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.Lemma_8_2_2_2 | [1306, 1] | [1330, 7] | apply Exists.intro (emptyRel Nat U) | case neg
U : Type
F : Set (Set U)
h : β A β F, ctble A
A : Set U
h2 : A β F
β’ β SA, A β F β fcnl_onto_from_nat SA A | case neg
U : Type
F : Set (Set U)
h : β A β F, ctble A
A : Set U
h2 : A β F
β’ A β F β fcnl_onto_from_nat (emptyRel β U) A | Please generate a tactic in lean4 to solve the state.
STATE:
case neg
U : Type
F : Set (Set U)
h : β A β F, ctble A
A : Set U
h2 : A β F
β’ β SA, A β F β fcnl_onto_from_nat SA A
TACTIC:
|
https://github.com/djvelleman/HTPILeanPackage.git | 4d23e94fff351c65b5e1345c43451f2aa9908c27 | HTPILib/Chap8Part2.lean | HTPI.Lemma_8_2_2_2 | [1306, 1] | [1330, 7] | assume h3 : A β F | case neg
U : Type
F : Set (Set U)
h : β A β F, ctble A
A : Set U
h2 : A β F
β’ A β F β fcnl_onto_from_nat (emptyRel β U) A | case neg
U : Type
F : Set (Set U)
h : β A β F, ctble A
A : Set U
h2 : A β F
h3 : A β F
β’ fcnl_onto_from_nat (emptyRel β U) A | Please generate a tactic in lean4 to solve the state.
STATE:
case neg
U : Type
F : Set (Set U)
h : β A β F, ctble A
A : Set U
h2 : A β F
β’ A β F β fcnl_onto_from_nat (emptyRel β U) A
TACTIC:
|
https://github.com/djvelleman/HTPILeanPackage.git | 4d23e94fff351c65b5e1345c43451f2aa9908c27 | HTPILib/Chap8Part2.lean | HTPI.Lemma_8_2_2_2 | [1306, 1] | [1330, 7] | show fcnl_onto_from_nat (emptyRel Nat U) A from absurd h3 h2 | case neg
U : Type
F : Set (Set U)
h : β A β F, ctble A
A : Set U
h2 : A β F
h3 : A β F
β’ fcnl_onto_from_nat (emptyRel β U) A | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case neg
U : Type
F : Set (Set U)
h : β A β F, ctble A
A : Set U
h2 : A β F
h3 : A β F
β’ fcnl_onto_from_nat (emptyRel β U) A
TACTIC:
|
https://github.com/djvelleman/HTPILeanPackage.git | 4d23e94fff351c65b5e1345c43451f2aa9908c27 | HTPILib/Chap8Part2.lean | HTPI.Theorem_8_2_2 | [1332, 1] | [1337, 7] | obtain (f : Set U β Rel Nat U) (h3 : β A β F, fcnl_onto_from_nat (f A) A)
from Lemma_8_2_2_2 h2 | U : Type
F : Set (Set U)
h1 : ctble F
h2 : β A β F, ctble A
β’ ctble (ββ F) | U : Type
F : Set (Set U)
h1 : ctble F
h2 : β A β F, ctble A
f : Set U β Rel β U
h3 : β A β F, fcnl_onto_from_nat (f A) A
β’ ctble (ββ F) | Please generate a tactic in lean4 to solve the state.
STATE:
U : Type
F : Set (Set U)
h1 : ctble F
h2 : β A β F, ctble A
β’ ctble (ββ F)
TACTIC:
|
https://github.com/djvelleman/HTPILeanPackage.git | 4d23e94fff351c65b5e1345c43451f2aa9908c27 | HTPILib/Chap8Part2.lean | HTPI.Theorem_8_2_2 | [1332, 1] | [1337, 7] | show ctble (ββ F) from Lemma_8_2_2_1 h1 h3 | U : Type
F : Set (Set U)
h1 : ctble F
h2 : β A β F, ctble A
f : Set U β Rel β U
h3 : β A β F, fcnl_onto_from_nat (f A) A
β’ ctble (ββ F) | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
U : Type
F : Set (Set U)
h1 : ctble F
h2 : β A β F, ctble A
f : Set U β Rel β U
h3 : β A β F, fcnl_onto_from_nat (f A) A
β’ ctble (ββ F)
TACTIC:
|
https://github.com/djvelleman/HTPILeanPackage.git | 4d23e94fff351c65b5e1345c43451f2aa9908c27 | HTPILib/Chap8Part2.lean | HTPI.seq_def | [1339, 1] | [1340, 41] | rfl | U : Type
A : Set U
l : List U
β’ l β seq A β β x β l, x β A | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
U : Type
A : Set U
l : List U
β’ l β seq A β β x β l, x β A
TACTIC:
|
https://github.com/djvelleman/HTPILeanPackage.git | 4d23e94fff351c65b5e1345c43451f2aa9908c27 | HTPILib/Chap8Part2.lean | HTPI.sbl_base | [1342, 1] | [1365, 7] | apply Set.ext | U : Type
A : Set U
β’ seq_by_length A 0 = {[]} | case h
U : Type
A : Set U
β’ β (x : List U), x β seq_by_length A 0 β x β {[]} | Please generate a tactic in lean4 to solve the state.
STATE:
U : Type
A : Set U
β’ seq_by_length A 0 = {[]}
TACTIC:
|
https://github.com/djvelleman/HTPILeanPackage.git | 4d23e94fff351c65b5e1345c43451f2aa9908c27 | HTPILib/Chap8Part2.lean | HTPI.sbl_base | [1342, 1] | [1365, 7] | fix l : List U | case h
U : Type
A : Set U
β’ β (x : List U), x β seq_by_length A 0 β x β {[]} | case h
U : Type
A : Set U
l : List U
β’ l β seq_by_length A 0 β l β {[]} | Please generate a tactic in lean4 to solve the state.
STATE:
case h
U : Type
A : Set U
β’ β (x : List U), x β seq_by_length A 0 β x β {[]}
TACTIC:
|
https://github.com/djvelleman/HTPILeanPackage.git | 4d23e94fff351c65b5e1345c43451f2aa9908c27 | HTPILib/Chap8Part2.lean | HTPI.sbl_base | [1342, 1] | [1365, 7] | apply Iff.intro | case h
U : Type
A : Set U
l : List U
β’ l β seq_by_length A 0 β l β {[]} | case h.mp
U : Type
A : Set U
l : List U
β’ l β seq_by_length A 0 β l β {[]}
case h.mpr
U : Type
A : Set U
l : List U
β’ l β {[]} β l β seq_by_length A 0 | Please generate a tactic in lean4 to solve the state.
STATE:
case h
U : Type
A : Set U
l : List U
β’ l β seq_by_length A 0 β l β {[]}
TACTIC:
|
https://github.com/djvelleman/HTPILeanPackage.git | 4d23e94fff351c65b5e1345c43451f2aa9908c27 | HTPILib/Chap8Part2.lean | HTPI.sbl_base | [1342, 1] | [1365, 7] | assume h1 : l β seq_by_length A 0 | case h.mp
U : Type
A : Set U
l : List U
β’ l β seq_by_length A 0 β l β {[]} | case h.mp
U : Type
A : Set U
l : List U
h1 : l β seq_by_length A 0
β’ l β {[]} | Please generate a tactic in lean4 to solve the state.
STATE:
case h.mp
U : Type
A : Set U
l : List U
β’ l β seq_by_length A 0 β l β {[]}
TACTIC:
|
https://github.com/djvelleman/HTPILeanPackage.git | 4d23e94fff351c65b5e1345c43451f2aa9908c27 | HTPILib/Chap8Part2.lean | HTPI.sbl_base | [1342, 1] | [1365, 7] | define at h1 | case h.mp
U : Type
A : Set U
l : List U
h1 : l β seq_by_length A 0
β’ l β {[]} | case h.mp
U : Type
A : Set U
l : List U
h1 : l β seq A β§ List.length l = 0
β’ l β {[]} | Please generate a tactic in lean4 to solve the state.
STATE:
case h.mp
U : Type
A : Set U
l : List U
h1 : l β seq_by_length A 0
β’ l β {[]}
TACTIC:
|
https://github.com/djvelleman/HTPILeanPackage.git | 4d23e94fff351c65b5e1345c43451f2aa9908c27 | HTPILib/Chap8Part2.lean | HTPI.sbl_base | [1342, 1] | [1365, 7] | rewrite [List.length_eq_zero] at h1 | case h.mp
U : Type
A : Set U
l : List U
h1 : l β seq A β§ List.length l = 0
β’ l β {[]} | case h.mp
U : Type
A : Set U
l : List U
h1 : l β seq A β§ l = []
β’ l β {[]} | Please generate a tactic in lean4 to solve the state.
STATE:
case h.mp
U : Type
A : Set U
l : List U
h1 : l β seq A β§ List.length l = 0
β’ l β {[]}
TACTIC:
|
https://github.com/djvelleman/HTPILeanPackage.git | 4d23e94fff351c65b5e1345c43451f2aa9908c27 | HTPILib/Chap8Part2.lean | HTPI.sbl_base | [1342, 1] | [1365, 7] | define | case h.mp
U : Type
A : Set U
l : List U
h1 : l β seq A β§ l = []
β’ l β {[]} | case h.mp
U : Type
A : Set U
l : List U
h1 : l β seq A β§ l = []
β’ l = [] | Please generate a tactic in lean4 to solve the state.
