set V
h1 : C β A
h2 : D β B
h3 : A βΌ D
h4 : C βΌ B
R : Rel U V
R_match_AD : rel_within R A D β§ fcnl_on R A β§ fcnl_on (invRel R) D
S : Rel U V
S_match_CB : rel_within S C B β§ fcnl_on S C β§ fcnl_on (invRel S) B
X0 : Set U := A \ C
X ... |
https://github.com/djvelleman/HTPILeanPackage.git | 4d23e94fff351c65b5e1345c43451f2aa9908c27 | HTPILib/Chap8Part2.lean | HTPI.Cantor_Schroeder_Bernstein_theorem | [1559, 1] | [1718, 7] | define | case left
U V : Type
A C : Set U
B D : Set V
h1 : C β A
h2 : D β B
h3 : A βΌ D
h4 : C βΌ B
R : Rel U V
R_match_AD : rel_within R A D β§ fcnl_on R A β§ fcnl_on (invRel R) D
S : Rel U V
S_match_CB : rel_within S C B β§ fcnl_on S C β§ fcnl_on (invRel S) B
X0 : Set U := A \ C
X : Set U := cum_rep_image R S X0
T : Rel U V := csb_... | case left
U V : Type
A C : Set U
B D : Set V
h1 : C β A
h2 : D β B
h3 : A βΌ D
h4 : C βΌ B
R : Rel U V
R_match_AD : rel_within R A D β§ fcnl_on R A β§ fcnl_on (invRel R) D
S : Rel U V
S_match_CB : rel_within S C B β§ fcnl_on S C β§ fcnl_on (invRel S) B
X0 : Set U := A \ C
X : Set U := cum_rep_image R S X0
T : Rel U V := csb_... | Please generate a tactic in lean4 to solve the state.
STATE:
case left
U V : Type
A C : Set U
B D : Set V
h1 : C β A
h2 : D β B
h3 : A βΌ D
h4 : C βΌ B
R : Rel U V
R_match_AD : rel_within R A D β§ fcnl_on R A β§ fcnl_on (invRel R) D
S : Rel U V
S_match_CB : rel_within S C B β§ fcnl_on S C β§ fcnl_on (invRel S) B
X0 : Set U :... |
https://github.com/djvelleman/HTPILeanPackage.git | 4d23e94fff351c65b5e1345c43451f2aa9908c27 | HTPILib/Chap8Part2.lean | HTPI.Cantor_Schroeder_Bernstein_theorem | [1559, 1] | [1718, 7] | fix a : U | case left
U V : Type
A C : Set U
B D : Set V
h1 : C β A
h2 : D β B
h3 : A βΌ D
h4 : C βΌ B
R : Rel U V
R_match_AD : rel_within R A D β§ fcnl_on R A β§ fcnl_on (invRel R) D
S : Rel U V
S_match_CB : rel_within S C B β§ fcnl_on S C β§ fcnl_on (invRel S) B
X0 : Set U := A \ C
X : Set U := cum_rep_image R S X0
T : Rel U V := csb_... | case left
U V : Type
A C : Set U
B D : Set V
h1 : C β A
h2 : D β B
h3 : A βΌ D
h4 : C βΌ B
R : Rel U V
R_match_AD : rel_within R A D β§ fcnl_on R A β§ fcnl_on (invRel R) D
S : Rel U V
S_match_CB : rel_within S C B β§ fcnl_on S C β§ fcnl_on (invRel S) B
X0 : Set U := A \ C
X : Set U := cum_rep_image R S X0
T : Rel U V := csb_... | Please generate a tactic in lean4 to solve the state.
STATE:
case left
U V : Type
A C : Set U
B D : Set V
h1 : C β A
h2 : D β B
h3 : A βΌ D
h4 : C βΌ B
R : Rel U V
R_match_AD : rel_within R A D β§ fcnl_on R A β§ fcnl_on (invRel R) D
S : Rel U V
S_match_CB : rel_within S C B β§ fcnl_on S C β§ fcnl_on (invRel S) B
X0 : Set U :... |
https://github.com/djvelleman/HTPILeanPackage.git | 4d23e94fff351c65b5e1345c43451f2aa9908c27 | HTPILib/Chap8Part2.lean | HTPI.Cantor_Schroeder_Bernstein_theorem | [1559, 1] | [1718, 7] | fix b : V | case left
U V : Type
A C : Set U
B D : Set V
h1 : C β A
h2 : D β B
h3 : A βΌ D
h4 : C βΌ B
R : Rel U V
R_match_AD : rel_within R A D β§ fcnl_on R A β§ fcnl_on (invRel R) D
S : Rel U V
S_match_CB : rel_within S C B β§ fcnl_on S C β§ fcnl_on (invRel S) B
X0 : Set U := A \ C
X : Set U := cum_rep_image R S X0
T : Rel U V := csb_... | case left
U V : Type
A C : Set U
B D : Set V
h1 : C β A
h2 : D β B
h3 : A βΌ D
h4 : C βΌ B
R : Rel U V
R_match_AD : rel_within R A D β§ fcnl_on R A β§ fcnl_on (invRel R) D
S : Rel U V
S_match_CB : rel_within S C B β§ fcnl_on S C β§ fcnl_on (invRel S) B
X0 : Set U := A \ C
X : Set U := cum_rep_image R S X0
T : Rel U V := csb_... | Please generate a tactic in lean4 to solve the state.
STATE:
case left
U V : Type
A C : Set U
B D : Set V
h1 : C β A
h2 : D β B
h3 : A βΌ D
h4 : C βΌ B
R : Rel U V
R_match_AD : rel_within R A D β§ fcnl_on R A β§ fcnl_on (invRel R) D
S : Rel U V
S_match_CB : rel_within S C B β§ fcnl_on S C β§ fcnl_on (invRel S) B
X0 : Set U :... |
https://github.com/djvelleman/HTPILeanPackage.git | 4d23e94fff351c65b5e1345c43451f2aa9908c27 | HTPILib/Chap8Part2.lean | HTPI.Cantor_Schroeder_Bernstein_theorem | [1559, 1] | [1718, 7] | assume h5 : T a b | case left
U V : Type
A C : Set U
B D : Set V
h1 : C β A
h2 : D β B
h3 : A βΌ D
h4 : C βΌ B
R : Rel U V
R_match_AD : rel_within R A D β§ fcnl_on R A β§ fcnl_on (invRel R) D
S : Rel U V
S_match_CB : rel_within S C B β§ fcnl_on S C β§ fcnl_on (invRel S) B
X0 : Set U := A \ C
X : Set U := cum_rep_image R S X0
T : Rel U V := csb_... | case left
U V : Type
A C : Set U
B D : Set V
h1 : C β A
h2 : D β B
h3 : A βΌ D
h4 : C βΌ B
R : Rel U V
R_match_AD : rel_within R A D β§ fcnl_on R A β§ fcnl_on (invRel R) D
S : Rel U V
S_match_CB : rel_within S C B β§ fcnl_on S C β§ fcnl_on (invRel S) B
X0 : Set U := A \ C
X : Set U := cum_rep_image R S X0
T : Rel U V := csb_... | Please generate a tactic in lean4 to solve the state.
STATE:
case left
U V : Type
A C : Set U
B D : Set V
h1 : C β A
h2 : D β B
h3 : A βΌ D
h4 : C βΌ B
R : Rel U V
R_match_AD : rel_within R A D β§ fcnl_on R A β§ fcnl_on (invRel R) D
S : Rel U V
S_match_CB : rel_within S C B β§ fcnl_on S C β§ fcnl_on (invRel S) B
X0 : Set U :... |
https://github.com/djvelleman/HTPILeanPackage.git | 4d23e94fff351c65b5e1345c43451f2aa9908c27 | HTPILib/Chap8Part2.lean | HTPI.Cantor_Schroeder_Bernstein_theorem | [1559, 1] | [1718, 7] | rewrite [Tdef] at h5 | case left
U V : Type
A C : Set U
B D : Set V
h1 : C β A
h2 : D β B
h3 : A βΌ D
h4 : C βΌ B
R : Rel U V
R_match_AD : rel_within R A D β§ fcnl_on R A β§ fcnl_on (invRel R) D
S : Rel U V
S_match_CB : rel_within S C B β§ fcnl_on S C β§ fcnl_on (invRel S) B
X0 : Set U := A \ C
X : Set U := cum_rep_image R S X0
T : Rel U V := csb_... | case left
U V : Type
A C : Set U
B D : Set V
h1 : C β A
h2 : D β B
h3 : A βΌ D
h4 : C βΌ B
R : Rel U V
R_match_AD : rel_within R A D β§ fcnl_on R A β§ fcnl_on (invRel R) D
S : Rel U V
S_match_CB : rel_within S C B β§ fcnl_on S C β§ fcnl_on (invRel S) B
X0 : Set U := A \ C
X : Set U := cum_rep_image R S X0
T : Rel U V := csb_... | Please generate a tactic in lean4 to solve the state.
STATE:
case left
U V : Type
A C : Set U
B D : Set V
h1 : C β A
h2 : D β B
h3 : A βΌ D
h4 : C βΌ B
R : Rel U V
R_match_AD : rel_within R A D β§ fcnl_on R A β§ fcnl_on (invRel R) D
S : Rel U V
S_match_CB : rel_within S C B β§ fcnl_on S C β§ fcnl_on (invRel S) B
X0 : Set U :... |
https://github.com/djvelleman/HTPILeanPackage.git | 4d23e94fff351c65b5e1345c43451f2aa9908c27 | HTPILib/Chap8Part2.lean | HTPI.Cantor_Schroeder_Bernstein_theorem | [1559, 1] | [1718, 7] | by_cases on h5 | case left
U V : Type
A C : Set U
B D : Set V
h1 : C β A
h2 : D β B
h3 : A βΌ D
h4 : C βΌ B
R : Rel U V
R_match_AD : rel_within R A D β§ fcnl_on R A β§ fcnl_on (invRel R) D
S : Rel U V
S_match_CB : rel_within S C B β§ fcnl_on S C β§ fcnl_on (invRel S) B
X0 : Set U := A \ C
X : Set U := cum_rep_image R S X0
T : Rel U V := csb_... | case left.Case_1
U V : Type
A C : Set U
B D : Set V
h1 : C β A
h2 : D β B
h3 : A βΌ D
h4 : C βΌ B
R : Rel U V
R_match_AD : rel_within R A D β§ fcnl_on R A β§ fcnl_on (invRel R) D
S : Rel U V
S_match_CB : rel_within S C B β§ fcnl_on S C β§ fcnl_on (invRel S) B
X0 : Set U := A \ C
X : Set U := cum_rep_image R S X0
T : Rel U V ... | Please generate a tactic in lean4 to solve the state.
