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/ianjauslin-rutgers/pythagoras4.git | f97e5d2375d2e350b15d79e541520f8ba81600ec | Pythagoras/euclid_I_extras.lean | B_of_three_online_ne_short | [216, 1] | [220, 91] | convert this | i : incidence_geometry
a b c : point
L : line
hlen : length a b < length a c
ab : a ≠ b
ac : a ≠ c
bc : b ≠ c
aL : online a L
bL : online b L
cL : online c L
this : B a b c ∨ B b a c ∨ B a c b
⊢ B a b c ∨ B b a c | case h.e'_2.a
i : incidence_geometry
a b c : point
L : line
hlen : length a b < length a c
ab : a ≠ b
ac : a ≠ c
bc : b ≠ c
aL : online a L
bL : online b L
cL : online c L
this : B a b c ∨ B b a c ∨ B a c b
⊢ B b a c ↔ B b a c ∨ B a c b | Please generate a tactic in lean4 to solve the state.
STATE:
i : incidence_geometry
a b c : point
L : line
hlen : length a b < length a c
ab : a ≠ b
ac : a ≠ c
bc : b ≠ c
aL : online a L
bL : online b L
cL : online c L
this : B a b c ∨ B b a c ∨ B a c b
⊢ B a b c ∨ B b a c
TACTIC:
|
https://github.com/ianjauslin-rutgers/pythagoras4.git | f97e5d2375d2e350b15d79e541520f8ba81600ec | Pythagoras/euclid_I_extras.lean | B_of_three_online_ne_short | [216, 1] | [220, 91] | simp [not_B_of_short hlen] | case h.e'_2.a
i : incidence_geometry
a b c : point
L : line
hlen : length a b < length a c
ab : a ≠ b
ac : a ≠ c
bc : b ≠ c
aL : online a L
bL : online b L
cL : online c L
this : B a b c ∨ B b a c ∨ B a c b
⊢ B b a c ↔ B b a c ∨ B a c b | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case h.e'_2.a
i : incidence_geometry
a b c : point
L : line
hlen : length a b < length a c
ab : a ≠ b
ac : a ≠ c
bc : b ≠ c
aL : online a L
bL : online b L
cL : online c L
this : B a b c ∨ B b a c ∨ B a c b
⊢ B b a c ↔ B b a c ∨ B a c b
TACTIC:
|
https://github.com/ianjauslin-rutgers/pythagoras4.git | f97e5d2375d2e350b15d79e541520f8ba81600ec | Pythagoras/euclid_I_extras.lean | same_length_B_of_ne_ge | [223, 1] | [248, 75] | have cd : c ≠ d := fun cd => by
rw [cd, length_eq_zero_iff.mpr rfl] at big;
exact not_lt_of_ge (length_nonneg a b) big | i : incidence_geometry
a b c d : point
ab : a ≠ b
big : length a b < length c d
⊢ ∃ p, B a b p ∧ length a p = length c d | i : incidence_geometry
a b c d : point
ab : a ≠ b
big : length a b < length c d
cd : c ≠ d
⊢ ∃ p, B a b p ∧ length a p = length c d | Please generate a tactic in lean4 to solve the state.
STATE:
i : incidence_geometry
a b c d : point
ab : a ≠ b
big : length a b < length c d
⊢ ∃ p, B a b p ∧ length a p = length c d
TACTIC:
|
https://github.com/ianjauslin-rutgers/pythagoras4.git | f97e5d2375d2e350b15d79e541520f8ba81600ec | Pythagoras/euclid_I_extras.lean | same_length_B_of_ne_ge | [223, 1] | [248, 75] | obtain ⟨q, Hq⟩ := length_eq_B_of_ne_four ab.symm cd | i : incidence_geometry
a b c d : point
ab : a ≠ b
big : length a b < length c d
cd : c ≠ d
⊢ ∃ p, B a b p ∧ length a p = length c d | case intro
i : incidence_geometry
a b c d : point
ab : a ≠ b
big : length a b < length c d
cd : c ≠ d
q : point
Hq : B b a q ∧ length c d = length a q
⊢ ∃ p, B a b p ∧ length a p = length c d | Please generate a tactic in lean4 to solve the state.
STATE:
i : incidence_geometry
a b c d : point
ab : a ≠ b
big : length a b < length c d
cd : c ≠ d
⊢ ∃ p, B a b p ∧ length a p = length c d
TACTIC:
|
https://github.com/ianjauslin-rutgers/pythagoras4.git | f97e5d2375d2e350b15d79e541520f8ba81600ec | Pythagoras/euclid_I_extras.lean | same_length_B_of_ne_ge | [223, 1] | [248, 75] | have aq : a ≠ q := fun aq => by
rw [aq, length_eq_zero_iff.mpr rfl] at Hq; rw [Hq.2] at big
exact not_lt_of_ge (length_nonneg a b) big | case intro
i : incidence_geometry
a b c d : point
ab : a ≠ b
big : length a b < length c d
cd : c ≠ d
q : point
Hq : B b a q ∧ length c d = length a q
⊢ ∃ p, B a b p ∧ length a p = length c d | case intro
i : incidence_geometry
a b c d : point
ab : a ≠ b
big : length a b < length c d
cd : c ≠ d
q : point
Hq : B b a q ∧ length c d = length a q
aq : a ≠ q
⊢ ∃ p, B a b p ∧ length a p = length c d | Please generate a tactic in lean4 to solve the state.
STATE:
case intro
i : incidence_geometry
a b c d : point
ab : a ≠ b
big : length a b < length c d
cd : c ≠ d
q : point
Hq : B b a q ∧ length c d = length a q
⊢ ∃ p, B a b p ∧ length a p = length c d
TACTIC:
|
https://github.com/ianjauslin-rutgers/pythagoras4.git | f97e5d2375d2e350b15d79e541520f8ba81600ec | Pythagoras/euclid_I_extras.lean | same_length_B_of_ne_ge | [223, 1] | [248, 75] | obtain ⟨C, hC⟩ := circle_of_ne aq | case intro
i : incidence_geometry
a b c d : point
ab : a ≠ b
big : length a b < length c d
cd : c ≠ d
q : point
Hq : B b a q ∧ length c d = length a q
aq : a ≠ q
⊢ ∃ p, B a b p ∧ length a p = length c d | case intro.intro
i : incidence_geometry
a b c d : point
ab : a ≠ b
big : length a b < length c d
cd : c ≠ d
q : point
Hq : B b a q ∧ length c d = length a q
aq : a ≠ q
C : circle
hC : center_circle a C ∧ on_circle q C
⊢ ∃ p, B a b p ∧ length a p = length c d | Please generate a tactic in lean4 to solve the state.
STATE:
case intro
i : incidence_geometry
a b c d : point
ab : a ≠ b
big : length a b < length c d
cd : c ≠ d
q : point
Hq : B b a q ∧ length c d = length a q
aq : a ≠ q
⊢ ∃ p, B a b p ∧ length a p = length c d
TACTIC:
|
https://github.com/ianjauslin-rutgers/pythagoras4.git | f97e5d2375d2e350b15d79e541520f8ba81600ec | Pythagoras/euclid_I_extras.lean | same_length_B_of_ne_ge | [223, 1] | [248, 75] | obtain ⟨p, Hp⟩ := pt_oncircle_of_inside_ne aq.symm (inside_circle_of_center hC.1) | case intro.intro
i : incidence_geometry
a b c d : point
ab : a ≠ b
big : length a b < length c d
cd : c ≠ d
q : point
Hq : B b a q ∧ length c d = length a q
aq : a ≠ q
C : circle
hC : center_circle a C ∧ on_circle q C
⊢ ∃ p, B a b p ∧ length a p = length c d | case intro.intro.intro
i : incidence_geometry
a b c d : point
ab : a ≠ b
big : length a b < length c d
cd : c ≠ d
q : point
Hq : B b a q ∧ length c d = length a q
aq : a ≠ q
C : circle
hC : center_circle a C ∧ on_circle q C
p : point
Hp : B q a p ∧ on_circle p C
⊢ ∃ p, B a b p ∧ length a p = length c d | Please generate a tactic in lean4 to solve the state.
STATE:
case intro.intro
i : incidence_geometry
a b c d : point
ab : a ≠ b
big : length a b < length c d
cd : c ≠ d
q : point
Hq : B b a q ∧ length c d = length a q
aq : a ≠ q
C : circle
hC : center_circle a C ∧ on_circle q C
⊢ ∃ p, B a b p ∧ length a p = length c d
... |
https://github.com/ianjauslin-rutgers/pythagoras4.git | f97e5d2375d2e350b15d79e541520f8ba81600ec | Pythagoras/euclid_I_extras.lean | same_length_B_of_ne_ge | [223, 1] | [248, 75] | obtain ⟨AB, aAB, bAB⟩ := line_of_pts a b | case intro.intro.intro
i : incidence_geometry
a b c d : point
ab : a ≠ b
big : length a b < length c d
cd : c ≠ d
q : point
Hq : B b a q ∧ length c d = length a q
aq : a ≠ q
C : circle
hC : center_circle a C ∧ on_circle q C
p : point
Hp : B q a p ∧ on_circle p C
⊢ ∃ p, B a b p ∧ length a p = length c d | case intro.intro.intro.intro.intro
i : incidence_geometry
a b c d : point
ab : a ≠ b
big : length a b < length c d
cd : c ≠ d
q : point
Hq : B b a q ∧ length c d = length a q
aq : a ≠ q
C : circle
hC : center_circle a C ∧ on_circle q C
p : point
Hp : B q a p ∧ on_circle p C
AB : line
aAB : online a AB
bAB : online b AB... | Please generate a tactic in lean4 to solve the state.
STATE:
case intro.intro.intro
i : incidence_geometry
a b c d : point
ab : a ≠ b
big : length a b < length c d
cd : c ≠ d
q : point
Hq : B b a q ∧ length c d = length a q
aq : a ≠ q
C : circle
hC : center_circle a C ∧ on_circle q C
p : point
Hp : B q a p ∧ on_circle ... |
https://github.com/ianjauslin-rutgers/pythagoras4.git | f97e5d2375d2e350b15d79e541520f8ba81600ec | Pythagoras/euclid_I_extras.lean | same_length_B_of_ne_ge | [223, 1] | [248, 75] | have qAB := online_3_of_B Hq.1 bAB aAB | case intro.intro.intro.intro.intro
i : incidence_geometry
a b c d : point
ab : a ≠ b
big : length a b < length c d
cd : c ≠ d
q : point
Hq : B b a q ∧ length c d = length a q
aq : a ≠ q
C : circle
hC : center_circle a C ∧ on_circle q C
p : point
Hp : B q a p ∧ on_circle p C
AB : line
aAB : online a AB
bAB : online b AB... | case intro.intro.intro.intro.intro
i : incidence_geometry
a b c d : point
ab : a ≠ b
big : length a b < length c d
cd : c ≠ d
q : point
Hq : B b a q ∧ length c d = length a q
aq : a ≠ q
C : circle
hC : center_circle a C ∧ on_circle q C
p : point
Hp : B q a p ∧ on_circle p C
AB : line
aAB : online a AB
bAB : online b AB... | Please generate a tactic in lean4 to solve the state.