STATE:
case h.mp
U : Type
A : Set U
l : List U
h1 : l β seq A β§ l = []
β’ l β {[]}
TACTIC:
|
https://github.com/djvelleman/HTPILeanPackage.git | 4d23e94fff351c65b5e1345c43451f2aa9908c27 | HTPILib/Chap8Part2.lean | HTPI.sbl_base | [1342, 1] | [1365, 7] | show l = [] from h1.right | case h.mp
U : Type
A : Set U
l : List U
h1 : l β seq A β§ l = []
β’ l = [] | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case h.mp
U : Type
A : Set U
l : List U
h1 : l β seq A β§ l = []
β’ l = []
TACTIC:
|
https://github.com/djvelleman/HTPILeanPackage.git | 4d23e94fff351c65b5e1345c43451f2aa9908c27 | HTPILib/Chap8Part2.lean | HTPI.sbl_base | [1342, 1] | [1365, 7] | assume h1 : l β {[]} | case h.mpr
U : Type
A : Set U
l : List U
β’ l β {[]} β l β seq_by_length A 0 | case h.mpr
U : Type
A : Set U
l : List U
h1 : l β {[]}
β’ l β seq_by_length A 0 | Please generate a tactic in lean4 to solve the state.
STATE:
case h.mpr
U : Type
A : Set U
l : List U
β’ l β {[]} β l β seq_by_length A 0
TACTIC:
|
https://github.com/djvelleman/HTPILeanPackage.git | 4d23e94fff351c65b5e1345c43451f2aa9908c27 | HTPILib/Chap8Part2.lean | HTPI.sbl_base | [1342, 1] | [1365, 7] | define at h1 | case h.mpr
U : Type
A : Set U
l : List U
h1 : l β {[]}
β’ l β seq_by_length A 0 | case h.mpr
U : Type
A : Set U
l : List U
h1 : l = []
β’ l β seq_by_length A 0 | Please generate a tactic in lean4 to solve the state.
STATE:
case h.mpr
U : Type
A : Set U
l : List U
h1 : l β {[]}
β’ l β seq_by_length A 0
TACTIC:
|
https://github.com/djvelleman/HTPILeanPackage.git | 4d23e94fff351c65b5e1345c43451f2aa9908c27 | HTPILib/Chap8Part2.lean | HTPI.sbl_base | [1342, 1] | [1365, 7] | define | case h.mpr
U : Type
A : Set U
l : List U
h1 : l = []
β’ l β seq_by_length A 0 | case h.mpr
U : Type
A : Set U
l : List U
h1 : l = []
β’ l β seq A β§ List.length l = 0 | Please generate a tactic in lean4 to solve the state.
STATE:
case h.mpr
U : Type
A : Set U
l : List U
h1 : l = []
β’ l β seq_by_length A 0
TACTIC:
|
https://github.com/djvelleman/HTPILeanPackage.git | 4d23e94fff351c65b5e1345c43451f2aa9908c27 | HTPILib/Chap8Part2.lean | HTPI.sbl_base | [1342, 1] | [1365, 7] | apply And.intro _ (List.length_eq_zero.rtl h1) | case h.mpr
U : Type
A : Set U
l : List U
h1 : l = []
β’ l β seq A β§ List.length l = 0 | U : Type
A : Set U
l : List U
h1 : l = []
β’ l β seq A | Please generate a tactic in lean4 to solve the state.
STATE:
case h.mpr
U : Type
A : Set U
l : List U
h1 : l = []
β’ l β seq A β§ List.length l = 0
TACTIC:
|
https://github.com/djvelleman/HTPILeanPackage.git | 4d23e94fff351c65b5e1345c43451f2aa9908c27 | HTPILib/Chap8Part2.lean | HTPI.sbl_base | [1342, 1] | [1365, 7] | define | U : Type
A : Set U
l : List U
h1 : l = []
β’ l β seq A | U : Type
A : Set U
l : List U
h1 : l = []
β’ β x β l, x β A | Please generate a tactic in lean4 to solve the state.
STATE:
U : Type
A : Set U
l : List U
h1 : l = []
β’ l β seq A
TACTIC:
|
https://github.com/djvelleman/HTPILeanPackage.git | 4d23e94fff351c65b5e1345c43451f2aa9908c27 | HTPILib/Chap8Part2.lean | HTPI.sbl_base | [1342, 1] | [1365, 7] | fix x : U | U : Type
A : Set U
l : List U
h1 : l = []
β’ β x β l, x β A | U : Type
A : Set U
l : List U
h1 : l = []
x : U
β’ x β l β x β A | Please generate a tactic in lean4 to solve the state.
STATE:
U : Type
A : Set U
l : List U
h1 : l = []
β’ β x β l, x β A
TACTIC:
|
https://github.com/djvelleman/HTPILeanPackage.git | 4d23e94fff351c65b5e1345c43451f2aa9908c27 | HTPILib/Chap8Part2.lean | HTPI.sbl_base | [1342, 1] | [1365, 7] | assume h2 : x β l | U : Type
A : Set U
l : List U
h1 : l = []
x : U
β’ x β l β x β A | U : Type
A : Set U
l : List U
h1 : l = []
x : U
h2 : x β l
β’ x β A | Please generate a tactic in lean4 to solve the state.
STATE:
U : Type
A : Set U
l : List U
h1 : l = []
x : U
β’ x β l β x β A
TACTIC:
|
https://github.com/djvelleman/HTPILeanPackage.git | 4d23e94fff351c65b5e1345c43451f2aa9908c27 | HTPILib/Chap8Part2.lean | HTPI.sbl_base | [1342, 1] | [1365, 7] | contradict h2 with h3 | U : Type
A : Set U
l : List U
h1 : l = []
x : U
h2 : x β l
β’ x β A | U : Type
A : Set U
l : List U
h1 : l = []
x : U
h2 : x β l
h3 : Β¬x β A
β’ x β l | Please generate a tactic in lean4 to solve the state.
STATE:
U : Type
A : Set U
l : List U
h1 : l = []
x : U
h2 : x β l
β’ x β A
TACTIC:
|
https://github.com/djvelleman/HTPILeanPackage.git | 4d23e94fff351c65b5e1345c43451f2aa9908c27 | HTPILib/Chap8Part2.lean | HTPI.sbl_base | [1342, 1] | [1365, 7] | rewrite [h1] | U : Type
A : Set U
l : List U
h1 : l = []
x : U
h2 : x β l
h3 : Β¬x β A
β’ x β l | U : Type
A : Set U
l : List U
h1 : l = []
x : U
h2 : x β l
h3 : Β¬x β A
β’ x β [] | Please generate a tactic in lean4 to solve the state.
STATE:
U : Type
A : Set U
l : List U
h1 : l = []
x : U
h2 : x β l
h3 : Β¬x β A
β’ x β l
TACTIC:
|
https://github.com/djvelleman/HTPILeanPackage.git | 4d23e94fff351c65b5e1345c43451f2aa9908c27 | HTPILib/Chap8Part2.lean | HTPI.sbl_base | [1342, 1] | [1365, 7] | show x β [] from List.not_mem_nil x | U : Type
A : Set U
l : List U
h1 : l = []
x : U
h2 : x β l
h3 : Β¬x β A
β’ x β [] | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
U : Type
A : Set U
l : List U
h1 : l = []
x : U
h2 : x β l
h3 : Β¬x β A
β’ x β []
TACTIC:
|
https://github.com/djvelleman/HTPILeanPackage.git | 4d23e94fff351c65b5e1345c43451f2aa9908c27 | HTPILib/Chap8Part2.lean | HTPI.seq_cons_def | [1367, 1] | [1368, 41] | rfl | U : Type
x : U
l : List U
β’ seq_cons U (x, l) = x :: l | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
U : Type
x : U
l : List U
β’ seq_cons U (x, l) = x :: l
TACTIC:
|
https://github.com/djvelleman/HTPILeanPackage.git | 4d23e94fff351c65b5e1345c43451f2aa9908c27 | HTPILib/Chap8Part2.lean | HTPI.seq_cons_one_one | [1370, 1] | [1377, 7] | fix (a1, l1) : U Γ List U | U : Type
β’ one_to_one (seq_cons U) | U : Type
a1 : U
l1 : List U
β’ β (x2 : U Γ List U), seq_cons U (a1, l1) = seq_cons U x2 β (a1, l1) = x2 | Please generate a tactic in lean4 to solve the state.
STATE:
U : Type
β’ one_to_one (seq_cons U)
TACTIC:
|
https://github.com/djvelleman/HTPILeanPackage.git | 4d23e94fff351c65b5e1345c43451f2aa9908c27 | HTPILib/Chap8Part2.lean | HTPI.seq_cons_one_one | [1370, 1] | [1377, 7] | fix (a2, l2) : U Γ List U | U : Type
a1 : U
l1 : List U
β’ β (x2 : U Γ List U), seq_cons U (a1, l1) = seq_cons U x2 β (a1, l1) = x2 | U : Type
a1 : U
l1 : List U
a2 : U
l2 : List U
β’ seq_cons U (a1, l1) = seq_cons U (a2, l2) β (a1, l1) = (a2, l2) | Please generate a tactic in lean4 to solve the state.
STATE:
U : Type
a1 : U
l1 : List U
β’ β (x2 : U Γ List U), seq_cons U (a1, l1) = seq_cons U x2 β (a1, l1) = x2
TACTIC:
|
https://github.com/djvelleman/HTPILeanPackage.git | 4d23e94fff351c65b5e1345c43451f2aa9908c27 | HTPILib/Chap8Part2.lean | HTPI.seq_cons_one_one | [1370, 1] | [1377, 7] | assume h1 : seq_cons U (a1, l1) = seq_cons U (a2, l2) | U : Type
a1 : U
l1 : List U
a2 : U
l2 : List U
β’ seq_cons U (a1, l1) = seq_cons U (a2, l2) β (a1, l1) = (a2, l2) | U : Type
a1 : U
l1 : List U
a2 : U
l2 : List U
h1 : seq_cons U (a1, l1) = seq_cons U (a2, l2)
β’ (a1, l1) = (a2, l2) | Please generate a tactic in lean4 to solve the state.