STATE:
case left
U V : Type
A C : Set U
B D : Set V
h1 : C β A
h2 : D β B
h3 : A βΌ D
h4 : C βΌ B
R : Rel U V
R_match_AD : rel_within R A D β§ fcnl_on R A β§ fcnl_on (invRel R) D
S : Rel U V
S_match_CB : rel_within S C B β§ fcnl_on S C β§ fcnl_on (invRel S) B
X0 : Set U :... |
https://github.com/djvelleman/HTPILeanPackage.git | 4d23e94fff351c65b5e1345c43451f2aa9908c27 | HTPILib/Chap8Part2.lean | HTPI.Cantor_Schroeder_Bernstein_theorem | [1559, 1] | [1718, 7] | have h6 : a β A β§ b β D := R_match_AD.left h5.right | case left.Case_1
U V : Type
A C : Set U
B D : Set V
h1 : C β A
h2 : D β B
h3 : A βΌ D
h4 : C βΌ B
R : Rel U V
R_match_AD : rel_within R A D β§ fcnl_on R A β§ fcnl_on (invRel R) D
S : Rel U V
S_match_CB : rel_within S C B β§ fcnl_on S C β§ fcnl_on (invRel S) B
X0 : Set U := A \ C
X : Set U := cum_rep_image R S X0
T : Rel U V ... | case left.Case_1
U V : Type
A C : Set U
B D : Set V
h1 : C β A
h2 : D β B
h3 : A βΌ D
h4 : C βΌ B
R : Rel U V
R_match_AD : rel_within R A D β§ fcnl_on R A β§ fcnl_on (invRel R) D
S : Rel U V
S_match_CB : rel_within S C B β§ fcnl_on S C β§ fcnl_on (invRel S) B
X0 : Set U := A \ C
X : Set U := cum_rep_image R S X0
T : Rel U V ... | Please generate a tactic in lean4 to solve the state.
STATE:
case left.Case_1
U V : Type
A C : Set U
B D : Set V
h1 : C β A
h2 : D β B
h3 : A βΌ D
h4 : C βΌ B
R : Rel U V
R_match_AD : rel_within R A D β§ fcnl_on R A β§ fcnl_on (invRel R) D
S : Rel U V
S_match_CB : rel_within S C B β§ fcnl_on S C β§ fcnl_on (invRel S) B
X0 : ... |
https://github.com/djvelleman/HTPILeanPackage.git | 4d23e94fff351c65b5e1345c43451f2aa9908c27 | HTPILib/Chap8Part2.lean | HTPI.Cantor_Schroeder_Bernstein_theorem | [1559, 1] | [1718, 7] | show a β A β§ b β B from And.intro h6.left (h2 h6.right) | case left.Case_1
U V : Type
A C : Set U
B D : Set V
h1 : C β A
h2 : D β B
h3 : A βΌ D
h4 : C βΌ B
R : Rel U V
R_match_AD : rel_within R A D β§ fcnl_on R A β§ fcnl_on (invRel R) D
S : Rel U V
S_match_CB : rel_within S C B β§ fcnl_on S C β§ fcnl_on (invRel S) B
X0 : Set U := A \ C
X : Set U := cum_rep_image R S X0
T : Rel U V ... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case left.Case_1
U V : Type
A C : Set U
B D : Set V
h1 : C β A
h2 : D β B
h3 : A βΌ D
h4 : C βΌ B
R : Rel U V
R_match_AD : rel_within R A D β§ fcnl_on R A β§ fcnl_on (invRel R) D
S : Rel U V
S_match_CB : rel_within S C B β§ fcnl_on S C β§ fcnl_on (invRel S) B
X0 : ... |
https://github.com/djvelleman/HTPILeanPackage.git | 4d23e94fff351c65b5e1345c43451f2aa9908c27 | HTPILib/Chap8Part2.lean | HTPI.Cantor_Schroeder_Bernstein_theorem | [1559, 1] | [1718, 7] | have h6 : a β C β§ b β B := S_match_CB.left h5.right | case left.Case_2
U V : Type
A C : Set U
B D : Set V
h1 : C β A
h2 : D β B
h3 : A βΌ D
h4 : C βΌ B
R : Rel U V
R_match_AD : rel_within R A D β§ fcnl_on R A β§ fcnl_on (invRel R) D
S : Rel U V
S_match_CB : rel_within S C B β§ fcnl_on S C β§ fcnl_on (invRel S) B
X0 : Set U := A \ C
X : Set U := cum_rep_image R S X0
T : Rel U V ... | case left.Case_2
U V : Type
A C : Set U
B D : Set V
h1 : C β A
h2 : D β B
h3 : A βΌ D
h4 : C βΌ B
R : Rel U V
R_match_AD : rel_within R A D β§ fcnl_on R A β§ fcnl_on (invRel R) D
S : Rel U V
S_match_CB : rel_within S C B β§ fcnl_on S C β§ fcnl_on (invRel S) B
X0 : Set U := A \ C
X : Set U := cum_rep_image R S X0
T : Rel U V ... | Please generate a tactic in lean4 to solve the state.
STATE:
case left.Case_2
U V : Type
A C : Set U
B D : Set V
h1 : C β A
h2 : D β B
h3 : A βΌ D
h4 : C βΌ B
R : Rel U V
R_match_AD : rel_within R A D β§ fcnl_on R A β§ fcnl_on (invRel R) D
S : Rel U V
S_match_CB : rel_within S C B β§ fcnl_on S C β§ fcnl_on (invRel S) B
X0 : ... |
https://github.com/djvelleman/HTPILeanPackage.git | 4d23e94fff351c65b5e1345c43451f2aa9908c27 | HTPILib/Chap8Part2.lean | HTPI.Cantor_Schroeder_Bernstein_theorem | [1559, 1] | [1718, 7] | show a β A β§ b β B from And.intro (h1 h6.left) h6.right | case left.Case_2
U V : Type
A C : Set U
B D : Set V
h1 : C β A
h2 : D β B
h3 : A βΌ D
h4 : C βΌ B
R : Rel U V
R_match_AD : rel_within R A D β§ fcnl_on R A β§ fcnl_on (invRel R) D
S : Rel U V
S_match_CB : rel_within S C B β§ fcnl_on S C β§ fcnl_on (invRel S) B
X0 : Set U := A \ C
X : Set U := cum_rep_image R S X0
T : Rel U V ... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case left.Case_2
U V : Type
A C : Set U
B D : Set V
h1 : C β A
h2 : D β B
h3 : A βΌ D
h4 : C βΌ B
R : Rel U V
R_match_AD : rel_within R A D β§ fcnl_on R A β§ fcnl_on (invRel R) D
S : Rel U V
S_match_CB : rel_within S C B β§ fcnl_on S C β§ fcnl_on (invRel S) B
X0 : ... |
https://github.com/djvelleman/HTPILeanPackage.git | 4d23e94fff351c65b5e1345c43451f2aa9908c27 | HTPILib/Chap8Part2.lean | HTPI.Cantor_Schroeder_Bernstein_theorem | [1559, 1] | [1718, 7] | apply And.intro | case right
U V : Type
A C : Set U
B D : Set V
h1 : C β A
h2 : D β B
h3 : A βΌ D
h4 : C βΌ B
R : Rel U V
R_match_AD : rel_within R A D β§ fcnl_on R A β§ fcnl_on (invRel R) D
S : Rel U V
S_match_CB : rel_within S C B β§ fcnl_on S C β§ fcnl_on (invRel S) B
X0 : Set U := A \ C
X : Set U := cum_rep_image R S X0
T : Rel U V := csb... | case right.left
U V : Type
A C : Set U
B D : Set V
h1 : C β A
h2 : D β B
h3 : A βΌ D
h4 : C βΌ B
R : Rel U V
R_match_AD : rel_within R A D β§ fcnl_on R A β§ fcnl_on (invRel R) D
S : Rel U V
S_match_CB : rel_within S C B β§ fcnl_on S C β§ fcnl_on (invRel S) B
X0 : Set U := A \ C
X : Set U := cum_rep_image R S X0
T : Rel U V :... | Please generate a tactic in lean4 to solve the state.
STATE:
case right
U V : Type
A C : Set U
B D : Set V
h1 : C β A
h2 : D β B
h3 : A βΌ D
h4 : C βΌ B
R : Rel U V
R_match_AD : rel_within R A D β§ fcnl_on R A β§ fcnl_on (invRel R) D
S : Rel U V
S_match_CB : rel_within S C B β§ fcnl_on S C β§ fcnl_on (invRel S) B
X0 : Set U ... |
https://github.com/djvelleman/HTPILeanPackage.git | 4d23e94fff351c65b5e1345c43451f2aa9908c27 | HTPILib/Chap8Part2.lean | HTPI.Cantor_Schroeder_Bernstein_theorem | [1559, 1] | [1718, 7] | define | case right.left
U V : Type
A C : Set U
B D : Set V
h1 : C β A
h2 : D β B
h3 : A βΌ D
h4 : C βΌ B
R : Rel U V
R_match_AD : rel_within R A D β§ fcnl_on R A β§ fcnl_on (invRel R) D
S : Rel U V
S_match_CB : rel_within S C B β§ fcnl_on S C β§ fcnl_on (invRel S) B
X0 : Set U := A \ C
X : Set U := cum_rep_image R S X0
T : Rel U V :... | case right.left
U V : Type
A C : Set U
B D : Set V
h1 : C β A
h2 : D β B
h3 : A βΌ D
h4 : C βΌ B
R : Rel U V
R_match_AD : rel_within R A D β§ fcnl_on R A β§ fcnl_on (invRel R) D
S : Rel U V
S_match_CB : rel_within S C B β§ fcnl_on S C β§ fcnl_on (invRel S) B
X0 : Set U := A \ C
X : Set U := cum_rep_image R S X0
T : Rel U V :... | Please generate a tactic in lean4 to solve the state.
STATE:
case right.left
U V : Type
A C : Set U
B D : Set V
h1 : C β A
h2 : D β B
h3 : A βΌ D
h4 : C βΌ B
R : Rel U V
R_match_AD : rel_within R A D β§ fcnl_on R A β§ fcnl_on (invRel R) D
S : Rel U V
S_match_CB : rel_within S C B β§ fcnl_on S C β§ fcnl_on (invRel S) B
X0 : S... |
https://github.com/djvelleman/HTPILeanPackage.git | 4d23e94fff351c65b5e1345c43451f2aa9908c27 | HTPILib/Chap8Part2.lean | HTPI.Cantor_Schroeder_Bernstein_theorem | [1559, 1] | [1718, 7] | fix a : U | case right.left
U V : Type
A C : Set U
B D : Set V
h1 : C β A
h2 : D β B
h3 : A βΌ D
h4 : C βΌ B
R : Rel U V
R_match_AD : rel_within R A D β§ fcnl_on R A β§ fcnl_on (invRel R) D
S : Rel U V
S_match_CB : rel_within S C B β§ fcnl_on S C β§ fcnl_on (invRel S) B
X0 : Set U := A \ C
X : Set U := cum_rep_image R S X0
T : Rel U V :... | case right.left
U V : Type
A C : Set U
B D : Set V
h1 : C β A
h2 : D β B
h3 : A βΌ D
h4 : C βΌ B
R : Rel U V
R_match_AD : rel_within R A D β§ fcnl_on R A β§ fcnl_on (invRel R) D
S : Rel U V
S_match_CB : rel_within S C B β§ fcnl_on S C β§ fcnl_on (invRel S) B
X0 : Set U := A \ C
X : Set U := cum_rep_image R S X0
T : Rel U V :... | Please generate a tactic in lean4 to solve the state.