STATE:
case intro.intro.intro.intro.intro
i : incidence_geometry
a b c d : point
ab : a ≠ b
big : length a b < length c d
cd : c ≠ d
q : point
Hq : B b a q ∧ length c d = length a q
aq : a ≠ q
C : circle
hC : center_circle a C ∧ on_circle q C
p : point
Hp : B q a p ... |
https://github.com/ianjauslin-rutgers/pythagoras4.git | f97e5d2375d2e350b15d79e541520f8ba81600ec | Pythagoras/euclid_I_extras.lean | same_length_B_of_ne_ge | [223, 1] | [248, 75] | have pAB := online_3_of_B Hp.1 qAB aAB | case intro.intro.intro.intro.intro
i : incidence_geometry
a b c d : point
ab : a ≠ b
big : length a b < length c d
cd : c ≠ d
q : point
Hq : B b a q ∧ length c d = length a q
aq : a ≠ q
C : circle
hC : center_circle a C ∧ on_circle q C
p : point
Hp : B q a p ∧ on_circle p C
AB : line
aAB : online a AB
bAB : online b AB... | case intro.intro.intro.intro.intro
i : incidence_geometry
a b c d : point
ab : a ≠ b
big : length a b < length c d
cd : c ≠ d
q : point
Hq : B b a q ∧ length c d = length a q
aq : a ≠ q
C : circle
hC : center_circle a C ∧ on_circle q C
p : point
Hp : B q a p ∧ on_circle p C
AB : line
aAB : online a AB
bAB : online b AB... | Please generate a tactic in lean4 to solve the state.
STATE:
case intro.intro.intro.intro.intro
i : incidence_geometry
a b c d : point
ab : a ≠ b
big : length a b < length c d
cd : c ≠ d
q : point
Hq : B b a q ∧ length c d = length a q
aq : a ≠ q
C : circle
hC : center_circle a C ∧ on_circle q C
p : point
Hp : B q a p ... |
https://github.com/ianjauslin-rutgers/pythagoras4.git | f97e5d2375d2e350b15d79e541520f8ba81600ec | Pythagoras/euclid_I_extras.lean | same_length_B_of_ne_ge | [223, 1] | [248, 75] | have := (on_circle_iff_length_eq hC.1 Hp.2).mpr hC.2 | case intro.intro.intro.intro.intro
i : incidence_geometry
a b c d : point
ab : a ≠ b
big : length a b < length c d
cd : c ≠ d
q : point
Hq : B b a q ∧ length c d = length a q
aq : a ≠ q
C : circle
hC : center_circle a C ∧ on_circle q C
p : point
Hp : B q a p ∧ on_circle p C
AB : line
aAB : online a AB
bAB : online b AB... | case intro.intro.intro.intro.intro
i : incidence_geometry
a b c d : point
ab : a ≠ b
big : length a b < length c d
cd : c ≠ d
q : point
Hq : B b a q ∧ length c d = length a q
aq : a ≠ q
C : circle
hC : center_circle a C ∧ on_circle q C
p : point
Hp : B q a p ∧ on_circle p C
AB : line
aAB : online a AB
bAB : online b AB... | Please generate a tactic in lean4 to solve the state.
STATE:
case intro.intro.intro.intro.intro
i : incidence_geometry
a b c d : point
ab : a ≠ b
big : length a b < length c d
cd : c ≠ d
q : point
Hq : B b a q ∧ length c d = length a q
aq : a ≠ q
C : circle
hC : center_circle a C ∧ on_circle q C
p : point
Hp : B q a p ... |
https://github.com/ianjauslin-rutgers/pythagoras4.git | f97e5d2375d2e350b15d79e541520f8ba81600ec | Pythagoras/euclid_I_extras.lean | same_length_B_of_ne_ge | [223, 1] | [248, 75] | rw [← this] at Hq | case intro.intro.intro.intro.intro
i : incidence_geometry
a b c d : point
ab : a ≠ b
big : length a b < length c d
cd : c ≠ d
q : point
Hq : B b a q ∧ length c d = length a q
aq : a ≠ q
C : circle
hC : center_circle a C ∧ on_circle q C
p : point
Hp : B q a p ∧ on_circle p C
AB : line
aAB : online a AB
bAB : online b AB... | case intro.intro.intro.intro.intro
i : incidence_geometry
a b c d : point
ab : a ≠ b
big : length a b < length c d
cd : c ≠ d
q : point
aq : a ≠ q
C : circle
hC : center_circle a C ∧ on_circle q C
p : point
Hq : B b a q ∧ length c d = length a p
Hp : B q a p ∧ on_circle p C
AB : line
aAB : online a AB
bAB : online b AB... | Please generate a tactic in lean4 to solve the state.
STATE:
case intro.intro.intro.intro.intro
i : incidence_geometry
a b c d : point
ab : a ≠ b
big : length a b < length c d
cd : c ≠ d
q : point
Hq : B b a q ∧ length c d = length a q
aq : a ≠ q
C : circle
hC : center_circle a C ∧ on_circle q C
p : point
Hp : B q a p ... |
https://github.com/ianjauslin-rutgers/pythagoras4.git | f97e5d2375d2e350b15d79e541520f8ba81600ec | Pythagoras/euclid_I_extras.lean | same_length_B_of_ne_ge | [223, 1] | [248, 75] | rw [Hq.2] at big | case intro.intro.intro.intro.intro
i : incidence_geometry
a b c d : point
ab : a ≠ b
big : length a b < length c d
cd : c ≠ d
q : point
aq : a ≠ q
C : circle
hC : center_circle a C ∧ on_circle q C
p : point
Hq : B b a q ∧ length c d = length a p
Hp : B q a p ∧ on_circle p C
AB : line
aAB : online a AB
bAB : online b AB... | case intro.intro.intro.intro.intro
i : incidence_geometry
a b c d : point
ab : a ≠ b
cd : c ≠ d
q : point
aq : a ≠ q
C : circle
hC : center_circle a C ∧ on_circle q C
p : point
big : length a b < length a p
Hq : B b a q ∧ length c d = length a p
Hp : B q a p ∧ on_circle p C
AB : line
aAB : online a AB
bAB : online b AB... | Please generate a tactic in lean4 to solve the state.
STATE:
case intro.intro.intro.intro.intro
i : incidence_geometry
a b c d : point
ab : a ≠ b
big : length a b < length c d
cd : c ≠ d
q : point
aq : a ≠ q
C : circle
hC : center_circle a C ∧ on_circle q C
p : point
Hq : B b a q ∧ length c d = length a p
Hp : B q a p ... |
https://github.com/ianjauslin-rutgers/pythagoras4.git | f97e5d2375d2e350b15d79e541520f8ba81600ec | Pythagoras/euclid_I_extras.lean | same_length_B_of_ne_ge | [223, 1] | [248, 75] | have bp : b ≠ p := fun bp => by
rw [←bp, bp] at Hq; rw [bp] at big
simp [lt_self_iff_false] at big | case intro.intro.intro.intro.intro
i : incidence_geometry
a b c d : point
ab : a ≠ b
cd : c ≠ d
q : point
aq : a ≠ q
C : circle
hC : center_circle a C ∧ on_circle q C
p : point
big : length a b < length a p
Hq : B b a q ∧ length c d = length a p
Hp : B q a p ∧ on_circle p C
AB : line
aAB : online a AB
bAB : online b AB... | case intro.intro.intro.intro.intro
i : incidence_geometry
a b c d : point
ab : a ≠ b
cd : c ≠ d
q : point
aq : a ≠ q
C : circle
hC : center_circle a C ∧ on_circle q C
p : point
big : length a b < length a p
Hq : B b a q ∧ length c d = length a p
Hp : B q a p ∧ on_circle p C
AB : line
aAB : online a AB
bAB : online b AB... | Please generate a tactic in lean4 to solve the state.
STATE:
case intro.intro.intro.intro.intro
i : incidence_geometry
a b c d : point
ab : a ≠ b
cd : c ≠ d
q : point
aq : a ≠ q
C : circle
hC : center_circle a C ∧ on_circle q C
p : point
big : length a b < length a p
Hq : B b a q ∧ length c d = length a p
Hp : B q a p ... |
https://github.com/ianjauslin-rutgers/pythagoras4.git | f97e5d2375d2e350b15d79e541520f8ba81600ec | Pythagoras/euclid_I_extras.lean | same_length_B_of_ne_ge | [223, 1] | [248, 75] | have ap := (ne_12_of_B (B_symm Hp.1)).symm | case intro.intro.intro.intro.intro
i : incidence_geometry
a b c d : point
ab : a ≠ b
cd : c ≠ d
q : point
aq : a ≠ q
C : circle
hC : center_circle a C ∧ on_circle q C
p : point
big : length a b < length a p
Hq : B b a q ∧ length c d = length a p
Hp : B q a p ∧ on_circle p C
AB : line
aAB : online a AB
bAB : online b AB... | case intro.intro.intro.intro.intro
i : incidence_geometry
a b c d : point
ab : a ≠ b
cd : c ≠ d
q : point
aq : a ≠ q
C : circle
hC : center_circle a C ∧ on_circle q C
p : point
big : length a b < length a p
Hq : B b a q ∧ length c d = length a p
Hp : B q a p ∧ on_circle p C
AB : line
aAB : online a AB
bAB : online b AB... | Please generate a tactic in lean4 to solve the state.
STATE:
case intro.intro.intro.intro.intro
i : incidence_geometry
a b c d : point
ab : a ≠ b
cd : c ≠ d
q : point
aq : a ≠ q
C : circle
hC : center_circle a C ∧ on_circle q C
p : point
big : length a b < length a p
Hq : B b a q ∧ length c d = length a p
Hp : B q a p ... |
https://github.com/ianjauslin-rutgers/pythagoras4.git | f97e5d2375d2e350b15d79e541520f8ba81600ec | Pythagoras/euclid_I_extras.lean | same_length_B_of_ne_ge | [223, 1] | [248, 75] | refine' ⟨p, _, Hq.2.symm⟩ | case intro.intro.intro.intro.intro
i : incidence_geometry
a b c d : point
ab : a ≠ b
cd : c ≠ d
q : point
aq : a ≠ q
C : circle
hC : center_circle a C ∧ on_circle q C
p : point
big : length a b < length a p
Hq : B b a q ∧ length c d = length a p
Hp : B q a p ∧ on_circle p C
AB : line
aAB : online a AB
bAB : online b AB... | case intro.intro.intro.intro.intro
i : incidence_geometry
a b c d : point
ab : a ≠ b
cd : c ≠ d
q : point
aq : a ≠ q
C : circle
hC : center_circle a C ∧ on_circle q C
p : point
big : length a b < length a p
Hq : B b a q ∧ length c d = length a p
Hp : B q a p ∧ on_circle p C
AB : line
aAB : online a AB
bAB : online b AB... | Please generate a tactic in lean4 to solve the state.