STATE:
U : Type
a1 : U
l1 : List U
a2 : U
l2 : List U
β’ seq_cons U (a1, l1) = seq_cons U (a2, l2) β (a1, l1) = (a2, l2)
TACTIC:
|
https://github.com/djvelleman/HTPILeanPackage.git | 4d23e94fff351c65b5e1345c43451f2aa9908c27 | HTPILib/Chap8Part2.lean | HTPI.seq_cons_one_one | [1370, 1] | [1377, 7] | rewrite [seq_cons_def, seq_cons_def] at h1 | U : Type
a1 : U
l1 : List U
a2 : U
l2 : List U
h1 : seq_cons U (a1, l1) = seq_cons U (a2, l2)
β’ (a1, l1) = (a2, l2) | U : Type
a1 : U
l1 : List U
a2 : U
l2 : List U
h1 : a1 :: l1 = a2 :: l2
β’ (a1, l1) = (a2, l2) | Please generate a tactic in lean4 to solve the state.
STATE:
U : Type
a1 : U
l1 : List U
a2 : U
l2 : List U
h1 : seq_cons U (a1, l1) = seq_cons U (a2, l2)
β’ (a1, l1) = (a2, l2)
TACTIC:
|
https://github.com/djvelleman/HTPILeanPackage.git | 4d23e94fff351c65b5e1345c43451f2aa9908c27 | HTPILib/Chap8Part2.lean | HTPI.seq_cons_one_one | [1370, 1] | [1377, 7] | rewrite [List.cons_eq_cons] at h1 | U : Type
a1 : U
l1 : List U
a2 : U
l2 : List U
h1 : a1 :: l1 = a2 :: l2
β’ (a1, l1) = (a2, l2) | U : Type
a1 : U
l1 : List U
a2 : U
l2 : List U
h1 : a1 = a2 β§ l1 = l2
β’ (a1, l1) = (a2, l2) | Please generate a tactic in lean4 to solve the state.
STATE:
U : Type
a1 : U
l1 : List U
a2 : U
l2 : List U
h1 : a1 :: l1 = a2 :: l2
β’ (a1, l1) = (a2, l2)
TACTIC:
|
https://github.com/djvelleman/HTPILeanPackage.git | 4d23e94fff351c65b5e1345c43451f2aa9908c27 | HTPILib/Chap8Part2.lean | HTPI.seq_cons_one_one | [1370, 1] | [1377, 7] | rewrite [h1.left, h1.right] | U : Type
a1 : U
l1 : List U
a2 : U
l2 : List U
h1 : a1 = a2 β§ l1 = l2
β’ (a1, l1) = (a2, l2) | U : Type
a1 : U
l1 : List U
a2 : U
l2 : List U
h1 : a1 = a2 β§ l1 = l2
β’ (a2, l2) = (a2, l2) | Please generate a tactic in lean4 to solve the state.
STATE:
U : Type
a1 : U
l1 : List U
a2 : U
l2 : List U
h1 : a1 = a2 β§ l1 = l2
β’ (a1, l1) = (a2, l2)
TACTIC:
|
https://github.com/djvelleman/HTPILeanPackage.git | 4d23e94fff351c65b5e1345c43451f2aa9908c27 | HTPILib/Chap8Part2.lean | HTPI.seq_cons_one_one | [1370, 1] | [1377, 7] | rfl | U : Type
a1 : U
l1 : List U
a2 : U
l2 : List U
h1 : a1 = a2 β§ l1 = l2
β’ (a2, l2) = (a2, l2) | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
U : Type
a1 : U
l1 : List U
a2 : U
l2 : List U
h1 : a1 = a2 β§ l1 = l2
β’ (a2, l2) = (a2, l2)
TACTIC:
|
https://github.com/djvelleman/HTPILeanPackage.git | 4d23e94fff351c65b5e1345c43451f2aa9908c27 | HTPILib/Chap8Part2.lean | HTPI.Lemma_8_2_4_2 | [1388, 1] | [1407, 7] | by_induc | U : Type
A : Set U
h1 : ctble A
β’ β (n : β), ctble (seq_by_length A n) | case Base_Case
U : Type
A : Set U
h1 : ctble A
β’ ctble (seq_by_length A 0)
case Induction_Step
U : Type
A : Set U
h1 : ctble A
β’ β (n : β), ctble (seq_by_length A n) β ctble (seq_by_length A (n + 1)) | Please generate a tactic in lean4 to solve the state.
STATE:
U : Type
A : Set U
h1 : ctble A
β’ β (n : β), ctble (seq_by_length A n)
TACTIC:
|
https://github.com/djvelleman/HTPILeanPackage.git | 4d23e94fff351c65b5e1345c43451f2aa9908c27 | HTPILib/Chap8Part2.lean | HTPI.Lemma_8_2_4_2 | [1388, 1] | [1407, 7] | rewrite [sbl_base] | case Base_Case
U : Type
A : Set U
h1 : ctble A
β’ ctble (seq_by_length A 0) | case Base_Case
U : Type
A : Set U
h1 : ctble A
β’ ctble {[]} | Please generate a tactic in lean4 to solve the state.
STATE:
case Base_Case
U : Type
A : Set U
h1 : ctble A
β’ ctble (seq_by_length A 0)
TACTIC:
|
https://github.com/djvelleman/HTPILeanPackage.git | 4d23e94fff351c65b5e1345c43451f2aa9908c27 | HTPILib/Chap8Part2.lean | HTPI.Lemma_8_2_4_2 | [1388, 1] | [1407, 7] | define | case Base_Case
U : Type
A : Set U
h1 : ctble A
β’ ctble {[]} | case Base_Case
U : Type
A : Set U
h1 : ctble A
β’ finite {[]} β¨ denum {[]} | Please generate a tactic in lean4 to solve the state.
STATE:
case Base_Case
U : Type
A : Set U
h1 : ctble A
β’ ctble {[]}
TACTIC:
|
https://github.com/djvelleman/HTPILeanPackage.git | 4d23e94fff351c65b5e1345c43451f2aa9908c27 | HTPILib/Chap8Part2.lean | HTPI.Lemma_8_2_4_2 | [1388, 1] | [1407, 7] | apply Or.inl | case Base_Case
U : Type
A : Set U
h1 : ctble A
β’ finite {[]} β¨ denum {[]} | case Base_Case.h
U : Type
A : Set U
h1 : ctble A
β’ finite {[]} | Please generate a tactic in lean4 to solve the state.
STATE:
case Base_Case
U : Type
A : Set U
h1 : ctble A
β’ finite {[]} β¨ denum {[]}
TACTIC:
|
https://github.com/djvelleman/HTPILeanPackage.git | 4d23e94fff351c65b5e1345c43451f2aa9908c27 | HTPILib/Chap8Part2.lean | HTPI.Lemma_8_2_4_2 | [1388, 1] | [1407, 7] | rewrite [finite_def] | case Base_Case.h
U : Type
A : Set U
h1 : ctble A
β’ finite {[]} | case Base_Case.h
U : Type
A : Set U
h1 : ctble A
β’ β n, numElts {[]} n | Please generate a tactic in lean4 to solve the state.
STATE:
case Base_Case.h
U : Type
A : Set U
h1 : ctble A
β’ finite {[]}
TACTIC:
|
https://github.com/djvelleman/HTPILeanPackage.git | 4d23e94fff351c65b5e1345c43451f2aa9908c27 | HTPILib/Chap8Part2.lean | HTPI.Lemma_8_2_4_2 | [1388, 1] | [1407, 7] | apply Exists.intro 1 | case Base_Case.h
U : Type
A : Set U
h1 : ctble A
β’ β n, numElts {[]} n | case Base_Case.h
U : Type
A : Set U
h1 : ctble A
β’ numElts {[]} 1 | Please generate a tactic in lean4 to solve the state.
STATE:
case Base_Case.h
U : Type
A : Set U
h1 : ctble A
β’ β n, numElts {[]} n
TACTIC:
|
https://github.com/djvelleman/HTPILeanPackage.git | 4d23e94fff351c65b5e1345c43451f2aa9908c27 | HTPILib/Chap8Part2.lean | HTPI.Lemma_8_2_4_2 | [1388, 1] | [1407, 7] | show numElts {[]} 1 from singleton_one_elt [] | case Base_Case.h
U : Type
A : Set U
h1 : ctble A
β’ numElts {[]} 1 | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case Base_Case.h
U : Type
A : Set U
h1 : ctble A
β’ numElts {[]} 1
TACTIC:
|
https://github.com/djvelleman/HTPILeanPackage.git | 4d23e94fff351c65b5e1345c43451f2aa9908c27 | HTPILib/Chap8Part2.lean | HTPI.Lemma_8_2_4_2 | [1388, 1] | [1407, 7] | fix n : Nat | case Induction_Step
U : Type
A : Set U
h1 : ctble A
β’ β (n : β), ctble (seq_by_length A n) β ctble (seq_by_length A (n + 1)) | case Induction_Step
U : Type
A : Set U
h1 : ctble A
n : β
β’ ctble (seq_by_length A n) β ctble (seq_by_length A (n + 1)) | Please generate a tactic in lean4 to solve the state.