STATE:
case right.left
U V : Type
A C : Set U
B D : Set V
h1 : C β A
h2 : D β B
h3 : A βΌ D
h4 : C βΌ B
R : Rel U V
R_match_AD : rel_within R A D β§ fcnl_on R A β§ fcnl_on (invRel R) D
S : Rel U V
S_match_CB : rel_within S C B β§ fcnl_on S C β§ fcnl_on (invRel S) B
X0 : S... |
https://github.com/djvelleman/HTPILeanPackage.git | 4d23e94fff351c65b5e1345c43451f2aa9908c27 | HTPILib/Chap8Part2.lean | HTPI.Cantor_Schroeder_Bernstein_theorem | [1559, 1] | [1718, 7] | assume aA : a β A | case right.left
U V : Type
A C : Set U
B D : Set V
h1 : C β A
h2 : D β B
h3 : A βΌ D
h4 : C βΌ B
R : Rel U V
R_match_AD : rel_within R A D β§ fcnl_on R A β§ fcnl_on (invRel R) D
S : Rel U V
S_match_CB : rel_within S C B β§ fcnl_on S C β§ fcnl_on (invRel S) B
X0 : Set U := A \ C
X : Set U := cum_rep_image R S X0
T : Rel U V :... | case right.left
U V : Type
A C : Set U
B D : Set V
h1 : C β A
h2 : D β B
h3 : A βΌ D
h4 : C βΌ B
R : Rel U V
R_match_AD : rel_within R A D β§ fcnl_on R A β§ fcnl_on (invRel R) D
S : Rel U V
S_match_CB : rel_within S C B β§ fcnl_on S C β§ fcnl_on (invRel S) B
X0 : Set U := A \ C
X : Set U := cum_rep_image R S X0
T : Rel U V :... | Please generate a tactic in lean4 to solve the state.
STATE:
case right.left
U V : Type
A C : Set U
B D : Set V
h1 : C β A
h2 : D β B
h3 : A βΌ D
h4 : C βΌ B
R : Rel U V
R_match_AD : rel_within R A D β§ fcnl_on R A β§ fcnl_on (invRel R) D
S : Rel U V
S_match_CB : rel_within S C B β§ fcnl_on S C β§ fcnl_on (invRel S) B
X0 : S... |
https://github.com/djvelleman/HTPILeanPackage.git | 4d23e94fff351c65b5e1345c43451f2aa9908c27 | HTPILib/Chap8Part2.lean | HTPI.Cantor_Schroeder_Bernstein_theorem | [1559, 1] | [1718, 7] | exists_unique | case right.left
U V : Type
A C : Set U
B D : Set V
h1 : C β A
h2 : D β B
h3 : A βΌ D
h4 : C βΌ B
R : Rel U V
R_match_AD : rel_within R A D β§ fcnl_on R A β§ fcnl_on (invRel R) D
S : Rel U V
S_match_CB : rel_within S C B β§ fcnl_on S C β§ fcnl_on (invRel S) B
X0 : Set U := A \ C
X : Set U := cum_rep_image R S X0
T : Rel U V :... | case right.left.Existence
U V : Type
A C : Set U
B D : Set V
h1 : C β A
h2 : D β B
h3 : A βΌ D
h4 : C βΌ B
R : Rel U V
R_match_AD : rel_within R A D β§ fcnl_on R A β§ fcnl_on (invRel R) D
S : Rel U V
S_match_CB : rel_within S C B β§ fcnl_on S C β§ fcnl_on (invRel S) B
X0 : Set U := A \ C
X : Set U := cum_rep_image R S X0
T :... | Please generate a tactic in lean4 to solve the state.
STATE:
case right.left
U V : Type
A C : Set U
B D : Set V
h1 : C β A
h2 : D β B
h3 : A βΌ D
h4 : C βΌ B
R : Rel U V
R_match_AD : rel_within R A D β§ fcnl_on R A β§ fcnl_on (invRel R) D
S : Rel U V
S_match_CB : rel_within S C B β§ fcnl_on S C β§ fcnl_on (invRel S) B
X0 : S... |
https://github.com/djvelleman/HTPILeanPackage.git | 4d23e94fff351c65b5e1345c43451f2aa9908c27 | HTPILib/Chap8Part2.lean | HTPI.Cantor_Schroeder_Bernstein_theorem | [1559, 1] | [1718, 7] | by_cases h5 : a β X | case right.left.Existence
U V : Type
A C : Set U
B D : Set V
h1 : C β A
h2 : D β B
h3 : A βΌ D
h4 : C βΌ B
R : Rel U V
R_match_AD : rel_within R A D β§ fcnl_on R A β§ fcnl_on (invRel R) D
S : Rel U V
S_match_CB : rel_within S C B β§ fcnl_on S C β§ fcnl_on (invRel S) B
X0 : Set U := A \ C
X : Set U := cum_rep_image R S X0
T :... | case pos
U V : Type
A C : Set U
B D : Set V
h1 : C β A
h2 : D β B
h3 : A βΌ D
h4 : C βΌ B
R : Rel U V
R_match_AD : rel_within R A D β§ fcnl_on R A β§ fcnl_on (invRel R) D
S : Rel U V
S_match_CB : rel_within S C B β§ fcnl_on S C β§ fcnl_on (invRel S) B
X0 : Set U := A \ C
X : Set U := cum_rep_image R S X0
T : Rel U V := csb_m... | Please generate a tactic in lean4 to solve the state.
STATE:
case right.left.Existence
U V : Type
A C : Set U
B D : Set V
h1 : C β A
h2 : D β B
h3 : A βΌ D
h4 : C βΌ B
R : Rel U V
R_match_AD : rel_within R A D β§ fcnl_on R A β§ fcnl_on (invRel R) D
S : Rel U V
S_match_CB : rel_within S C B β§ fcnl_on S C β§ fcnl_on (invRel S... |
https://github.com/djvelleman/HTPILeanPackage.git | 4d23e94fff351c65b5e1345c43451f2aa9908c27 | HTPILib/Chap8Part2.lean | HTPI.Cantor_Schroeder_Bernstein_theorem | [1559, 1] | [1718, 7] | obtain (b : V) (Rab : R a b) from
fcnl_exists R_match_AD.right.left aA | case pos
U V : Type
A C : Set U
B D : Set V
h1 : C β A
h2 : D β B
h3 : A βΌ D
h4 : C βΌ B
R : Rel U V
R_match_AD : rel_within R A D β§ fcnl_on R A β§ fcnl_on (invRel R) D
S : Rel U V
S_match_CB : rel_within S C B β§ fcnl_on S C β§ fcnl_on (invRel S) B
X0 : Set U := A \ C
X : Set U := cum_rep_image R S X0
T : Rel U V := csb_m... | case pos
U V : Type
A C : Set U
B D : Set V
h1 : C β A
h2 : D β B
h3 : A βΌ D
h4 : C βΌ B
R : Rel U V
R_match_AD : rel_within R A D β§ fcnl_on R A β§ fcnl_on (invRel R) D
S : Rel U V
S_match_CB : rel_within S C B β§ fcnl_on S C β§ fcnl_on (invRel S) B
X0 : Set U := A \ C
X : Set U := cum_rep_image R S X0
T : Rel U V := csb_m... | Please generate a tactic in lean4 to solve the state.
STATE:
case pos
U V : Type
A C : Set U
B D : Set V
h1 : C β A
h2 : D β B
h3 : A βΌ D
h4 : C βΌ B
R : Rel U V
R_match_AD : rel_within R A D β§ fcnl_on R A β§ fcnl_on (invRel R) D
S : Rel U V
S_match_CB : rel_within S C B β§ fcnl_on S C β§ fcnl_on (invRel S) B
X0 : Set U :=... |
https://github.com/djvelleman/HTPILeanPackage.git | 4d23e94fff351c65b5e1345c43451f2aa9908c27 | HTPILib/Chap8Part2.lean | HTPI.Cantor_Schroeder_Bernstein_theorem | [1559, 1] | [1718, 7] | apply Exists.intro b | case pos
U V : Type
A C : Set U
B D : Set V
h1 : C β A
h2 : D β B
h3 : A βΌ D
h4 : C βΌ B
R : Rel U V
R_match_AD : rel_within R A D β§ fcnl_on R A β§ fcnl_on (invRel R) D
S : Rel U V
S_match_CB : rel_within S C B β§ fcnl_on S C β§ fcnl_on (invRel S) B
X0 : Set U := A \ C
X : Set U := cum_rep_image R S X0
T : Rel U V := csb_m... | case pos
U V : Type
A C : Set U
B D : Set V
h1 : C β A
h2 : D β B
h3 : A βΌ D
h4 : C βΌ B
R : Rel U V
R_match_AD : rel_within R A D β§ fcnl_on R A β§ fcnl_on (invRel R) D
S : Rel U V
S_match_CB : rel_within S C B β§ fcnl_on S C β§ fcnl_on (invRel S) B
X0 : Set U := A \ C
X : Set U := cum_rep_image R S X0
T : Rel U V := csb_m... | Please generate a tactic in lean4 to solve the state.
STATE:
case pos
U V : Type
A C : Set U
B D : Set V
h1 : C β A
h2 : D β B
h3 : A βΌ D
h4 : C βΌ B
R : Rel U V
R_match_AD : rel_within R A D β§ fcnl_on R A β§ fcnl_on (invRel R) D
S : Rel U V
S_match_CB : rel_within S C B β§ fcnl_on S C β§ fcnl_on (invRel S) B
X0 : Set U :=... |
https://github.com/djvelleman/HTPILeanPackage.git | 4d23e94fff351c65b5e1345c43451f2aa9908c27 | HTPILib/Chap8Part2.lean | HTPI.Cantor_Schroeder_Bernstein_theorem | [1559, 1] | [1718, 7] | rewrite [Tdef] | case pos
U V : Type
A C : Set U
B D : Set V
h1 : C β A
h2 : D β B
h3 : A βΌ D
h4 : C βΌ B
R : Rel U V
R_match_AD : rel_within R A D β§ fcnl_on R A β§ fcnl_on (invRel R) D
S : Rel U V
S_match_CB : rel_within S C B β§ fcnl_on S C β§ fcnl_on (invRel S) B
X0 : Set U := A \ C
X : Set U := cum_rep_image R S X0
T : Rel U V := csb_m... | case pos
U V : Type
A C : Set U
B D : Set V
h1 : C β A
h2 : D β B
h3 : A βΌ D
h4 : C βΌ B
R : Rel U V
R_match_AD : rel_within R A D β§ fcnl_on R A β§ fcnl_on (invRel R) D
S : Rel U V
S_match_CB : rel_within S C B β§ fcnl_on S C β§ fcnl_on (invRel S) B
X0 : Set U := A \ C
X : Set U := cum_rep_image R S X0
T : Rel U V := csb_m... | Please generate a tactic in lean4 to solve the state.