STATE:
case intro.intro.intro.intro.intro
i : incidence_geometry
a b c d : point
ab : a ≠ b
cd : c ≠ d
q : point
aq : a ≠ q
C : circle
hC : center_circle a C ∧ on_circle q C
p : point
big : length a b < length a p
Hq : B b a q ∧ length c d = length a p
Hp : B q a p ... |
https://github.com/ianjauslin-rutgers/pythagoras4.git | f97e5d2375d2e350b15d79e541520f8ba81600ec | Pythagoras/euclid_I_extras.lean | same_length_B_of_ne_ge | [223, 1] | [248, 75] | have B3 := B_of_three_online_ne_short big ab ap bp aAB bAB pAB | case intro.intro.intro.intro.intro
i : incidence_geometry
a b c d : point
ab : a ≠ b
cd : c ≠ d
q : point
aq : a ≠ q
C : circle
hC : center_circle a C ∧ on_circle q C
p : point
big : length a b < length a p
Hq : B b a q ∧ length c d = length a p
Hp : B q a p ∧ on_circle p C
AB : line
aAB : online a AB
bAB : online b AB... | case intro.intro.intro.intro.intro
i : incidence_geometry
a b c d : point
ab : a ≠ b
cd : c ≠ d
q : point
aq : a ≠ q
C : circle
hC : center_circle a C ∧ on_circle q C
p : point
big : length a b < length a p
Hq : B b a q ∧ length c d = length a p
Hp : B q a p ∧ on_circle p C
AB : line
aAB : online a AB
bAB : online b AB... | Please generate a tactic in lean4 to solve the state.
STATE:
case intro.intro.intro.intro.intro
i : incidence_geometry
a b c d : point
ab : a ≠ b
cd : c ≠ d
q : point
aq : a ≠ q
C : circle
hC : center_circle a C ∧ on_circle q C
p : point
big : length a b < length a p
Hq : B b a q ∧ length c d = length a p
Hp : B q a p ... |
https://github.com/ianjauslin-rutgers/pythagoras4.git | f97e5d2375d2e350b15d79e541520f8ba81600ec | Pythagoras/euclid_I_extras.lean | same_length_B_of_ne_ge | [223, 1] | [248, 75] | cases B3 with
| inl B3 => exact B3
| inr B3 => exfalso; exact (not_B324_of_B123_B124 (B_symm Hq.1) Hp.1) B3 | case intro.intro.intro.intro.intro
i : incidence_geometry
a b c d : point
ab : a ≠ b
cd : c ≠ d
q : point
aq : a ≠ q
C : circle
hC : center_circle a C ∧ on_circle q C
p : point
big : length a b < length a p
Hq : B b a q ∧ length c d = length a p
Hp : B q a p ∧ on_circle p C
AB : line
aAB : online a AB
bAB : online b AB... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case intro.intro.intro.intro.intro
i : incidence_geometry
a b c d : point
ab : a ≠ b
cd : c ≠ d
q : point
aq : a ≠ q
C : circle
hC : center_circle a C ∧ on_circle q C
p : point
big : length a b < length a p
Hq : B b a q ∧ length c d = length a p
Hp : B q a p ... |
https://github.com/ianjauslin-rutgers/pythagoras4.git | f97e5d2375d2e350b15d79e541520f8ba81600ec | Pythagoras/euclid_I_extras.lean | same_length_B_of_ne_ge | [223, 1] | [248, 75] | rw [cd, length_eq_zero_iff.mpr rfl] at big | i : incidence_geometry
a b c d : point
ab : a ≠ b
big : length a b < length c d
cd : c = d
⊢ False | i : incidence_geometry
a b c d : point
ab : a ≠ b
big : length a b < 0
cd : c = d
⊢ False | Please generate a tactic in lean4 to solve the state.
STATE:
i : incidence_geometry
a b c d : point
ab : a ≠ b
big : length a b < length c d
cd : c = d
⊢ False
TACTIC:
|
https://github.com/ianjauslin-rutgers/pythagoras4.git | f97e5d2375d2e350b15d79e541520f8ba81600ec | Pythagoras/euclid_I_extras.lean | same_length_B_of_ne_ge | [223, 1] | [248, 75] | exact not_lt_of_ge (length_nonneg a b) big | i : incidence_geometry
a b c d : point
ab : a ≠ b
big : length a b < 0
cd : c = d
⊢ False | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
i : incidence_geometry
a b c d : point
ab : a ≠ b
big : length a b < 0
cd : c = d
⊢ False
TACTIC:
|
https://github.com/ianjauslin-rutgers/pythagoras4.git | f97e5d2375d2e350b15d79e541520f8ba81600ec | Pythagoras/euclid_I_extras.lean | same_length_B_of_ne_ge | [223, 1] | [248, 75] | rw [aq, length_eq_zero_iff.mpr rfl] at Hq | i : incidence_geometry
a b c d : point
ab : a ≠ b
big : length a b < length c d
cd : c ≠ d
q : point
Hq : B b a q ∧ length c d = length a q
aq : a = q
⊢ False | i : incidence_geometry
a b c d : point
ab : a ≠ b
big : length a b < length c d
cd : c ≠ d
q : point
Hq : B b q q ∧ length c d = 0
aq : a = q
⊢ False | Please generate a tactic in lean4 to solve the state.
STATE:
i : incidence_geometry
a b c d : point
ab : a ≠ b
big : length a b < length c d
cd : c ≠ d
q : point
Hq : B b a q ∧ length c d = length a q
aq : a = q
⊢ False
TACTIC:
|
https://github.com/ianjauslin-rutgers/pythagoras4.git | f97e5d2375d2e350b15d79e541520f8ba81600ec | Pythagoras/euclid_I_extras.lean | same_length_B_of_ne_ge | [223, 1] | [248, 75] | rw [Hq.2] at big | i : incidence_geometry
a b c d : point
ab : a ≠ b
big : length a b < length c d
cd : c ≠ d
q : point
Hq : B b q q ∧ length c d = 0
aq : a = q
⊢ False | i : incidence_geometry
a b c d : point
ab : a ≠ b
big : length a b < 0
cd : c ≠ d
q : point
Hq : B b q q ∧ length c d = 0
aq : a = q
⊢ False | Please generate a tactic in lean4 to solve the state.
STATE:
i : incidence_geometry
a b c d : point
ab : a ≠ b
big : length a b < length c d
cd : c ≠ d
q : point
Hq : B b q q ∧ length c d = 0
aq : a = q
⊢ False
TACTIC:
|
https://github.com/ianjauslin-rutgers/pythagoras4.git | f97e5d2375d2e350b15d79e541520f8ba81600ec | Pythagoras/euclid_I_extras.lean | same_length_B_of_ne_ge | [223, 1] | [248, 75] | exact not_lt_of_ge (length_nonneg a b) big | i : incidence_geometry
a b c d : point
ab : a ≠ b
big : length a b < 0
cd : c ≠ d
q : point
Hq : B b q q ∧ length c d = 0
aq : a = q
⊢ False | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
i : incidence_geometry
a b c d : point
ab : a ≠ b
big : length a b < 0
cd : c ≠ d
q : point
Hq : B b q q ∧ length c d = 0
aq : a = q
⊢ False
TACTIC:
|
https://github.com/ianjauslin-rutgers/pythagoras4.git | f97e5d2375d2e350b15d79e541520f8ba81600ec | Pythagoras/euclid_I_extras.lean | same_length_B_of_ne_ge | [223, 1] | [248, 75] | rw [←bp, bp] at Hq | i : incidence_geometry
a b c d : point
ab : a ≠ b
cd : c ≠ d
q : point
aq : a ≠ q
C : circle
hC : center_circle a C ∧ on_circle q C
p : point
big : length a b < length a p
Hq : B b a q ∧ length c d = length a p
Hp : B q a p ∧ on_circle p C
AB : line
aAB : online a AB
bAB : online b AB
qAB : online q AB
pAB : online p A... | i : incidence_geometry
a b c d : point
ab : a ≠ b
cd : c ≠ d
q : point
aq : a ≠ q
C : circle
hC : center_circle a C ∧ on_circle q C
p : point
big : length a b < length a p
Hq : B p a q ∧ length c d = length a p
Hp : B q a p ∧ on_circle p C
AB : line
aAB : online a AB
bAB : online b AB
qAB : online q AB
pAB : online p A... | Please generate a tactic in lean4 to solve the state.
STATE:
i : incidence_geometry
a b c d : point
ab : a ≠ b
cd : c ≠ d
q : point
aq : a ≠ q
C : circle
hC : center_circle a C ∧ on_circle q C
p : point
big : length a b < length a p
Hq : B b a q ∧ length c d = length a p
Hp : B q a p ∧ on_circle p C
AB : line
aAB : onl... |
https://github.com/ianjauslin-rutgers/pythagoras4.git | f97e5d2375d2e350b15d79e541520f8ba81600ec | Pythagoras/euclid_I_extras.lean | same_length_B_of_ne_ge | [223, 1] | [248, 75] | rw [bp] at big | i : incidence_geometry
a b c d : point
ab : a ≠ b
cd : c ≠ d
q : point
aq : a ≠ q
C : circle
hC : center_circle a C ∧ on_circle q C
p : point
big : length a b < length a p
Hq : B p a q ∧ length c d = length a p
Hp : B q a p ∧ on_circle p C
AB : line
aAB : online a AB
bAB : online b AB
qAB : online q AB
pAB : online p A... | i : incidence_geometry
a b c d : point
ab : a ≠ b
cd : c ≠ d
q : point
aq : a ≠ q
C : circle
hC : center_circle a C ∧ on_circle q C
p : point
big : length a p < length a p
Hq : B p a q ∧ length c d = length a p
Hp : B q a p ∧ on_circle p C
AB : line
aAB : online a AB
bAB : online b AB
qAB : online q AB
pAB : online p A... | Please generate a tactic in lean4 to solve the state.
STATE:
i : incidence_geometry
a b c d : point
ab : a ≠ b
cd : c ≠ d
q : point
aq : a ≠ q
C : circle
hC : center_circle a C ∧ on_circle q C
p : point
big : length a b < length a p
Hq : B p a q ∧ length c d = length a p
Hp : B q a p ∧ on_circle p C
AB : line
aAB : onl... |
https://github.com/ianjauslin-rutgers/pythagoras4.git | f97e5d2375d2e350b15d79e541520f8ba81600ec | Pythagoras/euclid_I_extras.lean | same_length_B_of_ne_ge | [223, 1] | [248, 75] | simp [lt_self_iff_false] at big | i : incidence_geometry
a b c d : point
ab : a ≠ b
cd : c ≠ d
q : point
aq : a ≠ q
C : circle
hC : center_circle a C ∧ on_circle q C
p : point
big : length a p < length a p
Hq : B p a q ∧ length c d = length a p
Hp : B q a p ∧ on_circle p C
AB : line
aAB : online a AB
bAB : online b AB
qAB : online q AB
pAB : online p A... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
i : incidence_geometry
a b c d : point
ab : a ≠ b
cd : c ≠ d
q : point
aq : a ≠ q
C : circle
hC : center_circle a C ∧ on_circle q C
p : point
big : length a p < length a p
Hq : B p a q ∧ length c d = length a p
Hp : B q a p ∧ on_circle p C
AB : line
aAB : onl... |
https://github.com/ianjauslin-rutgers/pythagoras4.git | f97e5d2375d2e350b15d79e541520f8ba81600ec | Pythagoras/euclid_I_extras.lean | same_length_B_of_ne_ge | [223, 1] | [248, 75] | exact B3 | case intro.intro.intro.intro.intro.inl
i : incidence_geometry
a b c d : point
ab : a ≠ b
cd : c ≠ d
q : point
aq : a ≠ q
C : circle
hC : center_circle a C ∧ on_circle q C
p : point
big : length a b < length a p
Hq : B b a q ∧ length c d = length a p
Hp : B q a p ∧ on_circle p C
AB : line
aAB : online a AB
bAB : online ... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case intro.intro.intro.intro.intro.inl
i : incidence_geometry
a b c d : point
ab : a ≠ b
cd : c ≠ d
q : point
aq : a ≠ q
C : circle
hC : center_circle a C ∧ on_circle q C
p : point
big : length a b < length a p
Hq : B b a q ∧ length c d = length a p
Hp : B q ... |
https://github.com/ianjauslin-rutgers/pythagoras4.git | f97e5d2375d2e350b15d79e541520f8ba81600ec | Pythagoras/euclid_I_extras.lean | same_length_B_of_ne_ge | [223, 1] | [248, 75] | exfalso | case intro.intro.intro.intro.intro.inr
i : incidence_geometry
a b c d : point
ab : a ≠ b
cd : c ≠ d
q : point
aq : a ≠ q
C : circle
hC : center_circle a C ∧ on_circle q C
p : point
big : length a b < length a p
Hq : B b a q ∧ length c d = length a p
Hp : B q a p ∧ on_circle p C
AB : line
aAB : online a AB
bAB : online ... | case intro.intro.intro.intro.intro.inr.h
i : incidence_geometry
a b c d : point
ab : a ≠ b
cd : c ≠ d
q : point
aq : a ≠ q
C : circle
hC : center_circle a C ∧ on_circle q C
p : point
big : length a b < length a p
Hq : B b a q ∧ length c d = length a p
Hp : B q a p ∧ on_circle p C
AB : line
aAB : online a AB
bAB : onlin... | Please generate a tactic in lean4 to solve the state.