STATE:
case Induction_Step
U : Type
A : Set U
h1 : ctble A
β’ β (n : β), ctble (seq_by_length A n) β ctble (seq_by_length A (n + 1))
TACTIC:
|
https://github.com/djvelleman/HTPILeanPackage.git | 4d23e94fff351c65b5e1345c43451f2aa9908c27 | HTPILib/Chap8Part2.lean | HTPI.Lemma_8_2_4_2 | [1388, 1] | [1407, 7] | assume ih : ctble (seq_by_length A n) | case Induction_Step
U : Type
A : Set U
h1 : ctble A
n : β
β’ ctble (seq_by_length A n) β ctble (seq_by_length A (n + 1)) | case Induction_Step
U : Type
A : Set U
h1 : ctble A
n : β
ih : ctble (seq_by_length A n)
β’ ctble (seq_by_length A (n + 1)) | Please generate a tactic in lean4 to solve the state.
STATE:
case Induction_Step
U : Type
A : Set U
h1 : ctble A
n : β
β’ ctble (seq_by_length A n) β ctble (seq_by_length A (n + 1))
TACTIC:
|
https://github.com/djvelleman/HTPILeanPackage.git | 4d23e94fff351c65b5e1345c43451f2aa9908c27 | HTPILib/Chap8Part2.lean | HTPI.Lemma_8_2_4_2 | [1388, 1] | [1407, 7] | have h2 : A Γβ (seq_by_length A n) βΌ seq_by_length A (n + 1) :=
Lemma_8_2_4_1 A n | case Induction_Step
U : Type
A : Set U
h1 : ctble A
n : β
ih : ctble (seq_by_length A n)
β’ ctble (seq_by_length A (n + 1)) | case Induction_Step
U : Type
A : Set U
h1 : ctble A
n : β
ih : ctble (seq_by_length A n)
h2 : A Γβ seq_by_length A n βΌ seq_by_length A (n + 1)
β’ ctble (seq_by_length A (n + 1)) | Please generate a tactic in lean4 to solve the state.
STATE:
case Induction_Step
U : Type
A : Set U
h1 : ctble A
n : β
ih : ctble (seq_by_length A n)
β’ ctble (seq_by_length A (n + 1))
TACTIC:
|
https://github.com/djvelleman/HTPILeanPackage.git | 4d23e94fff351c65b5e1345c43451f2aa9908c27 | HTPILib/Chap8Part2.lean | HTPI.Lemma_8_2_4_2 | [1388, 1] | [1407, 7] | have h3 : ctble (A Γβ (seq_by_length A n)) := Theorem_8_2_1_1 h1 ih | case Induction_Step
U : Type
A : Set U
h1 : ctble A
n : β
ih : ctble (seq_by_length A n)
h2 : A Γβ seq_by_length A n βΌ seq_by_length A (n + 1)
β’ ctble (seq_by_length A (n + 1)) | case Induction_Step
U : Type
A : Set U
h1 : ctble A
n : β
ih : ctble (seq_by_length A n)
h2 : A Γβ seq_by_length A n βΌ seq_by_length A (n + 1)
h3 : ctble (A Γβ seq_by_length A n)
β’ ctble (seq_by_length A (n + 1)) | Please generate a tactic in lean4 to solve the state.
STATE:
case Induction_Step
U : Type
A : Set U
h1 : ctble A
n : β
ih : ctble (seq_by_length A n)
h2 : A Γβ seq_by_length A n βΌ seq_by_length A (n + 1)
β’ ctble (seq_by_length A (n + 1))
TACTIC:
|
https://github.com/djvelleman/HTPILeanPackage.git | 4d23e94fff351c65b5e1345c43451f2aa9908c27 | HTPILib/Chap8Part2.lean | HTPI.Lemma_8_2_4_2 | [1388, 1] | [1407, 7] | show ctble (seq_by_length A (n + 1)) from ctble_of_equinum_ctble h2 h3 | case Induction_Step
U : Type
A : Set U
h1 : ctble A
n : β
ih : ctble (seq_by_length A n)
h2 : A Γβ seq_by_length A n βΌ seq_by_length A (n + 1)
h3 : ctble (A Γβ seq_by_length A n)
β’ ctble (seq_by_length A (n + 1)) | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case Induction_Step
U : Type
A : Set U
h1 : ctble A
n : β
ih : ctble (seq_by_length A n)
h2 : A Γβ seq_by_length A n βΌ seq_by_length A (n + 1)
h3 : ctble (A Γβ seq_by_length A n)
β’ ctble (seq_by_length A (n + 1))
TACTIC:
|
https://github.com/djvelleman/HTPILeanPackage.git | 4d23e94fff351c65b5e1345c43451f2aa9908c27 | HTPILib/Chap8Part2.lean | HTPI.Lemma_8_2_4_3 | [1409, 1] | [1442, 7] | apply Set.ext | U : Type
A : Set U
β’ ββ sbl_set A = seq A | case h
U : Type
A : Set U
β’ β (x : List U), x β ββ sbl_set A β x β seq A | Please generate a tactic in lean4 to solve the state.
STATE:
U : Type
A : Set U
β’ ββ sbl_set A = seq A
TACTIC:
|
https://github.com/djvelleman/HTPILeanPackage.git | 4d23e94fff351c65b5e1345c43451f2aa9908c27 | HTPILib/Chap8Part2.lean | HTPI.Lemma_8_2_4_3 | [1409, 1] | [1442, 7] | fix l : List U | case h
U : Type
A : Set U
β’ β (x : List U), x β ββ sbl_set A β x β seq A | case h
U : Type
A : Set U
l : List U
β’ l β ββ sbl_set A β l β seq A | Please generate a tactic in lean4 to solve the state.
STATE:
case h
U : Type
A : Set U
β’ β (x : List U), x β ββ sbl_set A β x β seq A
TACTIC:
|
https://github.com/djvelleman/HTPILeanPackage.git | 4d23e94fff351c65b5e1345c43451f2aa9908c27 | HTPILib/Chap8Part2.lean | HTPI.Lemma_8_2_4_3 | [1409, 1] | [1442, 7] | apply Iff.intro | case h
U : Type
A : Set U
l : List U
β’ l β ββ sbl_set A β l β seq A | case h.mp
U : Type
A : Set U
l : List U
β’ l β ββ sbl_set A β l β seq A
case h.mpr
U : Type
A : Set U
l : List U
β’ l β seq A β l β ββ sbl_set A | Please generate a tactic in lean4 to solve the state.
STATE:
case h
U : Type
A : Set U
l : List U
β’ l β ββ sbl_set A β l β seq A
TACTIC:
|
https://github.com/djvelleman/HTPILeanPackage.git | 4d23e94fff351c65b5e1345c43451f2aa9908c27 | HTPILib/Chap8Part2.lean | HTPI.Lemma_8_2_4_3 | [1409, 1] | [1442, 7] | assume h1 : l β ββ (sbl_set A) | case h.mp
U : Type
A : Set U
l : List U
β’ l β ββ sbl_set A β l β seq A | case h.mp
U : Type
A : Set U
l : List U
h1 : l β ββ sbl_set A
β’ l β seq A | Please generate a tactic in lean4 to solve the state.
STATE:
case h.mp
U : Type
A : Set U
l : List U
β’ l β ββ sbl_set A β l β seq A
TACTIC:
|
https://github.com/djvelleman/HTPILeanPackage.git | 4d23e94fff351c65b5e1345c43451f2aa9908c27 | HTPILib/Chap8Part2.lean | HTPI.Lemma_8_2_4_3 | [1409, 1] | [1442, 7] | define at h1 | case h.mp
U : Type
A : Set U
l : List U
h1 : l β ββ sbl_set A
β’ l β seq A | case h.mp
U : Type
A : Set U
l : List U
h1 : β t β sbl_set A, l β t
β’ l β seq A | Please generate a tactic in lean4 to solve the state.
STATE:
case h.mp
U : Type
A : Set U
l : List U
h1 : l β ββ sbl_set A
β’ l β seq A
TACTIC:
|
https://github.com/djvelleman/HTPILeanPackage.git | 4d23e94fff351c65b5e1345c43451f2aa9908c27 | HTPILib/Chap8Part2.lean | HTPI.Lemma_8_2_4_3 | [1409, 1] | [1442, 7] | obtain (S : Set (List U)) (h2 : S β sbl_set A β§ l β S) from h1 | case h.mp
U : Type
A : Set U
l : List U
h1 : β t β sbl_set A, l β t
β’ l β seq A | case h.mp
U : Type
A : Set U
l : List U
h1 : β t β sbl_set A, l β t
S : Set (List U)
h2 : S β sbl_set A β§ l β S
β’ l β seq A | Please generate a tactic in lean4 to solve the state.
STATE:
case h.mp
U : Type
A : Set U
l : List U
h1 : β t β sbl_set A, l β t
β’ l β seq A
TACTIC:
|
https://github.com/djvelleman/HTPILeanPackage.git | 4d23e94fff351c65b5e1345c43451f2aa9908c27 | HTPILib/Chap8Part2.lean | HTPI.Lemma_8_2_4_3 | [1409, 1] | [1442, 7] | have h3 : S β sbl_set A := h2.left | case h.mp
U : Type
A : Set U
l : List U
h1 : β t β sbl_set A, l β t
S : Set (List U)
h2 : S β sbl_set A β§ l β S
β’ l β seq A | case h.mp
U : Type
A : Set U
l : List U
h1 : β t β sbl_set A, l β t
S : Set (List U)
h2 : S β sbl_set A β§ l β S
h3 : S β sbl_set A
β’ l β seq A | Please generate a tactic in lean4 to solve the state.