STATE:
case pos
U V : Type
A C : Set U
B D : Set V
h1 : C β A
h2 : D β B
h3 : A βΌ D
h4 : C βΌ B
R : Rel U V
R_match_AD : rel_within R A D β§ fcnl_on R A β§ fcnl_on (invRel R) D
S : Rel U V
S_match_CB : rel_within S C B β§ fcnl_on S C β§ fcnl_on (invRel S) B
X0 : Set U :=... |
https://github.com/djvelleman/HTPILeanPackage.git | 4d23e94fff351c65b5e1345c43451f2aa9908c27 | HTPILib/Chap8Part2.lean | HTPI.Cantor_Schroeder_Bernstein_theorem | [1559, 1] | [1718, 7] | show a β X β§ R a b β¨ a β X β§ S a b from
Or.inl (And.intro h5 Rab) | case pos
U V : Type
A C : Set U
B D : Set V
h1 : C β A
h2 : D β B
h3 : A βΌ D
h4 : C βΌ B
R : Rel U V
R_match_AD : rel_within R A D β§ fcnl_on R A β§ fcnl_on (invRel R) D
S : Rel U V
S_match_CB : rel_within S C B β§ fcnl_on S C β§ fcnl_on (invRel S) B
X0 : Set U := A \ C
X : Set U := cum_rep_image R S X0
T : Rel U V := csb_m... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case pos
U V : Type
A C : Set U
B D : Set V
h1 : C β A
h2 : D β B
h3 : A βΌ D
h4 : C βΌ B
R : Rel U V
R_match_AD : rel_within R A D β§ fcnl_on R A β§ fcnl_on (invRel R) D
S : Rel U V
S_match_CB : rel_within S C B β§ fcnl_on S C β§ fcnl_on (invRel S) B
X0 : Set U :=... |
https://github.com/djvelleman/HTPILeanPackage.git | 4d23e94fff351c65b5e1345c43451f2aa9908c27 | HTPILib/Chap8Part2.lean | HTPI.Cantor_Schroeder_Bernstein_theorem | [1559, 1] | [1718, 7] | have aC : a β C := A_not_X_in_C (And.intro aA h5) | case neg
U V : Type
A C : Set U
B D : Set V
h1 : C β A
h2 : D β B
h3 : A βΌ D
h4 : C βΌ B
R : Rel U V
R_match_AD : rel_within R A D β§ fcnl_on R A β§ fcnl_on (invRel R) D
S : Rel U V
S_match_CB : rel_within S C B β§ fcnl_on S C β§ fcnl_on (invRel S) B
X0 : Set U := A \ C
X : Set U := cum_rep_image R S X0
T : Rel U V := csb_m... | case neg
U V : Type
A C : Set U
B D : Set V
h1 : C β A
h2 : D β B
h3 : A βΌ D
h4 : C βΌ B
R : Rel U V
R_match_AD : rel_within R A D β§ fcnl_on R A β§ fcnl_on (invRel R) D
S : Rel U V
S_match_CB : rel_within S C B β§ fcnl_on S C β§ fcnl_on (invRel S) B
X0 : Set U := A \ C
X : Set U := cum_rep_image R S X0
T : Rel U V := csb_m... | Please generate a tactic in lean4 to solve the state.
STATE:
case neg
U V : Type
A C : Set U
B D : Set V
h1 : C β A
h2 : D β B
h3 : A βΌ D
h4 : C βΌ B
R : Rel U V
R_match_AD : rel_within R A D β§ fcnl_on R A β§ fcnl_on (invRel R) D
S : Rel U V
S_match_CB : rel_within S C B β§ fcnl_on S C β§ fcnl_on (invRel S) B
X0 : Set U :=... |
https://github.com/djvelleman/HTPILeanPackage.git | 4d23e94fff351c65b5e1345c43451f2aa9908c27 | HTPILib/Chap8Part2.lean | HTPI.Cantor_Schroeder_Bernstein_theorem | [1559, 1] | [1718, 7] | obtain (b : V) (Sab : S a b) from
fcnl_exists S_match_CB.right.left aC | case neg
U V : Type
A C : Set U
B D : Set V
h1 : C β A
h2 : D β B
h3 : A βΌ D
h4 : C βΌ B
R : Rel U V
R_match_AD : rel_within R A D β§ fcnl_on R A β§ fcnl_on (invRel R) D
S : Rel U V
S_match_CB : rel_within S C B β§ fcnl_on S C β§ fcnl_on (invRel S) B
X0 : Set U := A \ C
X : Set U := cum_rep_image R S X0
T : Rel U V := csb_m... | case neg
U V : Type
A C : Set U
B D : Set V
h1 : C β A
h2 : D β B
h3 : A βΌ D
h4 : C βΌ B
R : Rel U V
R_match_AD : rel_within R A D β§ fcnl_on R A β§ fcnl_on (invRel R) D
S : Rel U V
S_match_CB : rel_within S C B β§ fcnl_on S C β§ fcnl_on (invRel S) B
X0 : Set U := A \ C
X : Set U := cum_rep_image R S X0
T : Rel U V := csb_m... | Please generate a tactic in lean4 to solve the state.
STATE:
case neg
U V : Type
A C : Set U
B D : Set V
h1 : C β A
h2 : D β B
h3 : A βΌ D
h4 : C βΌ B
R : Rel U V
R_match_AD : rel_within R A D β§ fcnl_on R A β§ fcnl_on (invRel R) D
S : Rel U V
S_match_CB : rel_within S C B β§ fcnl_on S C β§ fcnl_on (invRel S) B
X0 : Set U :=... |
https://github.com/djvelleman/HTPILeanPackage.git | 4d23e94fff351c65b5e1345c43451f2aa9908c27 | HTPILib/Chap8Part2.lean | HTPI.Cantor_Schroeder_Bernstein_theorem | [1559, 1] | [1718, 7] | apply Exists.intro b | case neg
U V : Type
A C : Set U
B D : Set V
h1 : C β A
h2 : D β B
h3 : A βΌ D
h4 : C βΌ B
R : Rel U V
R_match_AD : rel_within R A D β§ fcnl_on R A β§ fcnl_on (invRel R) D
S : Rel U V
S_match_CB : rel_within S C B β§ fcnl_on S C β§ fcnl_on (invRel S) B
X0 : Set U := A \ C
X : Set U := cum_rep_image R S X0
T : Rel U V := csb_m... | case neg
U V : Type
A C : Set U
B D : Set V
h1 : C β A
h2 : D β B
h3 : A βΌ D
h4 : C βΌ B
R : Rel U V
R_match_AD : rel_within R A D β§ fcnl_on R A β§ fcnl_on (invRel R) D
S : Rel U V
S_match_CB : rel_within S C B β§ fcnl_on S C β§ fcnl_on (invRel S) B
X0 : Set U := A \ C
X : Set U := cum_rep_image R S X0
T : Rel U V := csb_m... | Please generate a tactic in lean4 to solve the state.
STATE:
case neg
U V : Type
A C : Set U
B D : Set V
h1 : C β A
h2 : D β B
h3 : A βΌ D
h4 : C βΌ B
R : Rel U V
R_match_AD : rel_within R A D β§ fcnl_on R A β§ fcnl_on (invRel R) D
S : Rel U V
S_match_CB : rel_within S C B β§ fcnl_on S C β§ fcnl_on (invRel S) B
X0 : Set U :=... |
https://github.com/djvelleman/HTPILeanPackage.git | 4d23e94fff351c65b5e1345c43451f2aa9908c27 | HTPILib/Chap8Part2.lean | HTPI.Cantor_Schroeder_Bernstein_theorem | [1559, 1] | [1718, 7] | rewrite [Tdef] | case neg
U V : Type
A C : Set U
B D : Set V
h1 : C β A
h2 : D β B
h3 : A βΌ D
h4 : C βΌ B
R : Rel U V
R_match_AD : rel_within R A D β§ fcnl_on R A β§ fcnl_on (invRel R) D
S : Rel U V
S_match_CB : rel_within S C B β§ fcnl_on S C β§ fcnl_on (invRel S) B
X0 : Set U := A \ C
X : Set U := cum_rep_image R S X0
T : Rel U V := csb_m... | case neg
U V : Type
A C : Set U
B D : Set V
h1 : C β A
h2 : D β B
h3 : A βΌ D
h4 : C βΌ B
R : Rel U V
R_match_AD : rel_within R A D β§ fcnl_on R A β§ fcnl_on (invRel R) D
S : Rel U V
S_match_CB : rel_within S C B β§ fcnl_on S C β§ fcnl_on (invRel S) B
X0 : Set U := A \ C
X : Set U := cum_rep_image R S X0
T : Rel U V := csb_m... | Please generate a tactic in lean4 to solve the state.