STATE:
case intro.intro.intro.intro.intro.inr
i : incidence_geometry
a b c d : point
ab : a ≠ b
cd : c ≠ d
q : point
aq : a ≠ q
C : circle
hC : center_circle a C ∧ on_circle q C
p : point
big : length a b < length a p
Hq : B b a q ∧ length c d = length a p
Hp : B q ... |
https://github.com/ianjauslin-rutgers/pythagoras4.git | f97e5d2375d2e350b15d79e541520f8ba81600ec | Pythagoras/euclid_I_extras.lean | same_length_B_of_ne_ge | [223, 1] | [248, 75] | exact (not_B324_of_B123_B124 (B_symm Hq.1) Hp.1) B3 | case intro.intro.intro.intro.intro.inr.h
i : incidence_geometry
a b c d : point
ab : a ≠ b
cd : c ≠ d
q : point
aq : a ≠ q
C : circle
hC : center_circle a C ∧ on_circle q C
p : point
big : length a b < length a p
Hq : B b a q ∧ length c d = length a p
Hp : B q a p ∧ on_circle p C
AB : line
aAB : online a AB
bAB : onlin... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case intro.intro.intro.intro.intro.inr.h
i : incidence_geometry
a b c d : point
ab : a ≠ b
cd : c ≠ d
q : point
aq : a ≠ q
C : circle
hC : center_circle a C ∧ on_circle q C
p : point
big : length a b < length a p
Hq : B b a q ∧ length c d = length a p
Hp : B ... |
https://github.com/ianjauslin-rutgers/pythagoras4.git | f97e5d2375d2e350b15d79e541520f8ba81600ec | Pythagoras/euclid_I_extras.lean | para_len_parallelogram | [253, 1] | [266, 56] | have abc_bcd := alternate_eq_of_para aL bL bP cP cM dM aPd pLM | i : incidence_geometry
a b c d : point
L M N O P : line
aL : online a L
bL : online b L
cM : online c M
dM : online d M
aN : online a N
cN : online c N
bO : online b O
dO : online d O
bP : online b P
cP : online c P
cb : c ≠ b
aPd : diffside a d P
pLM : para L M
hlen : length a b = length c d
⊢ para N O | i : incidence_geometry
a b c d : point
L M N O P : line
aL : online a L
bL : online b L
cM : online c M
dM : online d M
aN : online a N
cN : online c N
bO : online b O
dO : online d O
bP : online b P
cP : online c P
cb : c ≠ b
aPd : diffside a d P
pLM : para L M
hlen : length a b = length c d
abc_bcd : angle a b c = an... | Please generate a tactic in lean4 to solve the state.
STATE:
i : incidence_geometry
a b c d : point
L M N O P : line
aL : online a L
bL : online b L
cM : online c M
dM : online d M
aN : online a N
cN : online c N
bO : online b O
dO : online d O
bP : online b P
cP : online c P
cb : c ≠ b
aPd : diffside a d P
pLM : para ... |
https://github.com/ianjauslin-rutgers/pythagoras4.git | f97e5d2375d2e350b15d79e541520f8ba81600ec | Pythagoras/euclid_I_extras.lean | para_len_parallelogram | [253, 1] | [266, 56] | obtain ⟨-, -, bca_cbd⟩ := sas (by perma) (by perm) (by perma) | i : incidence_geometry
a b c d : point
L M N O P : line
aL : online a L
bL : online b L
cM : online c M
dM : online d M
aN : online a N
cN : online c N
bO : online b O
dO : online d O
bP : online b P
cP : online c P
cb : c ≠ b
aPd : diffside a d P
pLM : para L M
hlen : length a b = length c d
abc_bcd : angle a b c = an... | case intro.intro
i : incidence_geometry
a b c d : point
L M N O P : line
aL : online a L
bL : online b L
cM : online c M
dM : online d M
aN : online a N
cN : online c N
bO : online b O
dO : online d O
bP : online b P
cP : online c P
cb : c ≠ b
aPd : diffside a d P
pLM : para L M
hlen : length a b = length c d
abc_bcd :... | Please generate a tactic in lean4 to solve the state.
STATE:
i : incidence_geometry
a b c d : point
L M N O P : line
aL : online a L
bL : online b L
cM : online c M
dM : online d M
aN : online a N
cN : online c N
bO : online b O
dO : online d O
bP : online b P
cP : online c P
cb : c ≠ b
aPd : diffside a d P
pLM : para ... |
https://github.com/ianjauslin-rutgers/pythagoras4.git | f97e5d2375d2e350b15d79e541520f8ba81600ec | Pythagoras/euclid_I_extras.lean | para_len_parallelogram | [253, 1] | [266, 56] | exact para_of_ang_eq cb aN cN cP bP bO dO aPd bca_cbd | case intro.intro
i : incidence_geometry
a b c d : point
L M N O P : line
aL : online a L
bL : online b L
cM : online c M
dM : online d M
aN : online a N
cN : online c N
bO : online b O
dO : online d O
bP : online b P
cP : online c P
cb : c ≠ b
aPd : diffside a d P
pLM : para L M
hlen : length a b = length c d
abc_bcd :... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case intro.intro
i : incidence_geometry
a b c d : point
L M N O P : line
aL : online a L
bL : online b L
cM : online c M
dM : online d M
aN : online a N
cN : online c N
bO : online b O
dO : online d O
bP : online b P
cP : online c P
cb : c ≠ b
aPd : diffside ... |
https://github.com/ianjauslin-rutgers/pythagoras4.git | f97e5d2375d2e350b15d79e541520f8ba81600ec | Pythagoras/euclid_I_extras.lean | para_len_parallelogram | [253, 1] | [266, 56] | perma | i : incidence_geometry
a b c d : point
L M N O P : line
aL : online a L
bL : online b L
cM : online c M
dM : online d M
aN : online a N
cN : online c N
bO : online b O
dO : online d O
bP : online b P
cP : online c P
cb : c ≠ b
aPd : diffside a d P
pLM : para L M
hlen : length a b = length c d
abc_bcd : angle a b c = an... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
i : incidence_geometry
a b c d : point
L M N O P : line
aL : online a L
bL : online b L
cM : online c M
dM : online d M
aN : online a N
cN : online c N
bO : online b O
dO : online d O
bP : online b P
cP : online c P
cb : c ≠ b
aPd : diffside a d P
pLM : para ... |
https://github.com/ianjauslin-rutgers/pythagoras4.git | f97e5d2375d2e350b15d79e541520f8ba81600ec | Pythagoras/euclid_I_extras.lean | para_len_parallelogram | [253, 1] | [266, 56] | perm | i : incidence_geometry
a b c d : point
L M N O P : line
aL : online a L
bL : online b L
cM : online c M
dM : online d M
aN : online a N
cN : online c N
bO : online b O
dO : online d O
bP : online b P
cP : online c P
cb : c ≠ b
aPd : diffside a d P
pLM : para L M
hlen : length a b = length c d
abc_bcd : angle a b c = an... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
i : incidence_geometry
a b c d : point
L M N O P : line
aL : online a L
bL : online b L
cM : online c M
dM : online d M
aN : online a N
cN : online c N
bO : online b O
dO : online d O
bP : online b P
cP : online c P
cb : c ≠ b
aPd : diffside a d P
pLM : para ... |
https://github.com/ianjauslin-rutgers/pythagoras4.git | f97e5d2375d2e350b15d79e541520f8ba81600ec | Pythagoras/euclid_I_extras.lean | para_len_parallelogram | [253, 1] | [266, 56] | perma | i : incidence_geometry
a b c d : point
L M N O P : line
aL : online a L
bL : online b L
cM : online c M
dM : online d M
aN : online a N
cN : online c N
bO : online b O
dO : online d O
bP : online b P
cP : online c P
cb : c ≠ b
aPd : diffside a d P
pLM : para L M
hlen : length a b = length c d
abc_bcd : angle a b c = an... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
i : incidence_geometry
a b c d : point
L M N O P : line
aL : online a L
bL : online b L
cM : online c M
dM : online d M
aN : online a N
cN : online c N
bO : online b O
dO : online d O
bP : online b P
cP : online c P
cb : c ≠ b
aPd : diffside a d P
pLM : para ... |
https://github.com/ianjauslin-rutgers/pythagoras4.git | f97e5d2375d2e350b15d79e541520f8ba81600ec | Pythagoras/euclid_I_extras.lean | eq_of_parallelogram_of_eq_basis_of_diffside | [271, 1] | [298, 43] | obtain ⟨ Q, bQ, eQ ⟩ := line_of_pts b e | i : incidence_geometry
a b c d e f g h : point
L M K N O P : line
aL : online a L
dL : online d L
eL : online e L
hL : online h L
bM : online b M
cM : online c M
fM : online f M
gM : online g M
aK : online a K
bK : online b K
dN : online d N
cN : online c N
eO : online e O
fO : online f O
hP : online h P
gP : online g ... | case intro.intro
i : incidence_geometry
a b c d e f g h : point
L M K N O P : line
aL : online a L
dL : online d L
eL : online e L
hL : online h L
bM : online b M
cM : online c M
fM : online f M
gM : online g M
aK : online a K
bK : online b K
dN : online d N
cN : online c N
eO : online e O
fO : online f O
hP : online h... | Please generate a tactic in lean4 to solve the state.
STATE:
i : incidence_geometry
a b c d e f g h : point
L M K N O P : line
aL : online a L
dL : online d L
eL : online e L
hL : online h L
bM : online b M
cM : online c M
fM : online f M
gM : online g M
aK : online a K
bK : online b K
dN : online d N
cN : online c N
e... |
https://github.com/ianjauslin-rutgers/pythagoras4.git | f97e5d2375d2e350b15d79e541520f8ba81600ec | Pythagoras/euclid_I_extras.lean | eq_of_parallelogram_of_eq_basis_of_diffside | [271, 1] | [298, 43] | obtain ⟨ R, cR, hR ⟩ := line_of_pts c h | case intro.intro
i : incidence_geometry
a b c d e f g h : point
L M K N O P : line
aL : online a L
dL : online d L
eL : online e L
hL : online h L
bM : online b M
cM : online c M
fM : online f M
gM : online g M
aK : online a K
bK : online b K
dN : online d N
cN : online c N
eO : online e O
fO : online f O
hP : online h... | case intro.intro.intro.intro
i : incidence_geometry
a b c d e f g h : point
L M K N O P : line
aL : online a L
dL : online d L
eL : online e L
hL : online h L
bM : online b M
cM : online c M
fM : online f M
gM : online g M
aK : online a K
bK : online b K
dN : online d N
cN : online c N
eO : online e O
fO : online f O
h... | Please generate a tactic in lean4 to solve the state.