STATE:
case h.mp
U : Type
A : Set U
l : List U
h1 : β t β sbl_set A, l β t
S : Set (List U)
h2 : S β sbl_set A β§ l β S
β’ l β seq A
TACTIC:
|
https://github.com/djvelleman/HTPILeanPackage.git | 4d23e94fff351c65b5e1345c43451f2aa9908c27 | HTPILib/Chap8Part2.lean | HTPI.Lemma_8_2_4_3 | [1409, 1] | [1442, 7] | define at h3 | case h.mp
U : Type
A : Set U
l : List U
h1 : β t β sbl_set A, l β t
S : Set (List U)
h2 : S β sbl_set A β§ l β S
h3 : S β sbl_set A
β’ l β seq A | case h.mp
U : Type
A : Set U
l : List U
h1 : β t β sbl_set A, l β t
S : Set (List U)
h2 : S β sbl_set A β§ l β S
h3 : β n, seq_by_length A n = S
β’ l β seq A | Please generate a tactic in lean4 to solve the state.
STATE:
case h.mp
U : Type
A : Set U
l : List U
h1 : β t β sbl_set A, l β t
S : Set (List U)
h2 : S β sbl_set A β§ l β S
h3 : S β sbl_set A
β’ l β seq A
TACTIC:
|
https://github.com/djvelleman/HTPILeanPackage.git | 4d23e94fff351c65b5e1345c43451f2aa9908c27 | HTPILib/Chap8Part2.lean | HTPI.Lemma_8_2_4_3 | [1409, 1] | [1442, 7] | obtain (n : Nat) (h4 : seq_by_length A n = S) from h3 | case h.mp
U : Type
A : Set U
l : List U
h1 : β t β sbl_set A, l β t
S : Set (List U)
h2 : S β sbl_set A β§ l β S
h3 : β n, seq_by_length A n = S
β’ l β seq A | case h.mp
U : Type
A : Set U
l : List U
h1 : β t β sbl_set A, l β t
S : Set (List U)
h2 : S β sbl_set A β§ l β S
h3 : β n, seq_by_length A n = S
n : β
h4 : seq_by_length A n = S
β’ l β seq A | Please generate a tactic in lean4 to solve the state.
STATE:
case h.mp
U : Type
A : Set U
l : List U
h1 : β t β sbl_set A, l β t
S : Set (List U)
h2 : S β sbl_set A β§ l β S
h3 : β n, seq_by_length A n = S
β’ l β seq A
TACTIC:
|
https://github.com/djvelleman/HTPILeanPackage.git | 4d23e94fff351c65b5e1345c43451f2aa9908c27 | HTPILib/Chap8Part2.lean | HTPI.Lemma_8_2_4_3 | [1409, 1] | [1442, 7] | have h5 : l β S := h2.right | case h.mp
U : Type
A : Set U
l : List U
h1 : β t β sbl_set A, l β t
S : Set (List U)
h2 : S β sbl_set A β§ l β S
h3 : β n, seq_by_length A n = S
n : β
h4 : seq_by_length A n = S
β’ l β seq A | case h.mp
U : Type
A : Set U
l : List U
h1 : β t β sbl_set A, l β t
S : Set (List U)
h2 : S β sbl_set A β§ l β S
h3 : β n, seq_by_length A n = S
n : β
h4 : seq_by_length A n = S
h5 : l β S
β’ l β seq A | Please generate a tactic in lean4 to solve the state.
STATE:
case h.mp
U : Type
A : Set U
l : List U
h1 : β t β sbl_set A, l β t
S : Set (List U)
h2 : S β sbl_set A β§ l β S
h3 : β n, seq_by_length A n = S
n : β
h4 : seq_by_length A n = S
β’ l β seq A
TACTIC:
|
https://github.com/djvelleman/HTPILeanPackage.git | 4d23e94fff351c65b5e1345c43451f2aa9908c27 | HTPILib/Chap8Part2.lean | HTPI.Lemma_8_2_4_3 | [1409, 1] | [1442, 7] | rewrite [βh4] at h5 | case h.mp
U : Type
A : Set U
l : List U
h1 : β t β sbl_set A, l β t
S : Set (List U)
h2 : S β sbl_set A β§ l β S
h3 : β n, seq_by_length A n = S
n : β
h4 : seq_by_length A n = S
h5 : l β S
β’ l β seq A | case h.mp
U : Type
A : Set U
l : List U
h1 : β t β sbl_set A, l β t
S : Set (List U)
h2 : S β sbl_set A β§ l β S
h3 : β n, seq_by_length A n = S
n : β
h4 : seq_by_length A n = S
h5 : l β seq_by_length A n
β’ l β seq A | Please generate a tactic in lean4 to solve the state.
STATE:
case h.mp
U : Type
A : Set U
l : List U
h1 : β t β sbl_set A, l β t
S : Set (List U)
h2 : S β sbl_set A β§ l β S
h3 : β n, seq_by_length A n = S
n : β
h4 : seq_by_length A n = S
h5 : l β S
β’ l β seq A
TACTIC:
|
https://github.com/djvelleman/HTPILeanPackage.git | 4d23e94fff351c65b5e1345c43451f2aa9908c27 | HTPILib/Chap8Part2.lean | HTPI.Lemma_8_2_4_3 | [1409, 1] | [1442, 7] | define at h5 | case h.mp
U : Type
A : Set U
l : List U
h1 : β t β sbl_set A, l β t
S : Set (List U)
h2 : S β sbl_set A β§ l β S
h3 : β n, seq_by_length A n = S
n : β
h4 : seq_by_length A n = S
h5 : l β seq_by_length A n
β’ l β seq A | case h.mp
U : Type
A : Set U
l : List U
h1 : β t β sbl_set A, l β t
S : Set (List U)
h2 : S β sbl_set A β§ l β S
h3 : β n, seq_by_length A n = S
n : β
h4 : seq_by_length A n = S
h5 : l β seq A β§ List.length l = n
β’ l β seq A | Please generate a tactic in lean4 to solve the state.
STATE:
case h.mp
U : Type
A : Set U
l : List U
h1 : β t β sbl_set A, l β t
S : Set (List U)
h2 : S β sbl_set A β§ l β S
h3 : β n, seq_by_length A n = S
n : β
h4 : seq_by_length A n = S
h5 : l β seq_by_length A n
β’ l β seq A
TACTIC:
|
https://github.com/djvelleman/HTPILeanPackage.git | 4d23e94fff351c65b5e1345c43451f2aa9908c27 | HTPILib/Chap8Part2.lean | HTPI.Lemma_8_2_4_3 | [1409, 1] | [1442, 7] | show l β seq A from h5.left | case h.mp
U : Type
A : Set U
l : List U
h1 : β t β sbl_set A, l β t
S : Set (List U)
h2 : S β sbl_set A β§ l β S
h3 : β n, seq_by_length A n = S
n : β
h4 : seq_by_length A n = S
h5 : l β seq A β§ List.length l = n
β’ l β seq A | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case h.mp
U : Type
A : Set U
l : List U
h1 : β t β sbl_set A, l β t
S : Set (List U)
h2 : S β sbl_set A β§ l β S
h3 : β n, seq_by_length A n = S
n : β
h4 : seq_by_length A n = S
h5 : l β seq A β§ List.length l = n
β’ l β seq A
TACTIC:
|
https://github.com/djvelleman/HTPILeanPackage.git | 4d23e94fff351c65b5e1345c43451f2aa9908c27 | HTPILib/Chap8Part2.lean | HTPI.Lemma_8_2_4_3 | [1409, 1] | [1442, 7] | assume h1 : l β seq A | case h.mpr
U : Type
A : Set U
l : List U
β’ l β seq A β l β ββ sbl_set A | case h.mpr
U : Type
A : Set U
l : List U
h1 : l β seq A
β’ l β ββ sbl_set A | Please generate a tactic in lean4 to solve the state.
STATE:
case h.mpr
U : Type
A : Set U
l : List U
β’ l β seq A β l β ββ sbl_set A
TACTIC:
|
https://github.com/djvelleman/HTPILeanPackage.git | 4d23e94fff351c65b5e1345c43451f2aa9908c27 | HTPILib/Chap8Part2.lean | HTPI.Lemma_8_2_4_3 | [1409, 1] | [1442, 7] | define | case h.mpr
U : Type
A : Set U
l : List U
h1 : l β seq A
β’ l β ββ sbl_set A | case h.mpr
U : Type
A : Set U
l : List U
h1 : l β seq A
β’ β t β sbl_set A, l β t | Please generate a tactic in lean4 to solve the state.
STATE:
case h.mpr
U : Type
A : Set U
l : List U
h1 : l β seq A
β’ l β ββ sbl_set A
TACTIC:
|
https://github.com/djvelleman/HTPILeanPackage.git | 4d23e94fff351c65b5e1345c43451f2aa9908c27 | HTPILib/Chap8Part2.lean | HTPI.Lemma_8_2_4_3 | [1409, 1] | [1442, 7] | set n : Nat := l.length | case h.mpr
U : Type
A : Set U
l : List U
h1 : l β seq A
β’ β t β sbl_set A, l β t | case h.mpr
U : Type
A : Set U
l : List U
h1 : l β seq A
n : β := List.length l
β’ β t β sbl_set A, l β t | Please generate a tactic in lean4 to solve the state.
STATE:
case h.mpr
U : Type
A : Set U
l : List U
h1 : l β seq A
β’ β t β sbl_set A, l β t
TACTIC:
|
https://github.com/djvelleman/HTPILeanPackage.git | 4d23e94fff351c65b5e1345c43451f2aa9908c27 | HTPILib/Chap8Part2.lean | HTPI.Lemma_8_2_4_3 | [1409, 1] | [1442, 7] | apply Exists.intro (seq_by_length A n) | case h.mpr
U : Type
A : Set U
l : List U
h1 : l β seq A
n : β := List.length l
β’ β t β sbl_set A, l β t | case h.mpr
U : Type
A : Set U
l : List U
h1 : l β seq A
n : β := List.length l
β’ seq_by_length A n β sbl_set A β§ l β seq_by_length A n | Please generate a tactic in lean4 to solve the state.