STATE:
case neg
U V : Type
A C : Set U
B D : Set V
h1 : C β A
h2 : D β B
h3 : A βΌ D
h4 : C βΌ B
R : Rel U V
R_match_AD : rel_within R A D β§ fcnl_on R A β§ fcnl_on (invRel R) D
S : Rel U V
S_match_CB : rel_within S C B β§ fcnl_on S C β§ fcnl_on (invRel S) B
X0 : Set U :=... |
https://github.com/djvelleman/HTPILeanPackage.git | 4d23e94fff351c65b5e1345c43451f2aa9908c27 | HTPILib/Chap8Part2.lean | HTPI.Cantor_Schroeder_Bernstein_theorem | [1559, 1] | [1718, 7] | show a β X β§ R a b β¨ a β X β§ S a b from
Or.inr (And.intro h5 Sab) | case neg
U V : Type
A C : Set U
B D : Set V
h1 : C β A
h2 : D β B
h3 : A βΌ D
h4 : C βΌ B
R : Rel U V
R_match_AD : rel_within R A D β§ fcnl_on R A β§ fcnl_on (invRel R) D
S : Rel U V
S_match_CB : rel_within S C B β§ fcnl_on S C β§ fcnl_on (invRel S) B
X0 : Set U := A \ C
X : Set U := cum_rep_image R S X0
T : Rel U V := csb_m... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case neg
U V : Type
A C : Set U
B D : Set V
h1 : C β A
h2 : D β B
h3 : A βΌ D
h4 : C βΌ B
R : Rel U V
R_match_AD : rel_within R A D β§ fcnl_on R A β§ fcnl_on (invRel R) D
S : Rel U V
S_match_CB : rel_within S C B β§ fcnl_on S C β§ fcnl_on (invRel S) B
X0 : Set U :=... |
https://github.com/djvelleman/HTPILeanPackage.git | 4d23e94fff351c65b5e1345c43451f2aa9908c27 | HTPILib/Chap8Part2.lean | HTPI.Cantor_Schroeder_Bernstein_theorem | [1559, 1] | [1718, 7] | fix b1 : V | case right.left.Uniqueness
U V : Type
A C : Set U
B D : Set V
h1 : C β A
h2 : D β B
h3 : A βΌ D
h4 : C βΌ B
R : Rel U V
R_match_AD : rel_within R A D β§ fcnl_on R A β§ fcnl_on (invRel R) D
S : Rel U V
S_match_CB : rel_within S C B β§ fcnl_on S C β§ fcnl_on (invRel S) B
X0 : Set U := A \ C
X : Set U := cum_rep_image R S X0
T ... | case right.left.Uniqueness
U V : Type
A C : Set U
B D : Set V
h1 : C β A
h2 : D β B
h3 : A βΌ D
h4 : C βΌ B
R : Rel U V
R_match_AD : rel_within R A D β§ fcnl_on R A β§ fcnl_on (invRel R) D
S : Rel U V
S_match_CB : rel_within S C B β§ fcnl_on S C β§ fcnl_on (invRel S) B
X0 : Set U := A \ C
X : Set U := cum_rep_image R S X0
T ... | Please generate a tactic in lean4 to solve the state.
STATE:
case right.left.Uniqueness
U V : Type
A C : Set U
B D : Set V
h1 : C β A
h2 : D β B
h3 : A βΌ D
h4 : C βΌ B
R : Rel U V
R_match_AD : rel_within R A D β§ fcnl_on R A β§ fcnl_on (invRel R) D
S : Rel U V
S_match_CB : rel_within S C B β§ fcnl_on S C β§ fcnl_on (invRel ... |
https://github.com/djvelleman/HTPILeanPackage.git | 4d23e94fff351c65b5e1345c43451f2aa9908c27 | HTPILib/Chap8Part2.lean | HTPI.Cantor_Schroeder_Bernstein_theorem | [1559, 1] | [1718, 7] | fix b2 : V | case right.left.Uniqueness
U V : Type
A C : Set U
B D : Set V
h1 : C β A
h2 : D β B
h3 : A βΌ D
h4 : C βΌ B
R : Rel U V
R_match_AD : rel_within R A D β§ fcnl_on R A β§ fcnl_on (invRel R) D
S : Rel U V
S_match_CB : rel_within S C B β§ fcnl_on S C β§ fcnl_on (invRel S) B
X0 : Set U := A \ C
X : Set U := cum_rep_image R S X0
T ... | case right.left.Uniqueness
U V : Type
A C : Set U
B D : Set V
h1 : C β A
h2 : D β B
h3 : A βΌ D
h4 : C βΌ B
R : Rel U V
R_match_AD : rel_within R A D β§ fcnl_on R A β§ fcnl_on (invRel R) D
S : Rel U V
S_match_CB : rel_within S C B β§ fcnl_on S C β§ fcnl_on (invRel S) B
X0 : Set U := A \ C
X : Set U := cum_rep_image R S X0
T ... | Please generate a tactic in lean4 to solve the state.
STATE:
case right.left.Uniqueness
U V : Type
A C : Set U
B D : Set V
h1 : C β A
h2 : D β B
h3 : A βΌ D
h4 : C βΌ B
R : Rel U V
R_match_AD : rel_within R A D β§ fcnl_on R A β§ fcnl_on (invRel R) D
S : Rel U V
S_match_CB : rel_within S C B β§ fcnl_on S C β§ fcnl_on (invRel ... |
https://github.com/djvelleman/HTPILeanPackage.git | 4d23e94fff351c65b5e1345c43451f2aa9908c27 | HTPILib/Chap8Part2.lean | HTPI.Cantor_Schroeder_Bernstein_theorem | [1559, 1] | [1718, 7] | assume Tab1 : T a b1 | case right.left.Uniqueness
U V : Type
A C : Set U
B D : Set V
h1 : C β A
h2 : D β B
h3 : A βΌ D
h4 : C βΌ B
R : Rel U V
R_match_AD : rel_within R A D β§ fcnl_on R A β§ fcnl_on (invRel R) D
S : Rel U V
S_match_CB : rel_within S C B β§ fcnl_on S C β§ fcnl_on (invRel S) B
X0 : Set U := A \ C
X : Set U := cum_rep_image R S X0
T ... | case right.left.Uniqueness
U V : Type
A C : Set U
B D : Set V
h1 : C β A
h2 : D β B
h3 : A βΌ D
h4 : C βΌ B
R : Rel U V
R_match_AD : rel_within R A D β§ fcnl_on R A β§ fcnl_on (invRel R) D
S : Rel U V
S_match_CB : rel_within S C B β§ fcnl_on S C β§ fcnl_on (invRel S) B
X0 : Set U := A \ C
X : Set U := cum_rep_image R S X0
T ... | Please generate a tactic in lean4 to solve the state.
STATE:
case right.left.Uniqueness
U V : Type
A C : Set U
B D : Set V
h1 : C β A
h2 : D β B
h3 : A βΌ D
h4 : C βΌ B
R : Rel U V
R_match_AD : rel_within R A D β§ fcnl_on R A β§ fcnl_on (invRel R) D
S : Rel U V
S_match_CB : rel_within S C B β§ fcnl_on S C β§ fcnl_on (invRel ... |
https://github.com/djvelleman/HTPILeanPackage.git | 4d23e94fff351c65b5e1345c43451f2aa9908c27 | HTPILib/Chap8Part2.lean | HTPI.Cantor_Schroeder_Bernstein_theorem | [1559, 1] | [1718, 7] | assume Tab2 : T a b2 | case right.left.Uniqueness
U V : Type
A C : Set U
B D : Set V
h1 : C β A
h2 : D β B
h3 : A βΌ D
h4 : C βΌ B
R : Rel U V
R_match_AD : rel_within R A D β§ fcnl_on R A β§ fcnl_on (invRel R) D
S : Rel U V
S_match_CB : rel_within S C B β§ fcnl_on S C β§ fcnl_on (invRel S) B
X0 : Set U := A \ C
X : Set U := cum_rep_image R S X0
T ... | case right.left.Uniqueness
U V : Type
A C : Set U
B D : Set V
h1 : C β A
h2 : D β B
h3 : A βΌ D
h4 : C βΌ B
R : Rel U V
R_match_AD : rel_within R A D β§ fcnl_on R A β§ fcnl_on (invRel R) D
S : Rel U V
S_match_CB : rel_within S C B β§ fcnl_on S C β§ fcnl_on (invRel S) B
X0 : Set U := A \ C
X : Set U := cum_rep_image R S X0
T ... | Please generate a tactic in lean4 to solve the state.
STATE:
case right.left.Uniqueness
U V : Type
A C : Set U
B D : Set V
h1 : C β A
h2 : D β B
h3 : A βΌ D
h4 : C βΌ B
R : Rel U V
R_match_AD : rel_within R A D β§ fcnl_on R A β§ fcnl_on (invRel R) D
S : Rel U V
S_match_CB : rel_within S C B β§ fcnl_on S C β§ fcnl_on (invRel ... |
https://github.com/djvelleman/HTPILeanPackage.git | 4d23e94fff351c65b5e1345c43451f2aa9908c27 | HTPILib/Chap8Part2.lean | HTPI.Cantor_Schroeder_Bernstein_theorem | [1559, 1] | [1718, 7] | by_cases h5 : a β X | case right.left.Uniqueness
U V : Type
A C : Set U
B D : Set V
h1 : C β A
h2 : D β B
h3 : A βΌ D
h4 : C βΌ B
R : Rel U V
R_match_AD : rel_within R A D β§ fcnl_on R A β§ fcnl_on (invRel R) D
S : Rel U V
S_match_CB : rel_within S C B β§ fcnl_on S C β§ fcnl_on (invRel S) B
X0 : Set U := A \ C
X : Set U := cum_rep_image R S X0
T ... | case pos
U V : Type
A C : Set U
B D : Set V
h1 : C β A
h2 : D β B
h3 : A βΌ D
h4 : C βΌ B
R : Rel U V
R_match_AD : rel_within R A D β§ fcnl_on R A β§ fcnl_on (invRel R) D
S : Rel U V
S_match_CB : rel_within S C B β§ fcnl_on S C β§ fcnl_on (invRel S) B
X0 : Set U := A \ C
X : Set U := cum_rep_image R S X0
T : Rel U V := csb_m... | Please generate a tactic in lean4 to solve the state.
STATE:
case right.left.Uniqueness
U V : Type
A C : Set U
B D : Set V
h1 : C β A
h2 : D β B
h3 : A βΌ D
h4 : C βΌ B
R : Rel U V
R_match_AD : rel_within R A D β§ fcnl_on R A β§ fcnl_on (invRel R) D
S : Rel U V
S_match_CB : rel_within S C B β§ fcnl_on S C β§ fcnl_on (invRel ... |
https://github.com/djvelleman/HTPILeanPackage.git | 4d23e94fff351c65b5e1345c43451f2aa9908c27 | HTPILib/Chap8Part2.lean | HTPI.Cantor_Schroeder_Bernstein_theorem | [1559, 1] | [1718, 7] | have Rab1 : R a b1 := csb_match_cri Tab1 h5 | case pos
U V : Type
A C : Set U
B D : Set V
h1 : C β A
h2 : D β B
h3 : A βΌ D
h4 : C βΌ B
R : Rel U V
R_match_AD : rel_within R A D β§ fcnl_on R A β§ fcnl_on (invRel R) D
S : Rel U V
S_match_CB : rel_within S C B β§ fcnl_on S C β§ fcnl_on (invRel S) B
X0 : Set U := A \ C
X : Set U := cum_rep_image R S X0
T : Rel U V := csb_m... | case pos
U V : Type
A C : Set U
B D : Set V
h1 : C β A
h2 : D β B
h3 : A βΌ D
h4 : C βΌ B
R : Rel U V
R_match_AD : rel_within R A D β§ fcnl_on R A β§ fcnl_on (invRel R) D
S : Rel U V
S_match_CB : rel_within S C B β§ fcnl_on S C β§ fcnl_on (invRel S) B
X0 : Set U := A \ C
X : Set U := cum_rep_image R S X0
T : Rel U V := csb_m... | Please generate a tactic in lean4 to solve the state.