STATE:
case intro.intro
i : incidence_geometry
a b c d e f g h : point
L M K N O P : line
aL : online a L
dL : online d L
eL : online e L
hL : online h L
bM : online b M
cM : online c M
fM : online f M
gM : online g M
aK : online a K
bK : online b K
dN : online d N
... |
https://github.com/ianjauslin-rutgers/pythagoras4.git | f97e5d2375d2e350b15d79e541520f8ba81600ec | Pythagoras/euclid_I_extras.lean | eq_of_parallelogram_of_eq_basis_of_diffside | [271, 1] | [298, 43] | have ec : e ≠ c := neq_of_para eL cM pLM | case intro.intro.intro.intro
i : incidence_geometry
a b c d e f g h : point
L M K N O P : line
aL : online a L
dL : online d L
eL : online e L
hL : online h L
bM : online b M
cM : online c M
fM : online f M
gM : online g M
aK : online a K
bK : online b K
dN : online d N
cN : online c N
eO : online e O
fO : online f O
h... | case intro.intro.intro.intro
i : incidence_geometry
a b c d e f g h : point
L M K N O P : line
aL : online a L
dL : online d L
eL : online e L
hL : online h L
bM : online b M
cM : online c M
fM : online f M
gM : online g M
aK : online a K
bK : online b K
dN : online d N
cN : online c N
eO : online e O
fO : online f O
h... | Please generate a tactic in lean4 to solve the state.
STATE:
case intro.intro.intro.intro
i : incidence_geometry
a b c d e f g h : point
L M K N O P : line
aL : online a L
dL : online d L
eL : online e L
hL : online h L
bM : online b M
cM : online c M
fM : online f M
gM : online g M
aK : online a K
bK : online b K
dN :... |
https://github.com/ianjauslin-rutgers/pythagoras4.git | f97e5d2375d2e350b15d79e541520f8ba81600ec | Pythagoras/euclid_I_extras.lean | eq_of_parallelogram_of_eq_basis_of_diffside | [271, 1] | [298, 43] | have ehgf : paragram e h g f L P M O := by splitAll <;> perma only [para] | case intro.intro.intro.intro
i : incidence_geometry
a b c d e f g h : point
L M K N O P : line
aL : online a L
dL : online d L
eL : online e L
hL : online h L
bM : online b M
cM : online c M
fM : online f M
gM : online g M
aK : online a K
bK : online b K
dN : online d N
cN : online c N
eO : online e O
fO : online f O
h... | case intro.intro.intro.intro
i : incidence_geometry
a b c d e f g h : point
L M K N O P : line
aL : online a L
dL : online d L
eL : online e L
hL : online h L
bM : online b M
cM : online c M
fM : online f M
gM : online g M
aK : online a K
bK : online b K
dN : online d N
cN : online c N
eO : online e O
fO : online f O
h... | Please generate a tactic in lean4 to solve the state.
STATE:
case intro.intro.intro.intro
i : incidence_geometry
a b c d e f g h : point
L M K N O P : line
aL : online a L
dL : online d L
eL : online e L
hL : online h L
bM : online b M
cM : online c M
fM : online f M
gM : online g M
aK : online a K
bK : online b K
dN :... |
https://github.com/ianjauslin-rutgers/pythagoras4.git | f97e5d2375d2e350b15d79e541520f8ba81600ec | Pythagoras/euclid_I_extras.lean | eq_of_parallelogram_of_eq_basis_of_diffside | [271, 1] | [298, 43] | have : length b c = length e h := by linperm [(len_ang_area_eq_of_parallelogram ehgf).1] | case intro.intro.intro.intro
i : incidence_geometry
a b c d e f g h : point
L M K N O P : line
aL : online a L
dL : online d L
eL : online e L
hL : online h L
bM : online b M
cM : online c M
fM : online f M
gM : online g M
aK : online a K
bK : online b K
dN : online d N
cN : online c N
eO : online e O
fO : online f O
h... | case intro.intro.intro.intro
i : incidence_geometry
a b c d e f g h : point
L M K N O P : line
aL : online a L
dL : online d L
eL : online e L
hL : online h L
bM : online b M
cM : online c M
fM : online f M
gM : online g M
aK : online a K
bK : online b K
dN : online d N
cN : online c N
eO : online e O
fO : online f O
h... | Please generate a tactic in lean4 to solve the state.
STATE:
case intro.intro.intro.intro
i : incidence_geometry
a b c d e f g h : point
L M K N O P : line
aL : online a L
dL : online d L
eL : online e L
hL : online h L
bM : online b M
cM : online c M
fM : online f M
gM : online g M
aK : online a K
bK : online b K
dN :... |
https://github.com/ianjauslin-rutgers/pythagoras4.git | f97e5d2375d2e350b15d79e541520f8ba81600ec | Pythagoras/euclid_I_extras.lean | eq_of_parallelogram_of_eq_basis_of_diffside | [271, 1] | [298, 43] | have' pQR := para_len_parallelogram bM cM eL hL bQ eQ cR hR cS eS ec aPd (para_symm pLM) this | case intro.intro.intro.intro
i : incidence_geometry
a b c d e f g h : point
L M K N O P : line
aL : online a L
dL : online d L
eL : online e L
hL : online h L
bM : online b M
cM : online c M
fM : online f M
gM : online g M
aK : online a K
bK : online b K
dN : online d N
cN : online c N
eO : online e O
fO : online f O
h... | case intro.intro.intro.intro
i : incidence_geometry
a b c d e f g h : point
L M K N O P : line
aL : online a L
dL : online d L
eL : online e L
hL : online h L
bM : online b M
cM : online c M
fM : online f M
gM : online g M
aK : online a K
bK : online b K
dN : online d N
cN : online c N
eO : online e O
fO : online f O
h... | Please generate a tactic in lean4 to solve the state.
STATE:
case intro.intro.intro.intro
i : incidence_geometry
a b c d e f g h : point
L M K N O P : line
aL : online a L
dL : online d L
eL : online e L
hL : online h L
bM : online b M
cM : online c M
fM : online f M
gM : online g M
aK : online a K
bK : online b K
dN :... |
https://github.com/ianjauslin-rutgers/pythagoras4.git | f97e5d2375d2e350b15d79e541520f8ba81600ec | Pythagoras/euclid_I_extras.lean | eq_of_parallelogram_of_eq_basis_of_diffside | [271, 1] | [298, 43] | have eq1 := parallelarea aL dL bM cM eL hL aK bK dN cN bQ eQ cR hR pLM pKN pQR | case intro.intro.intro.intro
i : incidence_geometry
a b c d e f g h : point
L M K N O P : line
aL : online a L
dL : online d L
eL : online e L
hL : online h L
bM : online b M
cM : online c M
fM : online f M
gM : online g M
aK : online a K
bK : online b K
dN : online d N
cN : online c N
eO : online e O
fO : online f O
h... | case intro.intro.intro.intro
i : incidence_geometry
a b c d e f g h : point
L M K N O P : line
aL : online a L
dL : online d L
eL : online e L
hL : online h L
bM : online b M
cM : online c M
fM : online f M
gM : online g M
aK : online a K
bK : online b K
dN : online d N
cN : online c N
eO : online e O
fO : online f O
h... | Please generate a tactic in lean4 to solve the state.
STATE:
case intro.intro.intro.intro
i : incidence_geometry
a b c d e f g h : point
L M K N O P : line
aL : online a L
dL : online d L
eL : online e L
hL : online h L
bM : online b M
cM : online c M
fM : online f M
gM : online g M
aK : online a K
bK : online b K
dN :... |
https://github.com/ianjauslin-rutgers/pythagoras4.git | f97e5d2375d2e350b15d79e541520f8ba81600ec | Pythagoras/euclid_I_extras.lean | eq_of_parallelogram_of_eq_basis_of_diffside | [271, 1] | [298, 43] | have eq2 := parallelarea bM cM eL hL fM gM bQ eQ cR hR eO fO hP gP (para_symm pLM) pQR pOP | case intro.intro.intro.intro
i : incidence_geometry
a b c d e f g h : point
L M K N O P : line
aL : online a L
dL : online d L
eL : online e L
hL : online h L
bM : online b M
cM : online c M
fM : online f M
gM : online g M
aK : online a K
bK : online b K
dN : online d N
cN : online c N
eO : online e O
fO : online f O
h... | case intro.intro.intro.intro
i : incidence_geometry
a b c d e f g h : point
L M K N O P : line
aL : online a L
dL : online d L
eL : online e L
hL : online h L
bM : online b M
cM : online c M
fM : online f M
gM : online g M
aK : online a K
bK : online b K
dN : online d N
cN : online c N
eO : online e O
fO : online f O
h... | Please generate a tactic in lean4 to solve the state.
STATE:
case intro.intro.intro.intro
i : incidence_geometry
a b c d e f g h : point
L M K N O P : line
aL : online a L
dL : online d L
eL : online e L
hL : online h L
bM : online b M
cM : online c M
fM : online f M
gM : online g M
aK : online a K
bK : online b K
dN :... |
https://github.com/ianjauslin-rutgers/pythagoras4.git | f97e5d2375d2e350b15d79e541520f8ba81600ec | Pythagoras/euclid_I_extras.lean | eq_of_parallelogram_of_eq_basis_of_diffside | [271, 1] | [298, 43] | have abcd : paragram a b c d K M N L := by splitAll <;> perma only [para] | case intro.intro.intro.intro
i : incidence_geometry
a b c d e f g h : point
L M K N O P : line
aL : online a L
dL : online d L
eL : online e L
hL : online h L
bM : online b M
cM : online c M
fM : online f M
gM : online g M
aK : online a K
bK : online b K
dN : online d N
cN : online c N
eO : online e O
fO : online f O
h... | case intro.intro.intro.intro
i : incidence_geometry
a b c d e f g h : point
L M K N O P : line
aL : online a L
dL : online d L
eL : online e L
hL : online h L
bM : online b M
cM : online c M
fM : online f M
gM : online g M
aK : online a K
bK : online b K
dN : online d N
cN : online c N
eO : online e O
fO : online f O
h... | Please generate a tactic in lean4 to solve the state.
STATE:
case intro.intro.intro.intro
i : incidence_geometry
a b c d e f g h : point
L M K N O P : line
aL : online a L
dL : online d L
eL : online e L
hL : online h L
bM : online b M
cM : online c M
fM : online f M
gM : online g M
aK : online a K
bK : online b K
dN :... |
https://github.com/ianjauslin-rutgers/pythagoras4.git | f97e5d2375d2e350b15d79e541520f8ba81600ec | Pythagoras/euclid_I_extras.lean | eq_of_parallelogram_of_eq_basis_of_diffside | [271, 1] | [298, 43] | have hgfe : paragram h g f e P M O L := by splitAll <;> perma only [para] | case intro.intro.intro.intro
i : incidence_geometry
a b c d e f g h : point
L M K N O P : line
aL : online a L
dL : online d L
eL : online e L
hL : online h L
bM : online b M
cM : online c M
fM : online f M
gM : online g M
aK : online a K
bK : online b K
dN : online d N
cN : online c N
eO : online e O
fO : online f O
h... | case intro.intro.intro.intro
i : incidence_geometry
a b c d e f g h : point
L M K N O P : line
aL : online a L
dL : online d L
eL : online e L
hL : online h L
bM : online b M
cM : online c M
fM : online f M
gM : online g M
aK : online a K
bK : online b K
dN : online d N
cN : online c N
eO : online e O
fO : online f O
h... | Please generate a tactic in lean4 to solve the state.