STATE:
case h.mpr
U : Type
A : Set U
l : List U
h1 : l β seq A
n : β := List.length l
β’ β t β sbl_set A, l β t
TACTIC:
|
https://github.com/djvelleman/HTPILeanPackage.git | 4d23e94fff351c65b5e1345c43451f2aa9908c27 | HTPILib/Chap8Part2.lean | HTPI.Lemma_8_2_4_3 | [1409, 1] | [1442, 7] | apply And.intro | case h.mpr
U : Type
A : Set U
l : List U
h1 : l β seq A
n : β := List.length l
β’ seq_by_length A n β sbl_set A β§ l β seq_by_length A n | case h.mpr.left
U : Type
A : Set U
l : List U
h1 : l β seq A
n : β := List.length l
β’ seq_by_length A n β sbl_set A
case h.mpr.right
U : Type
A : Set U
l : List U
h1 : l β seq A
n : β := List.length l
β’ l β seq_by_length A n | Please generate a tactic in lean4 to solve the state.
STATE:
case h.mpr
U : Type
A : Set U
l : List U
h1 : l β seq A
n : β := List.length l
β’ seq_by_length A n β sbl_set A β§ l β seq_by_length A n
TACTIC:
|
https://github.com/djvelleman/HTPILeanPackage.git | 4d23e94fff351c65b5e1345c43451f2aa9908c27 | HTPILib/Chap8Part2.lean | HTPI.Lemma_8_2_4_3 | [1409, 1] | [1442, 7] | define | case h.mpr.left
U : Type
A : Set U
l : List U
h1 : l β seq A
n : β := List.length l
β’ seq_by_length A n β sbl_set A | case h.mpr.left
U : Type
A : Set U
l : List U
h1 : l β seq A
n : β := List.length l
β’ β n_1, seq_by_length A n_1 = seq_by_length A n | Please generate a tactic in lean4 to solve the state.
STATE:
case h.mpr.left
U : Type
A : Set U
l : List U
h1 : l β seq A
n : β := List.length l
β’ seq_by_length A n β sbl_set A
TACTIC:
|
https://github.com/djvelleman/HTPILeanPackage.git | 4d23e94fff351c65b5e1345c43451f2aa9908c27 | HTPILib/Chap8Part2.lean | HTPI.Lemma_8_2_4_3 | [1409, 1] | [1442, 7] | apply Exists.intro n | case h.mpr.left
U : Type
A : Set U
l : List U
h1 : l β seq A
n : β := List.length l
β’ β n_1, seq_by_length A n_1 = seq_by_length A n | case h.mpr.left
U : Type
A : Set U
l : List U
h1 : l β seq A
n : β := List.length l
β’ seq_by_length A n = seq_by_length A n | Please generate a tactic in lean4 to solve the state.
STATE:
case h.mpr.left
U : Type
A : Set U
l : List U
h1 : l β seq A
n : β := List.length l
β’ β n_1, seq_by_length A n_1 = seq_by_length A n
TACTIC:
|
https://github.com/djvelleman/HTPILeanPackage.git | 4d23e94fff351c65b5e1345c43451f2aa9908c27 | HTPILib/Chap8Part2.lean | HTPI.Lemma_8_2_4_3 | [1409, 1] | [1442, 7] | rfl | case h.mpr.left
U : Type
A : Set U
l : List U
h1 : l β seq A
n : β := List.length l
β’ seq_by_length A n = seq_by_length A n | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case h.mpr.left
U : Type
A : Set U
l : List U
h1 : l β seq A
n : β := List.length l
β’ seq_by_length A n = seq_by_length A n
TACTIC:
|
https://github.com/djvelleman/HTPILeanPackage.git | 4d23e94fff351c65b5e1345c43451f2aa9908c27 | HTPILib/Chap8Part2.lean | HTPI.Lemma_8_2_4_3 | [1409, 1] | [1442, 7] | define | case h.mpr.right
U : Type
A : Set U
l : List U
h1 : l β seq A
n : β := List.length l
β’ l β seq_by_length A n | case h.mpr.right
U : Type
A : Set U
l : List U
h1 : l β seq A
n : β := List.length l
β’ l β seq A β§ List.length l = n | Please generate a tactic in lean4 to solve the state.
STATE:
case h.mpr.right
U : Type
A : Set U
l : List U
h1 : l β seq A
n : β := List.length l
β’ l β seq_by_length A n
TACTIC:
|
https://github.com/djvelleman/HTPILeanPackage.git | 4d23e94fff351c65b5e1345c43451f2aa9908c27 | HTPILib/Chap8Part2.lean | HTPI.Lemma_8_2_4_3 | [1409, 1] | [1442, 7] | apply And.intro h1 | case h.mpr.right
U : Type
A : Set U
l : List U
h1 : l β seq A
n : β := List.length l
β’ l β seq A β§ List.length l = n | case h.mpr.right
U : Type
A : Set U
l : List U
h1 : l β seq A
n : β := List.length l
β’ List.length l = n | Please generate a tactic in lean4 to solve the state.
STATE:
case h.mpr.right
U : Type
A : Set U
l : List U
h1 : l β seq A
n : β := List.length l
β’ l β seq A β§ List.length l = n
TACTIC:
|
https://github.com/djvelleman/HTPILeanPackage.git | 4d23e94fff351c65b5e1345c43451f2aa9908c27 | HTPILib/Chap8Part2.lean | HTPI.Lemma_8_2_4_3 | [1409, 1] | [1442, 7] | rfl | case h.mpr.right
U : Type
A : Set U
l : List U
h1 : l β seq A
n : β := List.length l
β’ List.length l = n | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case h.mpr.right
U : Type
A : Set U
l : List U
h1 : l β seq A
n : β := List.length l
β’ List.length l = n
TACTIC:
|
https://github.com/djvelleman/HTPILeanPackage.git | 4d23e94fff351c65b5e1345c43451f2aa9908c27 | HTPILib/Chap8Part2.lean | HTPI.Lemma_8_2_4_4 | [1447, 1] | [1455, 7] | have h1 : β S β sbl_set A, β (n : Nat), seq_by_length A n = S := by
fix S : Set (List U)
assume h1 : S β sbl_set A
define at h1
show β (n : Nat), seq_by_length A n = S from h1
done | U : Type
A : Set U
β’ ctble (sbl_set A) | U : Type
A : Set U
h1 : β S β sbl_set A, β n, seq_by_length A n = S
β’ ctble (sbl_set A) | Please generate a tactic in lean4 to solve the state.
STATE:
U : Type
A : Set U
β’ ctble (sbl_set A)
TACTIC:
|
https://github.com/djvelleman/HTPILeanPackage.git | 4d23e94fff351c65b5e1345c43451f2aa9908c27 | HTPILib/Chap8Part2.lean | HTPI.Lemma_8_2_4_4 | [1447, 1] | [1455, 7] | show ctble (sbl_set A) from ctble_of_onto_func_from_N h1 | U : Type
A : Set U
h1 : β S β sbl_set A, β n, seq_by_length A n = S
β’ ctble (sbl_set A) | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
U : Type
A : Set U
h1 : β S β sbl_set A, β n, seq_by_length A n = S
β’ ctble (sbl_set A)
TACTIC:
|
https://github.com/djvelleman/HTPILeanPackage.git | 4d23e94fff351c65b5e1345c43451f2aa9908c27 | HTPILib/Chap8Part2.lean | HTPI.Lemma_8_2_4_4 | [1447, 1] | [1455, 7] | fix S : Set (List U) | U : Type
A : Set U
β’ β S β sbl_set A, β n, seq_by_length A n = S | U : Type
A : Set U
S : Set (List U)
β’ S β sbl_set A β β n, seq_by_length A n = S | Please generate a tactic in lean4 to solve the state.
STATE:
U : Type
A : Set U
β’ β S β sbl_set A, β n, seq_by_length A n = S
TACTIC:
|
https://github.com/djvelleman/HTPILeanPackage.git | 4d23e94fff351c65b5e1345c43451f2aa9908c27 | HTPILib/Chap8Part2.lean | HTPI.Lemma_8_2_4_4 | [1447, 1] | [1455, 7] | assume h1 : S β sbl_set A | U : Type
A : Set U
S : Set (List U)
β’ S β sbl_set A β β n, seq_by_length A n = S | U : Type
A : Set U
S : Set (List U)
h1 : S β sbl_set A
β’ β n, seq_by_length A n = S | Please generate a tactic in lean4 to solve the state.
STATE:
U : Type
A : Set U
S : Set (List U)
β’ S β sbl_set A β β n, seq_by_length A n = S
TACTIC:
|
https://github.com/djvelleman/HTPILeanPackage.git | 4d23e94fff351c65b5e1345c43451f2aa9908c27 | HTPILib/Chap8Part2.lean | HTPI.Lemma_8_2_4_4 | [1447, 1] | [1455, 7] | define at h1 | U : Type
A : Set U
S : Set (List U)
h1 : S β sbl_set A
β’ β n, seq_by_length A n = S | U : Type
A : Set U
S : Set (List U)
h1 : β n, seq_by_length A n = S
β’ β n, seq_by_length A n = S | Please generate a tactic in lean4 to solve the state.