STATE:
case pos
U V : Type
A C : Set U
B D : Set V
h1 : C β A
h2 : D β B
h3 : A βΌ D
h4 : C βΌ B
R : Rel U V
R_match_AD : rel_within R A D β§ fcnl_on R A β§ fcnl_on (invRel R) D
S : Rel U V
S_match_CB : rel_within S C B β§ fcnl_on S C β§ fcnl_on (invRel S) B
X0 : Set U :=... |
https://github.com/djvelleman/HTPILeanPackage.git | 4d23e94fff351c65b5e1345c43451f2aa9908c27 | HTPILib/Chap8Part2.lean | HTPI.Cantor_Schroeder_Bernstein_theorem | [1559, 1] | [1718, 7] | have Rab2 : R a b2 := csb_match_cri Tab2 h5 | case pos
U V : Type
A C : Set U
B D : Set V
h1 : C β A
h2 : D β B
h3 : A βΌ D
h4 : C βΌ B
R : Rel U V
R_match_AD : rel_within R A D β§ fcnl_on R A β§ fcnl_on (invRel R) D
S : Rel U V
S_match_CB : rel_within S C B β§ fcnl_on S C β§ fcnl_on (invRel S) B
X0 : Set U := A \ C
X : Set U := cum_rep_image R S X0
T : Rel U V := csb_m... | case pos
U V : Type
A C : Set U
B D : Set V
h1 : C β A
h2 : D β B
h3 : A βΌ D
h4 : C βΌ B
R : Rel U V
R_match_AD : rel_within R A D β§ fcnl_on R A β§ fcnl_on (invRel R) D
S : Rel U V
S_match_CB : rel_within S C B β§ fcnl_on S C β§ fcnl_on (invRel S) B
X0 : Set U := A \ C
X : Set U := cum_rep_image R S X0
T : Rel U V := csb_m... | Please generate a tactic in lean4 to solve the state.
STATE:
case pos
U V : Type
A C : Set U
B D : Set V
h1 : C β A
h2 : D β B
h3 : A βΌ D
h4 : C βΌ B
R : Rel U V
R_match_AD : rel_within R A D β§ fcnl_on R A β§ fcnl_on (invRel R) D
S : Rel U V
S_match_CB : rel_within S C B β§ fcnl_on S C β§ fcnl_on (invRel S) B
X0 : Set U :=... |
https://github.com/djvelleman/HTPILeanPackage.git | 4d23e94fff351c65b5e1345c43451f2aa9908c27 | HTPILib/Chap8Part2.lean | HTPI.Cantor_Schroeder_Bernstein_theorem | [1559, 1] | [1718, 7] | show b1 = b2 from
fcnl_unique R_match_AD.right.left aA Rab1 Rab2 | case pos
U V : Type
A C : Set U
B D : Set V
h1 : C β A
h2 : D β B
h3 : A βΌ D
h4 : C βΌ B
R : Rel U V
R_match_AD : rel_within R A D β§ fcnl_on R A β§ fcnl_on (invRel R) D
S : Rel U V
S_match_CB : rel_within S C B β§ fcnl_on S C β§ fcnl_on (invRel S) B
X0 : Set U := A \ C
X : Set U := cum_rep_image R S X0
T : Rel U V := csb_m... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case pos
U V : Type
A C : Set U
B D : Set V
h1 : C β A
h2 : D β B
h3 : A βΌ D
h4 : C βΌ B
R : Rel U V
R_match_AD : rel_within R A D β§ fcnl_on R A β§ fcnl_on (invRel R) D
S : Rel U V
S_match_CB : rel_within S C B β§ fcnl_on S C β§ fcnl_on (invRel S) B
X0 : Set U :=... |
https://github.com/djvelleman/HTPILeanPackage.git | 4d23e94fff351c65b5e1345c43451f2aa9908c27 | HTPILib/Chap8Part2.lean | HTPI.Cantor_Schroeder_Bernstein_theorem | [1559, 1] | [1718, 7] | have Sab1 : S a b1 := csb_match_not_cri Tab1 h5 | case neg
U V : Type
A C : Set U
B D : Set V
h1 : C β A
h2 : D β B
h3 : A βΌ D
h4 : C βΌ B
R : Rel U V
R_match_AD : rel_within R A D β§ fcnl_on R A β§ fcnl_on (invRel R) D
S : Rel U V
S_match_CB : rel_within S C B β§ fcnl_on S C β§ fcnl_on (invRel S) B
X0 : Set U := A \ C
X : Set U := cum_rep_image R S X0
T : Rel U V := csb_m... | case neg
U V : Type
A C : Set U
B D : Set V
h1 : C β A
h2 : D β B
h3 : A βΌ D
h4 : C βΌ B
R : Rel U V
R_match_AD : rel_within R A D β§ fcnl_on R A β§ fcnl_on (invRel R) D
S : Rel U V
S_match_CB : rel_within S C B β§ fcnl_on S C β§ fcnl_on (invRel S) B
X0 : Set U := A \ C
X : Set U := cum_rep_image R S X0
T : Rel U V := csb_m... | Please generate a tactic in lean4 to solve the state.
STATE:
case neg
U V : Type
A C : Set U
B D : Set V
h1 : C β A
h2 : D β B
h3 : A βΌ D
h4 : C βΌ B
R : Rel U V
R_match_AD : rel_within R A D β§ fcnl_on R A β§ fcnl_on (invRel R) D
S : Rel U V
S_match_CB : rel_within S C B β§ fcnl_on S C β§ fcnl_on (invRel S) B
X0 : Set U :=... |
https://github.com/djvelleman/HTPILeanPackage.git | 4d23e94fff351c65b5e1345c43451f2aa9908c27 | HTPILib/Chap8Part2.lean | HTPI.Cantor_Schroeder_Bernstein_theorem | [1559, 1] | [1718, 7] | have Sab2 : S a b2 := csb_match_not_cri Tab2 h5 | case neg
U V : Type
A C : Set U
B D : Set V
h1 : C β A
h2 : D β B
h3 : A βΌ D
h4 : C βΌ B
R : Rel U V
R_match_AD : rel_within R A D β§ fcnl_on R A β§ fcnl_on (invRel R) D
S : Rel U V
S_match_CB : rel_within S C B β§ fcnl_on S C β§ fcnl_on (invRel S) B
X0 : Set U := A \ C
X : Set U := cum_rep_image R S X0
T : Rel U V := csb_m... | case neg
U V : Type
A C : Set U
B D : Set V
h1 : C β A
h2 : D β B
h3 : A βΌ D
h4 : C βΌ B
R : Rel U V
R_match_AD : rel_within R A D β§ fcnl_on R A β§ fcnl_on (invRel R) D
S : Rel U V
S_match_CB : rel_within S C B β§ fcnl_on S C β§ fcnl_on (invRel S) B
X0 : Set U := A \ C
X : Set U := cum_rep_image R S X0
T : Rel U V := csb_m... | Please generate a tactic in lean4 to solve the state.
STATE:
case neg
U V : Type
A C : Set U
B D : Set V
h1 : C β A
h2 : D β B
h3 : A βΌ D
h4 : C βΌ B
R : Rel U V
R_match_AD : rel_within R A D β§ fcnl_on R A β§ fcnl_on (invRel R) D
S : Rel U V
S_match_CB : rel_within S C B β§ fcnl_on S C β§ fcnl_on (invRel S) B
X0 : Set U :=... |
https://github.com/djvelleman/HTPILeanPackage.git | 4d23e94fff351c65b5e1345c43451f2aa9908c27 | HTPILib/Chap8Part2.lean | HTPI.Cantor_Schroeder_Bernstein_theorem | [1559, 1] | [1718, 7] | have aC : a β C := A_not_X_in_C (And.intro aA h5) | case neg
U V : Type
A C : Set U
B D : Set V
h1 : C β A
h2 : D β B
h3 : A βΌ D
h4 : C βΌ B
R : Rel U V
R_match_AD : rel_within R A D β§ fcnl_on R A β§ fcnl_on (invRel R) D
S : Rel U V
S_match_CB : rel_within S C B β§ fcnl_on S C β§ fcnl_on (invRel S) B
X0 : Set U := A \ C
X : Set U := cum_rep_image R S X0
T : Rel U V := csb_m... | case neg
U V : Type
A C : Set U
B D : Set V
h1 : C β A
h2 : D β B
h3 : A βΌ D
h4 : C βΌ B
R : Rel U V
R_match_AD : rel_within R A D β§ fcnl_on R A β§ fcnl_on (invRel R) D
S : Rel U V
S_match_CB : rel_within S C B β§ fcnl_on S C β§ fcnl_on (invRel S) B
X0 : Set U := A \ C
X : Set U := cum_rep_image R S X0
T : Rel U V := csb_m... | Please generate a tactic in lean4 to solve the state.
STATE:
case neg
U V : Type
A C : Set U
B D : Set V
h1 : C β A
h2 : D β B
h3 : A βΌ D
h4 : C βΌ B
R : Rel U V
R_match_AD : rel_within R A D β§ fcnl_on R A β§ fcnl_on (invRel R) D
S : Rel U V
S_match_CB : rel_within S C B β§ fcnl_on S C β§ fcnl_on (invRel S) B
X0 : Set U :=... |
https://github.com/djvelleman/HTPILeanPackage.git | 4d23e94fff351c65b5e1345c43451f2aa9908c27 | HTPILib/Chap8Part2.lean | HTPI.Cantor_Schroeder_Bernstein_theorem | [1559, 1] | [1718, 7] | show b1 = b2 from
fcnl_unique S_match_CB.right.left aC Sab1 Sab2 | case neg
U V : Type
A C : Set U
B D : Set V
h1 : C β A
h2 : D β B
h3 : A βΌ D
h4 : C βΌ B
R : Rel U V
R_match_AD : rel_within R A D β§ fcnl_on R A β§ fcnl_on (invRel R) D
S : Rel U V
S_match_CB : rel_within S C B β§ fcnl_on S C β§ fcnl_on (invRel S) B
X0 : Set U := A \ C
X : Set U := cum_rep_image R S X0
T : Rel U V := csb_m... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case neg
U V : Type
A C : Set U
B D : Set V
h1 : C β A
h2 : D β B
h3 : A βΌ D
h4 : C βΌ B
R : Rel U V
R_match_AD : rel_within R A D β§ fcnl_on R A β§ fcnl_on (invRel R) D
S : Rel U V
S_match_CB : rel_within S C B β§ fcnl_on S C β§ fcnl_on (invRel S) B
X0 : Set U :=... |
https://github.com/djvelleman/HTPILeanPackage.git | 4d23e94fff351c65b5e1345c43451f2aa9908c27 | HTPILib/Chap8Part2.lean | HTPI.Cantor_Schroeder_Bernstein_theorem | [1559, 1] | [1718, 7] | define | case right.right
U V : Type
A C : Set U
B D : Set V
h1 : C β A
h2 : D β B
h3 : A βΌ D
h4 : C βΌ B
R : Rel U V
R_match_AD : rel_within R A D β§ fcnl_on R A β§ fcnl_on (invRel R) D
S : Rel U V
S_match_CB : rel_within S C B β§ fcnl_on S C β§ fcnl_on (invRel S) B
X0 : Set U := A \ C
X : Set U := cum_rep_image R S X0
T : Rel U V ... | case right.right
U V : Type
A C : Set U
B D : Set V
h1 : C β A
h2 : D β B
h3 : A βΌ D
h4 : C βΌ B
R : Rel U V
R_match_AD : rel_within R A D β§ fcnl_on R A β§ fcnl_on (invRel R) D
S : Rel U V
S_match_CB : rel_within S C B β§ fcnl_on S C β§ fcnl_on (invRel S) B
X0 : Set U := A \ C
X : Set U := cum_rep_image R S X0
T : Rel U V ... | Please generate a tactic in lean4 to solve the state.