STATE:
case intro.intro.intro.intro
i : incidence_geometry
a b c d e f g h : point
L M K N O P : line
aL : online a L
dL : online d L
eL : online e L
hL : online h L
bM : online b M
cM : online c M
fM : online f M
gM : online g M
aK : online a K
bK : online b K
dN :... |
https://github.com/ianjauslin-rutgers/pythagoras4.git | f97e5d2375d2e350b15d79e541520f8ba81600ec | Pythagoras/euclid_I_extras.lean | eq_of_parallelogram_of_eq_basis_of_diffside | [271, 1] | [298, 43] | have: area a b c = area a c d := by linperm [(area_of_parallelogram abcd).1] | case intro.intro.intro.intro
i : incidence_geometry
a b c d e f g h : point
L M K N O P : line
aL : online a L
dL : online d L
eL : online e L
hL : online h L
bM : online b M
cM : online c M
fM : online f M
gM : online g M
aK : online a K
bK : online b K
dN : online d N
cN : online c N
eO : online e O
fO : online f O
h... | case intro.intro.intro.intro
i : incidence_geometry
a b c d e f g h : point
L M K N O P : line
aL : online a L
dL : online d L
eL : online e L
hL : online h L
bM : online b M
cM : online c M
fM : online f M
gM : online g M
aK : online a K
bK : online b K
dN : online d N
cN : online c N
eO : online e O
fO : online f O
h... | Please generate a tactic in lean4 to solve the state.
STATE:
case intro.intro.intro.intro
i : incidence_geometry
a b c d e f g h : point
L M K N O P : line
aL : online a L
dL : online d L
eL : online e L
hL : online h L
bM : online b M
cM : online c M
fM : online f M
gM : online g M
aK : online a K
bK : online b K
dN :... |
https://github.com/ianjauslin-rutgers/pythagoras4.git | f97e5d2375d2e350b15d79e541520f8ba81600ec | Pythagoras/euclid_I_extras.lean | eq_of_parallelogram_of_eq_basis_of_diffside | [271, 1] | [298, 43] | have: area f g h = area e f h := by linperm [(area_of_parallelogram hgfe).1] | case intro.intro.intro.intro
i : incidence_geometry
a b c d e f g h : point
L M K N O P : line
aL : online a L
dL : online d L
eL : online e L
hL : online h L
bM : online b M
cM : online c M
fM : online f M
gM : online g M
aK : online a K
bK : online b K
dN : online d N
cN : online c N
eO : online e O
fO : online f O
h... | case intro.intro.intro.intro
i : incidence_geometry
a b c d e f g h : point
L M K N O P : line
aL : online a L
dL : online d L
eL : online e L
hL : online h L
bM : online b M
cM : online c M
fM : online f M
gM : online g M
aK : online a K
bK : online b K
dN : online d N
cN : online c N
eO : online e O
fO : online f O
h... | Please generate a tactic in lean4 to solve the state.
STATE:
case intro.intro.intro.intro
i : incidence_geometry
a b c d e f g h : point
L M K N O P : line
aL : online a L
dL : online d L
eL : online e L
hL : online h L
bM : online b M
cM : online c M
fM : online f M
gM : online g M
aK : online a K
bK : online b K
dN :... |
https://github.com/ianjauslin-rutgers/pythagoras4.git | f97e5d2375d2e350b15d79e541520f8ba81600ec | Pythagoras/euclid_I_extras.lean | eq_of_parallelogram_of_eq_basis_of_diffside | [271, 1] | [298, 43] | have: 2 * area a b c = area f g h + area e f h := by linperm [(area_of_parallelogram abcd).2] | case intro.intro.intro.intro
i : incidence_geometry
a b c d e f g h : point
L M K N O P : line
aL : online a L
dL : online d L
eL : online e L
hL : online h L
bM : online b M
cM : online c M
fM : online f M
gM : online g M
aK : online a K
bK : online b K
dN : online d N
cN : online c N
eO : online e O
fO : online f O
h... | case intro.intro.intro.intro
i : incidence_geometry
a b c d e f g h : point
L M K N O P : line
aL : online a L
dL : online d L
eL : online e L
hL : online h L
bM : online b M
cM : online c M
fM : online f M
gM : online g M
aK : online a K
bK : online b K
dN : online d N
cN : online c N
eO : online e O
fO : online f O
h... | Please generate a tactic in lean4 to solve the state.
STATE:
case intro.intro.intro.intro
i : incidence_geometry
a b c d e f g h : point
L M K N O P : line
aL : online a L
dL : online d L
eL : online e L
hL : online h L
bM : online b M
cM : online c M
fM : online f M
gM : online g M
aK : online a K
bK : online b K
dN :... |
https://github.com/ianjauslin-rutgers/pythagoras4.git | f97e5d2375d2e350b15d79e541520f8ba81600ec | Pythagoras/euclid_I_extras.lean | eq_of_parallelogram_of_eq_basis_of_diffside | [271, 1] | [298, 43] | linperm [(area_of_parallelogram hgfe).2] | case intro.intro.intro.intro
i : incidence_geometry
a b c d e f g h : point
L M K N O P : line
aL : online a L
dL : online d L
eL : online e L
hL : online h L
bM : online b M
cM : online c M
fM : online f M
gM : online g M
aK : online a K
bK : online b K
dN : online d N
cN : online c N
eO : online e O
fO : online f O
h... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case intro.intro.intro.intro
i : incidence_geometry
a b c d e f g h : point
L M K N O P : line
aL : online a L
dL : online d L
eL : online e L
hL : online h L
bM : online b M
cM : online c M
fM : online f M
gM : online g M
aK : online a K
bK : online b K
dN :... |
https://github.com/ianjauslin-rutgers/pythagoras4.git | f97e5d2375d2e350b15d79e541520f8ba81600ec | Pythagoras/euclid_I_extras.lean | eq_of_parallelogram_of_eq_basis_of_diffside | [271, 1] | [298, 43] | splitAll <;> perma only [para] | i : incidence_geometry
a b c d e f g h : point
L M K N O P : line
aL : online a L
dL : online d L
eL : online e L
hL : online h L
bM : online b M
cM : online c M
fM : online f M
gM : online g M
aK : online a K
bK : online b K
dN : online d N
cN : online c N
eO : online e O
fO : online f O
hP : online h P
gP : online g ... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
i : incidence_geometry
a b c d e f g h : point
L M K N O P : line
aL : online a L
dL : online d L
eL : online e L
hL : online h L
bM : online b M
cM : online c M
fM : online f M
gM : online g M
aK : online a K
bK : online b K
dN : online d N
cN : online c N
e... |
https://github.com/ianjauslin-rutgers/pythagoras4.git | f97e5d2375d2e350b15d79e541520f8ba81600ec | Pythagoras/euclid_I_extras.lean | eq_of_parallelogram_of_eq_basis_of_diffside | [271, 1] | [298, 43] | linperm [(len_ang_area_eq_of_parallelogram ehgf).1] | i : incidence_geometry
a b c d e f g h : point
L M K N O P : line
aL : online a L
dL : online d L
eL : online e L
hL : online h L
bM : online b M
cM : online c M
fM : online f M
gM : online g M
aK : online a K
bK : online b K
dN : online d N
cN : online c N
eO : online e O
fO : online f O
hP : online h P
gP : online g ... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
i : incidence_geometry
a b c d e f g h : point
L M K N O P : line
aL : online a L
dL : online d L
eL : online e L
hL : online h L
bM : online b M
cM : online c M
fM : online f M
gM : online g M
aK : online a K
bK : online b K
dN : online d N
cN : online c N
e... |
https://github.com/ianjauslin-rutgers/pythagoras4.git | f97e5d2375d2e350b15d79e541520f8ba81600ec | Pythagoras/euclid_I_extras.lean | eq_of_parallelogram_of_eq_basis_of_diffside | [271, 1] | [298, 43] | splitAll <;> perma only [para] | i : incidence_geometry
a b c d e f g h : point
L M K N O P : line
aL : online a L
dL : online d L
eL : online e L
hL : online h L
bM : online b M
cM : online c M
fM : online f M
gM : online g M
aK : online a K
bK : online b K
dN : online d N
cN : online c N
eO : online e O
fO : online f O
hP : online h P
gP : online g ... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
i : incidence_geometry
a b c d e f g h : point
L M K N O P : line
aL : online a L
dL : online d L
eL : online e L
hL : online h L
bM : online b M
cM : online c M
fM : online f M
gM : online g M
aK : online a K
bK : online b K
dN : online d N
cN : online c N
e... |
https://github.com/ianjauslin-rutgers/pythagoras4.git | f97e5d2375d2e350b15d79e541520f8ba81600ec | Pythagoras/euclid_I_extras.lean | eq_of_parallelogram_of_eq_basis_of_diffside | [271, 1] | [298, 43] | splitAll <;> perma only [para] | i : incidence_geometry
a b c d e f g h : point
L M K N O P : line
aL : online a L
dL : online d L
eL : online e L
hL : online h L
bM : online b M
cM : online c M
fM : online f M
gM : online g M
aK : online a K
bK : online b K
dN : online d N
cN : online c N
eO : online e O
fO : online f O
hP : online h P
gP : online g ... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
i : incidence_geometry
a b c d e f g h : point
L M K N O P : line
aL : online a L
dL : online d L
eL : online e L
hL : online h L
bM : online b M
cM : online c M
fM : online f M
gM : online g M
aK : online a K
bK : online b K
dN : online d N
cN : online c N
e... |
https://github.com/ianjauslin-rutgers/pythagoras4.git | f97e5d2375d2e350b15d79e541520f8ba81600ec | Pythagoras/euclid_I_extras.lean | eq_of_parallelogram_of_eq_basis_of_diffside | [271, 1] | [298, 43] | linperm [(area_of_parallelogram abcd).1] | i : incidence_geometry
a b c d e f g h : point
L M K N O P : line
aL : online a L
dL : online d L
eL : online e L
hL : online h L
bM : online b M
cM : online c M
fM : online f M
gM : online g M
aK : online a K
bK : online b K
dN : online d N
cN : online c N
eO : online e O
fO : online f O
hP : online h P
gP : online g ... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
i : incidence_geometry
a b c d e f g h : point
L M K N O P : line
aL : online a L
dL : online d L
eL : online e L
hL : online h L
bM : online b M
cM : online c M
fM : online f M
gM : online g M
aK : online a K
bK : online b K
dN : online d N
cN : online c N
e... |
https://github.com/ianjauslin-rutgers/pythagoras4.git | f97e5d2375d2e350b15d79e541520f8ba81600ec | Pythagoras/euclid_I_extras.lean | eq_of_parallelogram_of_eq_basis_of_diffside | [271, 1] | [298, 43] | linperm [(area_of_parallelogram hgfe).1] | i : incidence_geometry
a b c d e f g h : point
L M K N O P : line
aL : online a L
dL : online d L
eL : online e L
hL : online h L
bM : online b M
cM : online c M
fM : online f M
gM : online g M
aK : online a K
bK : online b K
dN : online d N
cN : online c N
eO : online e O
fO : online f O
hP : online h P
gP : online g ... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
i : incidence_geometry
a b c d e f g h : point
L M K N O P : line
aL : online a L
dL : online d L
eL : online e L
hL : online h L
bM : online b M
cM : online c M
fM : online f M
gM : online g M
aK : online a K
bK : online b K
dN : online d N
cN : online c N
e... |
https://github.com/ianjauslin-rutgers/pythagoras4.git | f97e5d2375d2e350b15d79e541520f8ba81600ec | Pythagoras/euclid_I_extras.lean | eq_of_parallelogram_of_eq_basis_of_diffside | [271, 1] | [298, 43] | linperm [(area_of_parallelogram abcd).2] | i : incidence_geometry
a b c d e f g h : point
L M K N O P : line
aL : online a L
dL : online d L
eL : online e L
hL : online h L
bM : online b M
cM : online c M
fM : online f M
gM : online g M
aK : online a K
bK : online b K
dN : online d N
cN : online c N
eO : online e O
fO : online f O
hP : online h P
gP : online g ... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
i : incidence_geometry
a b c d e f g h : point
L M K N O P : line
aL : online a L
dL : online d L
eL : online e L
hL : online h L
bM : online b M
cM : online c M
fM : online f M
gM : online g M
aK : online a K
bK : online b K
dN : online d N
cN : online c N
e... |
https://github.com/ianjauslin-rutgers/pythagoras4.git | f97e5d2375d2e350b15d79e541520f8ba81600ec | Pythagoras/euclid_I_extras.lean | eq_of_parallelogram_of_eq_basis | [301, 1] | [334, 55] | have bcda: paragram b c d a M N L K := by splitAll <;> perma only [para] | i : incidence_geometry
a b c d e f g h : point
L M K N O P : line
aL : online a L
dL : online d L
eL : online e L
hL : online h L
bM : online b M
cM : online c M
fM : online f M
gM : online g M
aK : online a K
bK : online b K
dN : online d N
cN : online c N
eO : online e O
fO : online f O
hP : online h P
gP : online g ... | i : incidence_geometry
a b c d e f g h : point
L M K N O P : line
aL : online a L
dL : online d L
eL : online e L
hL : online h L
bM : online b M
cM : online c M
fM : online f M
gM : online g M
aK : online a K
bK : online b K
dN : online d N
cN : online c N
eO : online e O
fO : online f O
hP : online h P
gP : online g ... | Please generate a tactic in lean4 to solve the state.