STATE:
U : Type
A : Set U
S : Set (List U)
h1 : S β sbl_set A
β’ β n, seq_by_length A n = S
TACTIC:
|
https://github.com/djvelleman/HTPILeanPackage.git | 4d23e94fff351c65b5e1345c43451f2aa9908c27 | HTPILib/Chap8Part2.lean | HTPI.Lemma_8_2_4_4 | [1447, 1] | [1455, 7] | show β (n : Nat), seq_by_length A n = S from h1 | U : Type
A : Set U
S : Set (List U)
h1 : β n, seq_by_length A n = S
β’ β n, seq_by_length A n = S | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
U : Type
A : Set U
S : Set (List U)
h1 : β n, seq_by_length A n = S
β’ β n, seq_by_length A n = S
TACTIC:
|
https://github.com/djvelleman/HTPILeanPackage.git | 4d23e94fff351c65b5e1345c43451f2aa9908c27 | HTPILib/Chap8Part2.lean | HTPI.Theorem_8_2_4 | [1457, 1] | [1471, 7] | set F : Set (Set (List U)) := sbl_set A | U : Type
A : Set U
h1 : ctble A
β’ ctble (seq A) | U : Type
A : Set U
h1 : ctble A
F : Set (Set (List U)) := sbl_set A
β’ ctble (seq A) | Please generate a tactic in lean4 to solve the state.
STATE:
U : Type
A : Set U
h1 : ctble A
β’ ctble (seq A)
TACTIC:
|
https://github.com/djvelleman/HTPILeanPackage.git | 4d23e94fff351c65b5e1345c43451f2aa9908c27 | HTPILib/Chap8Part2.lean | HTPI.Theorem_8_2_4 | [1457, 1] | [1471, 7] | have h2 : ctble F := Lemma_8_2_4_4 A | U : Type
A : Set U
h1 : ctble A
F : Set (Set (List U)) := sbl_set A
β’ ctble (seq A) | U : Type
A : Set U
h1 : ctble A
F : Set (Set (List U)) := sbl_set A
h2 : ctble F
β’ ctble (seq A) | Please generate a tactic in lean4 to solve the state.
STATE:
U : Type
A : Set U
h1 : ctble A
F : Set (Set (List U)) := sbl_set A
β’ ctble (seq A)
TACTIC:
|
https://github.com/djvelleman/HTPILeanPackage.git | 4d23e94fff351c65b5e1345c43451f2aa9908c27 | HTPILib/Chap8Part2.lean | HTPI.Theorem_8_2_4 | [1457, 1] | [1471, 7] | have h3 : β S β F, ctble S := by
fix S : Set (List U)
assume h3 : S β F
define at h3
obtain (n : Nat) (h4 : seq_by_length A n = S) from h3
rewrite [βh4]
show ctble (seq_by_length A n) from Lemma_8_2_4_2 h1 n
done | U : Type
A : Set U
h1 : ctble A
F : Set (Set (List U)) := sbl_set A
h2 : ctble F
β’ ctble (seq A) | U : Type
A : Set U
h1 : ctble A
F : Set (Set (List U)) := sbl_set A
h2 : ctble F
h3 : β S β F, ctble S
β’ ctble (seq A) | Please generate a tactic in lean4 to solve the state.
STATE:
U : Type
A : Set U
h1 : ctble A
F : Set (Set (List U)) := sbl_set A
h2 : ctble F
β’ ctble (seq A)
TACTIC:
|
https://github.com/djvelleman/HTPILeanPackage.git | 4d23e94fff351c65b5e1345c43451f2aa9908c27 | HTPILib/Chap8Part2.lean | HTPI.Theorem_8_2_4 | [1457, 1] | [1471, 7] | rewrite [βLemma_8_2_4_3 A] | U : Type
A : Set U
h1 : ctble A
F : Set (Set (List U)) := sbl_set A
h2 : ctble F
h3 : β S β F, ctble S
β’ ctble (seq A) | U : Type
A : Set U
h1 : ctble A
F : Set (Set (List U)) := sbl_set A
h2 : ctble F
h3 : β S β F, ctble S
β’ ctble (ββ sbl_set A) | Please generate a tactic in lean4 to solve the state.
STATE:
U : Type
A : Set U
h1 : ctble A
F : Set (Set (List U)) := sbl_set A
h2 : ctble F
h3 : β S β F, ctble S
β’ ctble (seq A)
TACTIC:
|
https://github.com/djvelleman/HTPILeanPackage.git | 4d23e94fff351c65b5e1345c43451f2aa9908c27 | HTPILib/Chap8Part2.lean | HTPI.Theorem_8_2_4 | [1457, 1] | [1471, 7] | show ctble (ββ sbl_set A) from Theorem_8_2_2 h2 h3 | U : Type
A : Set U
h1 : ctble A
F : Set (Set (List U)) := sbl_set A
h2 : ctble F
h3 : β S β F, ctble S
β’ ctble (ββ sbl_set A) | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
U : Type
A : Set U
h1 : ctble A
F : Set (Set (List U)) := sbl_set A
h2 : ctble F
h3 : β S β F, ctble S
β’ ctble (ββ sbl_set A)
TACTIC:
|
https://github.com/djvelleman/HTPILeanPackage.git | 4d23e94fff351c65b5e1345c43451f2aa9908c27 | HTPILib/Chap8Part2.lean | HTPI.Theorem_8_2_4 | [1457, 1] | [1471, 7] | fix S : Set (List U) | U : Type
A : Set U
h1 : ctble A
F : Set (Set (List U)) := sbl_set A
h2 : ctble F
β’ β S β F, ctble S | U : Type
A : Set U
h1 : ctble A
F : Set (Set (List U)) := sbl_set A
h2 : ctble F
S : Set (List U)
β’ S β F β ctble S | Please generate a tactic in lean4 to solve the state.
STATE:
U : Type
A : Set U
h1 : ctble A
F : Set (Set (List U)) := sbl_set A
h2 : ctble F
β’ β S β F, ctble S
TACTIC:
|
https://github.com/djvelleman/HTPILeanPackage.git | 4d23e94fff351c65b5e1345c43451f2aa9908c27 | HTPILib/Chap8Part2.lean | HTPI.Theorem_8_2_4 | [1457, 1] | [1471, 7] | assume h3 : S β F | U : Type
A : Set U
h1 : ctble A
F : Set (Set (List U)) := sbl_set A
h2 : ctble F
S : Set (List U)
β’ S β F β ctble S | U : Type
A : Set U
h1 : ctble A
F : Set (Set (List U)) := sbl_set A
h2 : ctble F
S : Set (List U)
h3 : S β F
β’ ctble S | Please generate a tactic in lean4 to solve the state.
STATE:
U : Type
A : Set U
h1 : ctble A
F : Set (Set (List U)) := sbl_set A
h2 : ctble F
S : Set (List U)
β’ S β F β ctble S
TACTIC:
|
https://github.com/djvelleman/HTPILeanPackage.git | 4d23e94fff351c65b5e1345c43451f2aa9908c27 | HTPILib/Chap8Part2.lean | HTPI.Theorem_8_2_4 | [1457, 1] | [1471, 7] | define at h3 | U : Type
A : Set U
h1 : ctble A
F : Set (Set (List U)) := sbl_set A
h2 : ctble F
S : Set (List U)
h3 : S β F
β’ ctble S | U : Type
A : Set U
h1 : ctble A
F : Set (Set (List U)) := sbl_set A
h2 : ctble F
S : Set (List U)
h3 : β n, seq_by_length A n = S
β’ ctble S | Please generate a tactic in lean4 to solve the state.
STATE:
U : Type
A : Set U
h1 : ctble A
F : Set (Set (List U)) := sbl_set A
h2 : ctble F
S : Set (List U)
h3 : S β F
β’ ctble S
TACTIC:
|
https://github.com/djvelleman/HTPILeanPackage.git | 4d23e94fff351c65b5e1345c43451f2aa9908c27 | HTPILib/Chap8Part2.lean | HTPI.Theorem_8_2_4 | [1457, 1] | [1471, 7] | obtain (n : Nat) (h4 : seq_by_length A n = S) from h3 | U : Type
A : Set U
h1 : ctble A
F : Set (Set (List U)) := sbl_set A
h2 : ctble F
S : Set (List U)
h3 : β n, seq_by_length A n = S
β’ ctble S | U : Type
A : Set U
h1 : ctble A
F : Set (Set (List U)) := sbl_set A
h2 : ctble F
S : Set (List U)
h3 : β n, seq_by_length A n = S
n : β
h4 : seq_by_length A n = S
β’ ctble S | Please generate a tactic in lean4 to solve the state.
STATE:
U : Type
A : Set U
h1 : ctble A
F : Set (Set (List U)) := sbl_set A
h2 : ctble F
S : Set (List U)
h3 : β n, seq_by_length A n = S
β’ ctble S
TACTIC:
|
https://github.com/djvelleman/HTPILeanPackage.git | 4d23e94fff351c65b5e1345c43451f2aa9908c27 | HTPILib/Chap8Part2.lean | HTPI.Theorem_8_2_4 | [1457, 1] | [1471, 7] | rewrite [βh4] | U : Type
A : Set U
h1 : ctble A
F : Set (Set (List U)) := sbl_set A
h2 : ctble F
S : Set (List U)
h3 : β n, seq_by_length A n = S
n : β
h4 : seq_by_length A n = S
β’ ctble S | U : Type
A : Set U
h1 : ctble A
F : Set (Set (List U)) := sbl_set A
h2 : ctble F
S : Set (List U)
h3 : β n, seq_by_length A n = S
n : β
h4 : seq_by_length A n = S
β’ ctble (seq_by_length A n) | Please generate a tactic in lean4 to solve the state.