STATE:
case right.right
U V : Type
A C : Set U
B D : Set V
h1 : C β A
h2 : D β B
h3 : A βΌ D
h4 : C βΌ B
R : Rel U V
R_match_AD : rel_within R A D β§ fcnl_on R A β§ fcnl_on (invRel R) D
S : Rel U V
S_match_CB : rel_within S C B β§ fcnl_on S C β§ fcnl_on (invRel S) B
X0 : ... |
https://github.com/djvelleman/HTPILeanPackage.git | 4d23e94fff351c65b5e1345c43451f2aa9908c27 | HTPILib/Chap8Part2.lean | HTPI.Cantor_Schroeder_Bernstein_theorem | [1559, 1] | [1718, 7] | fix b : V | case right.right
U V : Type
A C : Set U
B D : Set V
h1 : C β A
h2 : D β B
h3 : A βΌ D
h4 : C βΌ B
R : Rel U V
R_match_AD : rel_within R A D β§ fcnl_on R A β§ fcnl_on (invRel R) D
S : Rel U V
S_match_CB : rel_within S C B β§ fcnl_on S C β§ fcnl_on (invRel S) B
X0 : Set U := A \ C
X : Set U := cum_rep_image R S X0
T : Rel U V ... | case right.right
U V : Type
A C : Set U
B D : Set V
h1 : C β A
h2 : D β B
h3 : A βΌ D
h4 : C βΌ B
R : Rel U V
R_match_AD : rel_within R A D β§ fcnl_on R A β§ fcnl_on (invRel R) D
S : Rel U V
S_match_CB : rel_within S C B β§ fcnl_on S C β§ fcnl_on (invRel S) B
X0 : Set U := A \ C
X : Set U := cum_rep_image R S X0
T : Rel U V ... | Please generate a tactic in lean4 to solve the state.
STATE:
case right.right
U V : Type
A C : Set U
B D : Set V
h1 : C β A
h2 : D β B
h3 : A βΌ D
h4 : C βΌ B
R : Rel U V
R_match_AD : rel_within R A D β§ fcnl_on R A β§ fcnl_on (invRel R) D
S : Rel U V
S_match_CB : rel_within S C B β§ fcnl_on S C β§ fcnl_on (invRel S) B
X0 : ... |
https://github.com/djvelleman/HTPILeanPackage.git | 4d23e94fff351c65b5e1345c43451f2aa9908c27 | HTPILib/Chap8Part2.lean | HTPI.Cantor_Schroeder_Bernstein_theorem | [1559, 1] | [1718, 7] | assume bB : b β B | case right.right
U V : Type
A C : Set U
B D : Set V
h1 : C β A
h2 : D β B
h3 : A βΌ D
h4 : C βΌ B
R : Rel U V
R_match_AD : rel_within R A D β§ fcnl_on R A β§ fcnl_on (invRel R) D
S : Rel U V
S_match_CB : rel_within S C B β§ fcnl_on S C β§ fcnl_on (invRel S) B
X0 : Set U := A \ C
X : Set U := cum_rep_image R S X0
T : Rel U V ... | case right.right
U V : Type
A C : Set U
B D : Set V
h1 : C β A
h2 : D β B
h3 : A βΌ D
h4 : C βΌ B
R : Rel U V
R_match_AD : rel_within R A D β§ fcnl_on R A β§ fcnl_on (invRel R) D
S : Rel U V
S_match_CB : rel_within S C B β§ fcnl_on S C β§ fcnl_on (invRel S) B
X0 : Set U := A \ C
X : Set U := cum_rep_image R S X0
T : Rel U V ... | Please generate a tactic in lean4 to solve the state.
STATE:
case right.right
U V : Type
A C : Set U
B D : Set V
h1 : C β A
h2 : D β B
h3 : A βΌ D
h4 : C βΌ B
R : Rel U V
R_match_AD : rel_within R A D β§ fcnl_on R A β§ fcnl_on (invRel R) D
S : Rel U V
S_match_CB : rel_within S C B β§ fcnl_on S C β§ fcnl_on (invRel S) B
X0 : ... |
https://github.com/djvelleman/HTPILeanPackage.git | 4d23e94fff351c65b5e1345c43451f2aa9908c27 | HTPILib/Chap8Part2.lean | HTPI.Cantor_Schroeder_Bernstein_theorem | [1559, 1] | [1718, 7] | obtain (c : U) (Scb : S c b) from
fcnl_exists S_match_CB.right.right bB | case right.right
U V : Type
A C : Set U
B D : Set V
h1 : C β A
h2 : D β B
h3 : A βΌ D
h4 : C βΌ B
R : Rel U V
R_match_AD : rel_within R A D β§ fcnl_on R A β§ fcnl_on (invRel R) D
S : Rel U V
S_match_CB : rel_within S C B β§ fcnl_on S C β§ fcnl_on (invRel S) B
X0 : Set U := A \ C
X : Set U := cum_rep_image R S X0
T : Rel U V ... | case right.right
U V : Type
A C : Set U
B D : Set V
h1 : C β A
h2 : D β B
h3 : A βΌ D
h4 : C βΌ B
R : Rel U V
R_match_AD : rel_within R A D β§ fcnl_on R A β§ fcnl_on (invRel R) D
S : Rel U V
S_match_CB : rel_within S C B β§ fcnl_on S C β§ fcnl_on (invRel S) B
X0 : Set U := A \ C
X : Set U := cum_rep_image R S X0
T : Rel U V ... | Please generate a tactic in lean4 to solve the state.
STATE:
case right.right
U V : Type
A C : Set U
B D : Set V
h1 : C β A
h2 : D β B
h3 : A βΌ D
h4 : C βΌ B
R : Rel U V
R_match_AD : rel_within R A D β§ fcnl_on R A β§ fcnl_on (invRel R) D
S : Rel U V
S_match_CB : rel_within S C B β§ fcnl_on S C β§ fcnl_on (invRel S) B
X0 : ... |
https://github.com/djvelleman/HTPILeanPackage.git | 4d23e94fff351c65b5e1345c43451f2aa9908c27 | HTPILib/Chap8Part2.lean | HTPI.Cantor_Schroeder_Bernstein_theorem | [1559, 1] | [1718, 7] | have cC : c β C := (S_match_CB.left Scb).left | case right.right
U V : Type
A C : Set U
B D : Set V
h1 : C β A
h2 : D β B
h3 : A βΌ D
h4 : C βΌ B
R : Rel U V
R_match_AD : rel_within R A D β§ fcnl_on R A β§ fcnl_on (invRel R) D
S : Rel U V
S_match_CB : rel_within S C B β§ fcnl_on S C β§ fcnl_on (invRel S) B
X0 : Set U := A \ C
X : Set U := cum_rep_image R S X0
T : Rel U V ... | case right.right
U V : Type
A C : Set U
B D : Set V
h1 : C β A
h2 : D β B
h3 : A βΌ D
h4 : C βΌ B
R : Rel U V
R_match_AD : rel_within R A D β§ fcnl_on R A β§ fcnl_on (invRel R) D
S : Rel U V
S_match_CB : rel_within S C B β§ fcnl_on S C β§ fcnl_on (invRel S) B
X0 : Set U := A \ C
X : Set U := cum_rep_image R S X0
T : Rel U V ... | Please generate a tactic in lean4 to solve the state.
STATE:
case right.right
U V : Type
A C : Set U
B D : Set V
h1 : C β A
h2 : D β B
h3 : A βΌ D
h4 : C βΌ B
R : Rel U V
R_match_AD : rel_within R A D β§ fcnl_on R A β§ fcnl_on (invRel R) D
S : Rel U V
S_match_CB : rel_within S C B β§ fcnl_on S C β§ fcnl_on (invRel S) B
X0 : ... |
https://github.com/djvelleman/HTPILeanPackage.git | 4d23e94fff351c65b5e1345c43451f2aa9908c27 | HTPILib/Chap8Part2.lean | HTPI.Cantor_Schroeder_Bernstein_theorem | [1559, 1] | [1718, 7] | exists_unique | case right.right
U V : Type
A C : Set U
B D : Set V
h1 : C β A
h2 : D β B
h3 : A βΌ D
h4 : C βΌ B
R : Rel U V
R_match_AD : rel_within R A D β§ fcnl_on R A β§ fcnl_on (invRel R) D
S : Rel U V
S_match_CB : rel_within S C B β§ fcnl_on S C β§ fcnl_on (invRel S) B
X0 : Set U := A \ C
X : Set U := cum_rep_image R S X0
T : Rel U V ... | case right.right.Existence
U V : Type
A C : Set U
B D : Set V
h1 : C β A
h2 : D β B
h3 : A βΌ D
h4 : C βΌ B
R : Rel U V
R_match_AD : rel_within R A D β§ fcnl_on R A β§ fcnl_on (invRel R) D
S : Rel U V
S_match_CB : rel_within S C B β§ fcnl_on S C β§ fcnl_on (invRel S) B
X0 : Set U := A \ C
X : Set U := cum_rep_image R S X0
T ... | Please generate a tactic in lean4 to solve the state.