STATE:
i : incidence_geometry
a b c d e f g h : point
L M K N O P : line
aL : online a L
dL : online d L
eL : online e L
hL : online h L
bM : online b M
cM : online c M
fM : online f M
gM : online g M
aK : online a K
bK : online b K
dN : online d N
cN : online c N
e... |
https://github.com/ianjauslin-rutgers/pythagoras4.git | f97e5d2375d2e350b15d79e541520f8ba81600ec | Pythagoras/euclid_I_extras.lean | eq_of_parallelogram_of_eq_basis | [301, 1] | [334, 55] | have fghe: paragram f g h e M P L O := by splitAll <;> perma only [para] | i : incidence_geometry
a b c d e f g h : point
L M K N O P : line
aL : online a L
dL : online d L
eL : online e L
hL : online h L
bM : online b M
cM : online c M
fM : online f M
gM : online g M
aK : online a K
bK : online b K
dN : online d N
cN : online c N
eO : online e O
fO : online f O
hP : online h P
gP : online g ... | i : incidence_geometry
a b c d e f g h : point
L M K N O P : line
aL : online a L
dL : online d L
eL : online e L
hL : online h L
bM : online b M
cM : online c M
fM : online f M
gM : online g M
aK : online a K
bK : online b K
dN : online d N
cN : online c N
eO : online e O
fO : online f O
hP : online h P
gP : online g ... | Please generate a tactic in lean4 to solve the state.
STATE:
i : incidence_geometry
a b c d e f g h : point
L M K N O P : line
aL : online a L
dL : online d L
eL : online e L
hL : online h L
bM : online b M
cM : online c M
fM : online f M
gM : online g M
aK : online a K
bK : online b K
dN : online d N
cN : online c N
e... |
https://github.com/ianjauslin-rutgers/pythagoras4.git | f97e5d2375d2e350b15d79e541520f8ba81600ec | Pythagoras/euclid_I_extras.lean | eq_of_parallelogram_of_eq_basis | [301, 1] | [334, 55] | have fg_he := (len_ang_area_eq_of_parallelogram fghe).1 | i : incidence_geometry
a b c d e f g h : point
L M K N O P : line
aL : online a L
dL : online d L
eL : online e L
hL : online h L
bM : online b M
cM : online c M
fM : online f M
gM : online g M
aK : online a K
bK : online b K
dN : online d N
cN : online c N
eO : online e O
fO : online f O
hP : online h P
gP : online g ... | i : incidence_geometry
a b c d e f g h : point
L M K N O P : line
aL : online a L
dL : online d L
eL : online e L
hL : online h L
bM : online b M
cM : online c M
fM : online f M
gM : online g M
aK : online a K
bK : online b K
dN : online d N
cN : online c N
eO : online e O
fO : online f O
hP : online h P
gP : online g ... | Please generate a tactic in lean4 to solve the state.
STATE:
i : incidence_geometry
a b c d e f g h : point
L M K N O P : line
aL : online a L
dL : online d L
eL : online e L
hL : online h L
bM : online b M
cM : online c M
fM : online f M
gM : online g M
aK : online a K
bK : online b K
dN : online d N
cN : online c N
e... |
https://github.com/ianjauslin-rutgers/pythagoras4.git | f97e5d2375d2e350b15d79e541520f8ba81600ec | Pythagoras/euclid_I_extras.lean | eq_of_parallelogram_of_eq_basis | [301, 1] | [334, 55] | by_cases bc: b = c | i : incidence_geometry
a b c d e f g h : point
L M K N O P : line
aL : online a L
dL : online d L
eL : online e L
hL : online h L
bM : online b M
cM : online c M
fM : online f M
gM : online g M
aK : online a K
bK : online b K
dN : online d N
cN : online c N
eO : online e O
fO : online f O
hP : online h P
gP : online g ... | case pos
i : incidence_geometry
a b c d e f g h : point
L M K N O P : line
aL : online a L
dL : online d L
eL : online e L
hL : online h L
bM : online b M
cM : online c M
fM : online f M
gM : online g M
aK : online a K
bK : online b K
dN : online d N
cN : online c N
eO : online e O
fO : online f O
hP : online h P
gP : ... | Please generate a tactic in lean4 to solve the state.
STATE:
i : incidence_geometry
a b c d e f g h : point
L M K N O P : line
aL : online a L
dL : online d L
eL : online e L
hL : online h L
bM : online b M
cM : online c M
fM : online f M
gM : online g M
aK : online a K
bK : online b K
dN : online d N
cN : online c N
e... |
https://github.com/ianjauslin-rutgers/pythagoras4.git | f97e5d2375d2e350b15d79e541520f8ba81600ec | Pythagoras/euclid_I_extras.lean | eq_of_parallelogram_of_eq_basis | [301, 1] | [334, 55] | splitAll <;> perma only [para] | i : incidence_geometry
a b c d e f g h : point
L M K N O P : line
aL : online a L
dL : online d L
eL : online e L
hL : online h L
bM : online b M
cM : online c M
fM : online f M
gM : online g M
aK : online a K
bK : online b K
dN : online d N
cN : online c N
eO : online e O
fO : online f O
hP : online h P
gP : online g ... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
i : incidence_geometry
a b c d e f g h : point
L M K N O P : line
aL : online a L
dL : online d L
eL : online e L
hL : online h L
bM : online b M
cM : online c M
fM : online f M
gM : online g M
aK : online a K
bK : online b K
dN : online d N
cN : online c N
e... |
https://github.com/ianjauslin-rutgers/pythagoras4.git | f97e5d2375d2e350b15d79e541520f8ba81600ec | Pythagoras/euclid_I_extras.lean | eq_of_parallelogram_of_eq_basis | [301, 1] | [334, 55] | splitAll <;> perma only [para] | i : incidence_geometry
a b c d e f g h : point
L M K N O P : line
aL : online a L
dL : online d L
eL : online e L
hL : online h L
bM : online b M
cM : online c M
fM : online f M
gM : online g M
aK : online a K
bK : online b K
dN : online d N
cN : online c N
eO : online e O
fO : online f O
hP : online h P
gP : online g ... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
i : incidence_geometry
a b c d e f g h : point
L M K N O P : line
aL : online a L
dL : online d L
eL : online e L
hL : online h L
bM : online b M
cM : online c M
fM : online f M
gM : online g M
aK : online a K
bK : online b K
dN : online d N
cN : online c N
e... |
https://github.com/ianjauslin-rutgers/pythagoras4.git | f97e5d2375d2e350b15d79e541520f8ba81600ec | Pythagoras/euclid_I_extras.lean | eq_of_parallelogram_of_eq_basis | [301, 1] | [334, 55] | have hg := (same_len_pts_coincide_iff hlen).mp bc | case pos
i : incidence_geometry
a b c d e f g h : point
L M K N O P : line
aL : online a L
dL : online d L
eL : online e L
hL : online h L
bM : online b M
cM : online c M
fM : online f M
gM : online g M
aK : online a K
bK : online b K
dN : online d N
cN : online c N
eO : online e O
fO : online f O
hP : online h P
gP : ... | case pos
i : incidence_geometry
a b c d e f g h : point
L M K N O P : line
aL : online a L
dL : online d L
eL : online e L
hL : online h L
bM : online b M
cM : online c M
fM : online f M
gM : online g M
aK : online a K
bK : online b K
dN : online d N
cN : online c N
eO : online e O
fO : online f O
hP : online h P
gP : ... | Please generate a tactic in lean4 to solve the state.
STATE:
case pos
i : incidence_geometry
a b c d e f g h : point
L M K N O P : line
aL : online a L
dL : online d L
eL : online e L
hL : online h L
bM : online b M
cM : online c M
fM : online f M
gM : online g M
aK : online a K
bK : online b K
dN : online d N
cN : onl... |
https://github.com/ianjauslin-rutgers/pythagoras4.git | f97e5d2375d2e350b15d79e541520f8ba81600ec | Pythagoras/euclid_I_extras.lean | eq_of_parallelogram_of_eq_basis | [301, 1] | [334, 55] | have he := (same_len_pts_coincide_iff fg_he).mp hg | case pos
i : incidence_geometry
a b c d e f g h : point
L M K N O P : line
aL : online a L
dL : online d L
eL : online e L
hL : online h L
bM : online b M
cM : online c M
fM : online f M
gM : online g M
aK : online a K
bK : online b K
dN : online d N
cN : online c N
eO : online e O
fO : online f O
hP : online h P
gP : ... | case pos
i : incidence_geometry
a b c d e f g h : point
L M K N O P : line
aL : online a L
dL : online d L
eL : online e L
hL : online h L
bM : online b M
cM : online c M
fM : online f M
gM : online g M
aK : online a K
bK : online b K
dN : online d N
cN : online c N
eO : online e O
fO : online f O
hP : online h P
gP : ... | Please generate a tactic in lean4 to solve the state.