STATE:
U : Type
A : Set U
h1 : ctble A
F : Set (Set (List U)) := sbl_set A
h2 : ctble F
S : Set (List U)
h3 : β n, seq_by_length A n = S
n : β
h4 : seq_by_length A n = S
β’ ctble S
TACTIC:
|
https://github.com/djvelleman/HTPILeanPackage.git | 4d23e94fff351c65b5e1345c43451f2aa9908c27 | HTPILib/Chap8Part2.lean | HTPI.Theorem_8_2_4 | [1457, 1] | [1471, 7] | show ctble (seq_by_length A n) from Lemma_8_2_4_2 h1 n | U : Type
A : Set U
h1 : ctble A
F : Set (Set (List U)) := sbl_set A
h2 : ctble F
S : Set (List U)
h3 : β n, seq_by_length A n = S
n : β
h4 : seq_by_length A n = S
β’ ctble (seq_by_length A n) | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
U : Type
A : Set U
h1 : ctble A
F : Set (Set (List U)) := sbl_set A
h2 : ctble F
S : Set (List U)
h3 : β n, seq_by_length A n = S
n : β
h4 : seq_by_length A n = S
β’ ctble (seq_by_length A n)
TACTIC:
|
https://github.com/djvelleman/HTPILeanPackage.git | 4d23e94fff351c65b5e1345c43451f2aa9908c27 | HTPILib/Chap8Part2.lean | HTPI.set_elt_powerset_univ | [1473, 1] | [1478, 7] | fix x : U | U : Type
A : Set U
β’ A β π« Univ U | U : Type
A : Set U
x : U
β’ x β A β x β Univ U | Please generate a tactic in lean4 to solve the state.
STATE:
U : Type
A : Set U
β’ A β π« Univ U
TACTIC:
|
https://github.com/djvelleman/HTPILeanPackage.git | 4d23e94fff351c65b5e1345c43451f2aa9908c27 | HTPILib/Chap8Part2.lean | HTPI.set_elt_powerset_univ | [1473, 1] | [1478, 7] | assume h : x β A | U : Type
A : Set U
x : U
β’ x β A β x β Univ U | U : Type
A : Set U
x : U
h : x β A
β’ x β Univ U | Please generate a tactic in lean4 to solve the state.
STATE:
U : Type
A : Set U
x : U
β’ x β A β x β Univ U
TACTIC:
|
https://github.com/djvelleman/HTPILeanPackage.git | 4d23e94fff351c65b5e1345c43451f2aa9908c27 | HTPILib/Chap8Part2.lean | HTPI.set_elt_powerset_univ | [1473, 1] | [1478, 7] | show x β Univ U from elt_Univ x | U : Type
A : Set U
x : U
h : x β A
β’ x β Univ U | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
U : Type
A : Set U
x : U
h : x β A
β’ x β Univ U
TACTIC:
|
https://github.com/djvelleman/HTPILeanPackage.git | 4d23e94fff351c65b5e1345c43451f2aa9908c27 | HTPILib/Chap8Part2.lean | HTPI.Cantor's_theorem | [1480, 1] | [1508, 7] | by_contra h1 | β’ Β¬ctble (π« Univ β) | h1 : ctble (π« Univ β)
β’ False | Please generate a tactic in lean4 to solve the state.
STATE:
β’ Β¬ctble (π« Univ β)
TACTIC:
|
https://github.com/djvelleman/HTPILeanPackage.git | 4d23e94fff351c65b5e1345c43451f2aa9908c27 | HTPILib/Chap8Part2.lean | HTPI.Cantor's_theorem | [1480, 1] | [1508, 7] | rewrite [Theorem_8_1_5_2] at h1 | h1 : ctble (π« Univ β)
β’ False | h1 : β R, fcnl_onto_from_nat R (π« Univ β)
β’ False | Please generate a tactic in lean4 to solve the state.
STATE:
h1 : ctble (π« Univ β)
β’ False
TACTIC:
|
https://github.com/djvelleman/HTPILeanPackage.git | 4d23e94fff351c65b5e1345c43451f2aa9908c27 | HTPILib/Chap8Part2.lean | HTPI.Cantor's_theorem | [1480, 1] | [1508, 7] | obtain (R : Rel Nat (Set Nat))
(h2 : fcnl_onto_from_nat R (π« (Univ Nat))) from h1 | h1 : β R, fcnl_onto_from_nat R (π« Univ β)
β’ False | h1 : β R, fcnl_onto_from_nat R (π« Univ β)
R : Rel β (Set β)
h2 : fcnl_onto_from_nat R (π« Univ β)
β’ False | Please generate a tactic in lean4 to solve the state.
STATE:
h1 : β R, fcnl_onto_from_nat R (π« Univ β)
β’ False
TACTIC:
|
https://github.com/djvelleman/HTPILeanPackage.git | 4d23e94fff351c65b5e1345c43451f2aa9908c27 | HTPILib/Chap8Part2.lean | HTPI.Cantor's_theorem | [1480, 1] | [1508, 7] | define at h2 | h1 : β R, fcnl_onto_from_nat R (π« Univ β)
R : Rel β (Set β)
h2 : fcnl_onto_from_nat R (π« Univ β)
β’ False | 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)
β’ False | Please generate a tactic in lean4 to solve the state.
STATE:
h1 : β R, fcnl_onto_from_nat R (π« Univ β)
R : Rel β (Set β)
h2 : fcnl_onto_from_nat R (π« Univ β)
β’ False
TACTIC:
|
https://github.com/djvelleman/HTPILeanPackage.git | 4d23e94fff351c65b5e1345c43451f2aa9908c27 | HTPILib/Chap8Part2.lean | HTPI.Cantor's_theorem | [1480, 1] | [1508, 7] | have h3 : unique_val_on_N R := h2.left | 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)
β’ False | 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
β’ False | Please generate a tactic in lean4 to solve the state.
STATE:
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)
β’ False
TACTIC:
|
https://github.com/djvelleman/HTPILeanPackage.git | 4d23e94fff351c65b5e1345c43451f2aa9908c27 | HTPILib/Chap8Part2.lean | HTPI.Cantor's_theorem | [1480, 1] | [1508, 7] | have h4 : nat_rel_onto R (π« (Univ Nat)) := h2.right | 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
β’ False | 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 : nat_rel_onto R (π« Univ β)
β’ False | Please generate a tactic in lean4 to solve the state.
STATE:
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
β’ False
TACTIC:
|
https://github.com/djvelleman/HTPILeanPackage.git | 4d23e94fff351c65b5e1345c43451f2aa9908c27 | HTPILib/Chap8Part2.lean | HTPI.Cantor's_theorem | [1480, 1] | [1508, 7] | set D : Set Nat := {n : Nat | β (X : Set Nat), R n X β§ n β X} | 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 : nat_rel_onto R (π« Univ β)
β’ False | 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 : nat_rel_onto R (π« Univ β)
D : Set β := {n | β X, R n X β§ n β X}
β’ False | Please generate a tactic in lean4 to solve the state.
STATE:
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 : nat_rel_onto R (π« Univ β)
β’ False
TACTIC:
|
https://github.com/djvelleman/HTPILeanPackage.git | 4d23e94fff351c65b5e1345c43451f2aa9908c27 | HTPILib/Chap8Part2.lean | HTPI.Cantor's_theorem | [1480, 1] | [1508, 7] | have h5 : D β π« (Univ Nat) := set_elt_powerset_univ D | 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 : nat_rel_onto R (π« Univ β)
D : Set β := {n | β X, R n X β§ n β X}
β’ False | 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 : nat_rel_onto R (π« Univ β)
D : Set β := {n | β X, R n X β§ n β X}
h5 : D β π« Univ β
β’ False | Please generate a tactic in lean4 to solve the state.
STATE:
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 : nat_rel_onto R (π« Univ β)
D : Set β := {n | β X, R n X β§ n β X}
β’ False
TACTIC:
|
https://github.com/djvelleman/HTPILeanPackage.git | 4d23e94fff351c65b5e1345c43451f2aa9908c27 | HTPILib/Chap8Part2.lean | HTPI.Cantor's_theorem | [1480, 1] | [1508, 7] | define at h4 | 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 : nat_rel_onto R (π« Univ β)
D : Set β := {n | β X, R n X β§ n β X}
h5 : D β π« Univ β
β’ False | 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
β’ False | Please generate a tactic in lean4 to solve the state.
STATE:
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 : nat_rel_onto R (π« Univ β)
D : Set β := {n | β X, R n X β§ n β X}
h5 : D β π« Univ β
β’ False
TACTIC:
|
https://github.com/djvelleman/HTPILeanPackage.git | 4d23e94fff351c65b5e1345c43451f2aa9908c27 | HTPILib/Chap8Part2.lean | HTPI.Cantor's_theorem | [1480, 1] | [1508, 7] | obtain (n : Nat) (h6 : R n D) from h4 h5 | 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
β’ False | 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
β’ False | Please generate a tactic in lean4 to solve the state.
STATE:
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
β’ False
TACTIC:
|
https://github.com/djvelleman/HTPILeanPackage.git | 4d23e94fff351c65b5e1345c43451f2aa9908c27 | HTPILib/Chap8Part2.lean | HTPI.Cantor's_theorem | [1480, 1] | [1508, 7] | by_cases h7 : n β D | 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
β’ False | 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’ False
case neg
h1 : β R, fcnl_onto_from_... | Please generate a tactic in lean4 to solve the state.
STATE:
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
β’ ... |
https://github.com/djvelleman/HTPILeanPackage.git | 4d23e94fff351c65b5e1345c43451f2aa9908c27 | HTPILib/Chap8Part2.lean | HTPI.Cantor's_theorem | [1480, 1] | [1508, 7] | contradict 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’ False | 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 | 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 :... |
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