STATE:
case right.right
U V : Type
A C : Set U
B D : Set V
h1 : C β A
h2 : D β B
h3 : A βΌ D
h4 : C βΌ B
R : Rel U V
R_match_AD : rel_within R A D β§ fcnl_on R A β§ fcnl_on (invRel R) D
S : Rel U V
S_match_CB : rel_within S C B β§ fcnl_on S C β§ fcnl_on (invRel S) B
X0 : ... |
https://github.com/djvelleman/HTPILeanPackage.git | 4d23e94fff351c65b5e1345c43451f2aa9908c27 | HTPILib/Chap8Part2.lean | HTPI.Cantor_Schroeder_Bernstein_theorem | [1559, 1] | [1718, 7] | by_cases h5 : c β X | case right.right.Existence
U V : Type
A C : Set U
B D : Set V
h1 : C β A
h2 : D β B
h3 : A βΌ D
h4 : C βΌ B
R : Rel U V
R_match_AD : rel_within R A D β§ fcnl_on R A β§ fcnl_on (invRel R) D
S : Rel U V
S_match_CB : rel_within S C B β§ fcnl_on S C β§ fcnl_on (invRel S) B
X0 : Set U := A \ C
X : Set U := cum_rep_image R S X0
T ... | case pos
U V : Type
A C : Set U
B D : Set V
h1 : C β A
h2 : D β B
h3 : A βΌ D
h4 : C βΌ B
R : Rel U V
R_match_AD : rel_within R A D β§ fcnl_on R A β§ fcnl_on (invRel R) D
S : Rel U V
S_match_CB : rel_within S C B β§ fcnl_on S C β§ fcnl_on (invRel S) B
X0 : Set U := A \ C
X : Set U := cum_rep_image R S X0
T : Rel U V := csb_m... | Please generate a tactic in lean4 to solve the state.
STATE:
case right.right.Existence
U V : Type
A C : Set U
B D : Set V
h1 : C β A
h2 : D β B
h3 : A βΌ D
h4 : C βΌ B
R : Rel U V
R_match_AD : rel_within R A D β§ fcnl_on R A β§ fcnl_on (invRel R) D
S : Rel U V
S_match_CB : rel_within S C B β§ fcnl_on S C β§ fcnl_on (invRel ... |
https://github.com/djvelleman/HTPILeanPackage.git | 4d23e94fff351c65b5e1345c43451f2aa9908c27 | HTPILib/Chap8Part2.lean | HTPI.Cantor_Schroeder_Bernstein_theorem | [1559, 1] | [1718, 7] | define at h5 | case pos
U V : Type
A C : Set U
B D : Set V
h1 : C β A
h2 : D β B
h3 : A βΌ D
h4 : C βΌ B
R : Rel U V
R_match_AD : rel_within R A D β§ fcnl_on R A β§ fcnl_on (invRel R) D
S : Rel U V
S_match_CB : rel_within S C B β§ fcnl_on S C β§ fcnl_on (invRel S) B
X0 : Set U := A \ C
X : Set U := cum_rep_image R S X0
T : Rel U V := csb_m... | case pos
U V : Type
A C : Set U
B D : Set V
h1 : C β A
h2 : D β B
h3 : A βΌ D
h4 : C βΌ B
R : Rel U V
R_match_AD : rel_within R A D β§ fcnl_on R A β§ fcnl_on (invRel R) D
S : Rel U V
S_match_CB : rel_within S C B β§ fcnl_on S C β§ fcnl_on (invRel S) B
X0 : Set U := A \ C
X : Set U := cum_rep_image R S X0
T : Rel U V := csb_m... | Please generate a tactic in lean4 to solve the state.
STATE:
case pos
U V : Type
A C : Set U
B D : Set V
h1 : C β A
h2 : D β B
h3 : A βΌ D
h4 : C βΌ B
R : Rel U V
R_match_AD : rel_within R A D β§ fcnl_on R A β§ fcnl_on (invRel R) D
S : Rel U V
S_match_CB : rel_within S C B β§ fcnl_on S C β§ fcnl_on (invRel S) B
X0 : Set U :=... |
https://github.com/djvelleman/HTPILeanPackage.git | 4d23e94fff351c65b5e1345c43451f2aa9908c27 | HTPILib/Chap8Part2.lean | HTPI.Cantor_Schroeder_Bernstein_theorem | [1559, 1] | [1718, 7] | obtain (n : Nat) (h6 : c β rep_common_image R S X0 n) from h5 | case pos
U V : Type
A C : Set U
B D : Set V
h1 : C β A
h2 : D β B
h3 : A βΌ D
h4 : C βΌ B
R : Rel U V
R_match_AD : rel_within R A D β§ fcnl_on R A β§ fcnl_on (invRel R) D
S : Rel U V
S_match_CB : rel_within S C B β§ fcnl_on S C β§ fcnl_on (invRel S) B
X0 : Set U := A \ C
X : Set U := cum_rep_image R S X0
T : Rel U V := csb_m... | case pos
U V : Type
A C : Set U
B D : Set V
h1 : C β A
h2 : D β B
h3 : A βΌ D
h4 : C βΌ B
R : Rel U V
R_match_AD : rel_within R A D β§ fcnl_on R A β§ fcnl_on (invRel R) D
S : Rel U V
S_match_CB : rel_within S C B β§ fcnl_on S C β§ fcnl_on (invRel S) B
X0 : Set U := A \ C
X : Set U := cum_rep_image R S X0
T : Rel U V := csb_m... | Please generate a tactic in lean4 to solve the state.
STATE:
case pos
U V : Type
A C : Set U
B D : Set V
h1 : C β A
h2 : D β B
h3 : A βΌ D
h4 : C βΌ B
R : Rel U V
R_match_AD : rel_within R A D β§ fcnl_on R A β§ fcnl_on (invRel R) D
S : Rel U V
S_match_CB : rel_within S C B β§ fcnl_on S C β§ fcnl_on (invRel S) B
X0 : Set U :=... |
https://github.com/djvelleman/HTPILeanPackage.git | 4d23e94fff351c65b5e1345c43451f2aa9908c27 | HTPILib/Chap8Part2.lean | HTPI.Cantor_Schroeder_Bernstein_theorem | [1559, 1] | [1718, 7] | have h7 : n β 0 := by
by_contra h7
rewrite [h7] at h6
define at h6 show False from h6.right cC
done | case pos
U V : Type
A C : Set U
B D : Set V
h1 : C β A
h2 : D β B
h3 : A βΌ D
h4 : C βΌ B
R : Rel U V
R_match_AD : rel_within R A D β§ fcnl_on R A β§ fcnl_on (invRel R) D
S : Rel U V
S_match_CB : rel_within S C B β§ fcnl_on S C β§ fcnl_on (invRel S) B
X0 : Set U := A \ C
X : Set U := cum_rep_image R S X0
T : Rel U V := csb_m... | case pos
U V : Type
A C : Set U
B D : Set V
h1 : C β A
h2 : D β B
h3 : A βΌ D
h4 : C βΌ B
R : Rel U V
R_match_AD : rel_within R A D β§ fcnl_on R A β§ fcnl_on (invRel R) D
S : Rel U V
S_match_CB : rel_within S C B β§ fcnl_on S C β§ fcnl_on (invRel S) B
X0 : Set U := A \ C
X : Set U := cum_rep_image R S X0
T : Rel U V := csb_m... | Please generate a tactic in lean4 to solve the state.
STATE:
case pos
U V : Type
A C : Set U
B D : Set V
h1 : C β A
h2 : D β B
h3 : A βΌ D
h4 : C βΌ B
R : Rel U V
R_match_AD : rel_within R A D β§ fcnl_on R A β§ fcnl_on (invRel R) D
S : Rel U V
S_match_CB : rel_within S C B β§ fcnl_on S C β§ fcnl_on (invRel S) B
X0 : Set U :=... |
https://github.com/djvelleman/HTPILeanPackage.git | 4d23e94fff351c65b5e1345c43451f2aa9908c27 | HTPILib/Chap8Part2.lean | HTPI.Cantor_Schroeder_Bernstein_theorem | [1559, 1] | [1718, 7] | obtain (m : Nat) (h8 : n = m + 1) from
exists_eq_add_one_of_ne_zero h7 | case pos
U V : Type
A C : Set U
B D : Set V
h1 : C β A
h2 : D β B
h3 : A βΌ D
h4 : C βΌ B
R : Rel U V
R_match_AD : rel_within R A D β§ fcnl_on R A β§ fcnl_on (invRel R) D
S : Rel U V
S_match_CB : rel_within S C B β§ fcnl_on S C β§ fcnl_on (invRel S) B
X0 : Set U := A \ C
X : Set U := cum_rep_image R S X0
T : Rel U V := csb_m... | case pos
U V : Type
A C : Set U
B D : Set V
h1 : C β A
h2 : D β B
h3 : A βΌ D
h4 : C βΌ B
R : Rel U V
R_match_AD : rel_within R A D β§ fcnl_on R A β§ fcnl_on (invRel R) D
S : Rel U V
S_match_CB : rel_within S C B β§ fcnl_on S C β§ fcnl_on (invRel S) B
X0 : Set U := A \ C
X : Set U := cum_rep_image R S X0
T : Rel U V := csb_m... | Please generate a tactic in lean4 to solve the state.
STATE:
case pos
U V : Type
A C : Set U
B D : Set V
h1 : C β A
h2 : D β B
h3 : A βΌ D
h4 : C βΌ B
R : Rel U V
R_match_AD : rel_within R A D β§ fcnl_on R A β§ fcnl_on (invRel R) D
S : Rel U V
S_match_CB : rel_within S C B β§ fcnl_on S C β§ fcnl_on (invRel S) B
X0 : Set U :=... |
https://github.com/djvelleman/HTPILeanPackage.git | 4d23e94fff351c65b5e1345c43451f2aa9908c27 | HTPILib/Chap8Part2.lean | HTPI.Cantor_Schroeder_Bernstein_theorem | [1559, 1] | [1718, 7] | rewrite [h8] at h6 | case pos
U V : Type
A C : Set U
B D : Set V
h1 : C β A
h2 : D β B
h3 : A βΌ D
h4 : C βΌ B
R : Rel U V
R_match_AD : rel_within R A D β§ fcnl_on R A β§ fcnl_on (invRel R) D
S : Rel U V
S_match_CB : rel_within S C B β§ fcnl_on S C β§ fcnl_on (invRel S) B
X0 : Set U := A \ C
X : Set U := cum_rep_image R S X0
T : Rel U V := csb_m... | case pos
U V : Type
A C : Set U
B D : Set V
h1 : C β A
h2 : D β B
h3 : A βΌ D
h4 : C βΌ B
R : Rel U V
R_match_AD : rel_within R A D β§ fcnl_on R A β§ fcnl_on (invRel R) D
S : Rel U V
S_match_CB : rel_within S C B β§ fcnl_on S C β§ fcnl_on (invRel S) B
X0 : Set U := A \ C
X : Set U := cum_rep_image R S X0
T : Rel U V := csb_m... | Please generate a tactic in lean4 to solve the state.
STATE:
case pos
U V : Type
A C : Set U
B D : Set V
h1 : C β A
h2 : D β B
h3 : A βΌ D
h4 : C βΌ B
R : Rel U V
R_match_AD : rel_within R A D β§ fcnl_on R A β§ fcnl_on (invRel R) D
S : Rel U V
S_match_CB : rel_within S C B β§ fcnl_on S C β§ fcnl_on (invRel S) B
X0 : Set U :=... |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.