STATE:
case pos
i : incidence_geometry
a b c d e f g h : point
L M K N O P : line
aL : online a L
dL : online d L
eL : online e L
hL : online h L
bM : online b M
cM : online c M
fM : online f M
gM : online g M
aK : online a K
bK : online b K
dN : online d N
cN : onl... |
https://github.com/ianjauslin-rutgers/pythagoras4.git | f97e5d2375d2e350b15d79e541520f8ba81600ec | Pythagoras/euclid_I_extras.lean | eq_of_parallelogram_of_eq_basis | [301, 1] | [334, 55] | have da := (same_len_pts_coincide_iff (len_ang_area_eq_of_parallelogram bcda).1).mp bc | case pos
i : incidence_geometry
a b c d e f g h : point
L M K N O P : line
aL : online a L
dL : online d L
eL : online e L
hL : online h L
bM : online b M
cM : online c M
fM : online f M
gM : online g M
aK : online a K
bK : online b K
dN : online d N
cN : online c N
eO : online e O
fO : online f O
hP : online h P
gP : ... | case pos
i : incidence_geometry
a b c d e f g h : point
L M K N O P : line
aL : online a L
dL : online d L
eL : online e L
hL : online h L
bM : online b M
cM : online c M
fM : online f M
gM : online g M
aK : online a K
bK : online b K
dN : online d N
cN : online c N
eO : online e O
fO : online f O
hP : online h P
gP : ... | Please generate a tactic in lean4 to solve the state.
STATE:
case pos
i : incidence_geometry
a b c d e f g h : point
L M K N O P : line
aL : online a L
dL : online d L
eL : online e L
hL : online h L
bM : online b M
cM : online c M
fM : online f M
gM : online g M
aK : online a K
bK : online b K
dN : online d N
cN : onl... |
https://github.com/ianjauslin-rutgers/pythagoras4.git | f97e5d2375d2e350b15d79e541520f8ba81600ec | Pythagoras/euclid_I_extras.lean | eq_of_parallelogram_of_eq_basis | [301, 1] | [334, 55] | conv in (occs := *) area _ _ _ => all_goals rw [area_of_eq _ _ _ (by tauto)] | case pos
i : incidence_geometry
a b c d e f g h : point
L M K N O P : line
aL : online a L
dL : online d L
eL : online e L
hL : online h L
bM : online b M
cM : online c M
fM : online f M
gM : online g M
aK : online a K
bK : online b K
dN : online d N
cN : online c N
eO : online e O
fO : online f O
hP : online h P
gP : ... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case pos
i : incidence_geometry
a b c d e f g h : point
L M K N O P : line
aL : online a L
dL : online d L
eL : online e L
hL : online h L
bM : online b M
cM : online c M
fM : online f M
gM : online g M
aK : online a K
bK : online b K
dN : online d N
cN : onl... |
https://github.com/ianjauslin-rutgers/pythagoras4.git | f97e5d2375d2e350b15d79e541520f8ba81600ec | Pythagoras/euclid_I_extras.lean | eq_of_parallelogram_of_eq_basis | [301, 1] | [334, 55] | tauto | i : incidence_geometry
a b c d e f g h : point
L M K N O P : line
aL : online a L
dL : online d L
eL : online e L
hL : online h L
bM : online b M
cM : online c M
fM : online f M
gM : online g M
aK : online a K
bK : online b K
dN : online d N
cN : online c N
eO : online e O
fO : online f O
hP : online h P
gP : online g ... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
i : incidence_geometry
a b c d e f g h : point
L M K N O P : line
aL : online a L
dL : online d L
eL : online e L
hL : online h L
bM : online b M
cM : online c M
fM : online f M
gM : online g M
aK : online a K
bK : online b K
dN : online d N
cN : online c N
e... |
https://github.com/ianjauslin-rutgers/pythagoras4.git | f97e5d2375d2e350b15d79e541520f8ba81600ec | Pythagoras/euclid_I_extras.lean | eq_of_parallelogram_of_eq_basis | [301, 1] | [334, 55] | rw [(Ne.def b c).symm] at bc | case neg
i : incidence_geometry
a b c d e f g h : point
L M K N O P : line
aL : online a L
dL : online d L
eL : online e L
hL : online h L
bM : online b M
cM : online c M
fM : online f M
gM : online g M
aK : online a K
bK : online b K
dN : online d N
cN : online c N
eO : online e O
fO : online f O
hP : online h P
gP : ... | case neg
i : incidence_geometry
a b c d e f g h : point
L M K N O P : line
aL : online a L
dL : online d L
eL : online e L
hL : online h L
bM : online b M
cM : online c M
fM : online f M
gM : online g M
aK : online a K
bK : online b K
dN : online d N
cN : online c N
eO : online e O
fO : online f O
hP : online h P
gP : ... | Please generate a tactic in lean4 to solve the state.
STATE:
case neg
i : incidence_geometry
a b c d e f g h : point
L M K N O P : line
aL : online a L
dL : online d L
eL : online e L
hL : online h L
bM : online b M
cM : online c M
fM : online f M
gM : online g M
aK : online a K
bK : online b K
dN : online d N
cN : onl... |
https://github.com/ianjauslin-rutgers/pythagoras4.git | f97e5d2375d2e350b15d79e541520f8ba81600ec | Pythagoras/euclid_I_extras.lean | eq_of_parallelogram_of_eq_basis | [301, 1] | [334, 55] | have he : h ≠ e := ne_of_ne_len bc (hlen.trans fg_he) | case neg
i : incidence_geometry
a b c d e f g h : point
L M K N O P : line
aL : online a L
dL : online d L
eL : online e L
hL : online h L
bM : online b M
cM : online c M
fM : online f M
gM : online g M
aK : online a K
bK : online b K
dN : online d N
cN : online c N
eO : online e O
fO : online f O
hP : online h P
gP : ... | case neg
i : incidence_geometry
a b c d e f g h : point
L M K N O P : line
aL : online a L
dL : online d L
eL : online e L
hL : online h L
bM : online b M
cM : online c M
fM : online f M
gM : online g M
aK : online a K
bK : online b K
dN : online d N
cN : online c N
eO : online e O
fO : online f O
hP : online h P
gP : ... | Please generate a tactic in lean4 to solve the state.
STATE:
case neg
i : incidence_geometry
a b c d e f g h : point
L M K N O P : line
aL : online a L
dL : online d L
eL : online e L
hL : online h L
bM : online b M
cM : online c M
fM : online f M
gM : online g M
aK : online a K
bK : online b K
dN : online d N
cN : onl... |
https://github.com/ianjauslin-rutgers/pythagoras4.git | f97e5d2375d2e350b15d79e541520f8ba81600ec | Pythagoras/euclid_I_extras.lean | eq_of_parallelogram_of_eq_basis | [301, 1] | [334, 55] | obtain ⟨ S, cS, eS ⟩ := line_of_pts c e | case neg
i : incidence_geometry
a b c d e f g h : point
L M K N O P : line
aL : online a L
dL : online d L
eL : online e L
hL : online h L
bM : online b M
cM : online c M
fM : online f M
gM : online g M
aK : online a K
bK : online b K
dN : online d N
cN : online c N
eO : online e O
fO : online f O
hP : online h P
gP : ... | case neg.intro.intro
i : incidence_geometry
a b c d e f g h : point
L M K N O P : line
aL : online a L
dL : online d L
eL : online e L
hL : online h L
bM : online b M
cM : online c M
fM : online f M
gM : online g M
aK : online a K
bK : online b K
dN : online d N
cN : online c N
eO : online e O
fO : online f O
hP : onli... | Please generate a tactic in lean4 to solve the state.
STATE:
case neg
i : incidence_geometry
a b c d e f g h : point
L M K N O P : line
aL : online a L
dL : online d L
eL : online e L
hL : online h L
bM : online b M
cM : online c M
fM : online f M
gM : online g M
aK : online a K
bK : online b K
dN : online d N
cN : onl... |
https://github.com/ianjauslin-rutgers/pythagoras4.git | f97e5d2375d2e350b15d79e541520f8ba81600ec | Pythagoras/euclid_I_extras.lean | eq_of_parallelogram_of_eq_basis | [301, 1] | [334, 55] | obtain ⟨ Q, bQ, eQ ⟩ := line_of_pts b e | case neg.intro.intro
i : incidence_geometry
a b c d e f g h : point
L M K N O P : line
aL : online a L
dL : online d L
eL : online e L
hL : online h L
bM : online b M
cM : online c M
fM : online f M
gM : online g M
aK : online a K
bK : online b K
dN : online d N
cN : online c N
eO : online e O
fO : online f O
hP : onli... | case neg.intro.intro.intro.intro
i : incidence_geometry
a b c d e f g h : point
L M K N O P : line
aL : online a L
dL : online d L
eL : online e L
hL : online h L
bM : online b M
cM : online c M
fM : online f M
gM : online g M
aK : online a K
bK : online b K
dN : online d N
cN : online c N
eO : online e O
fO : online f... | Please generate a tactic in lean4 to solve the state.
STATE:
case neg.intro.intro
i : incidence_geometry
a b c d e f g h : point
L M K N O P : line
aL : online a L
dL : online d L
eL : online e L
hL : online h L
bM : online b M
cM : online c M
fM : online f M
gM : online g M
aK : online a K
bK : online b K
dN : online ... |
https://github.com/ianjauslin-rutgers/pythagoras4.git | f97e5d2375d2e350b15d79e541520f8ba81600ec | Pythagoras/euclid_I_extras.lean | eq_of_parallelogram_of_eq_basis | [301, 1] | [334, 55] | have aPd := diffside_of_trapezoid hL eL eQ bQ bM cM eS cS pLM ⟨ he, bc ⟩ | case neg.intro.intro.intro.intro
i : incidence_geometry
a b c d e f g h : point
L M K N O P : line
aL : online a L
dL : online d L
eL : online e L
hL : online h L
bM : online b M
cM : online c M
fM : online f M
gM : online g M
aK : online a K
bK : online b K
dN : online d N
cN : online c N
eO : online e O
fO : online f... | case neg.intro.intro.intro.intro
i : incidence_geometry
a b c d e f g h : point
L M K N O P : line
aL : online a L
dL : online d L
eL : online e L
hL : online h L
bM : online b M
cM : online c M
fM : online f M
gM : online g M
aK : online a K
bK : online b K
dN : online d N
cN : online c N
eO : online e O
fO : online f... | Please generate a tactic in lean4 to solve the state.
STATE:
case neg.intro.intro.intro.intro
i : incidence_geometry
a b c d e f g h : point
L M K N O P : line
aL : online a L
dL : online d L
eL : online e L
hL : online h L
bM : online b M
cM : online c M
fM : online f M
gM : online g M
aK : online a K
bK : online b K
... |
https://github.com/ianjauslin-rutgers/pythagoras4.git | f97e5d2375d2e350b15d79e541520f8ba81600ec | Pythagoras/euclid_I_extras.lean | eq_of_parallelogram_of_eq_basis | [301, 1] | [334, 55] | cases aPd with
| inl aPd =>
exact eq_of_parallelogram_of_eq_basis_of_diffside aL dL eL hL bM cM fM gM aK bK dN cN eO fO hP gP pLM pKN pOP hlen cS eS (diffside_symm aPd) bc
| inr aPd =>
rw [← eq_of_parallelogram_of_eq_basis_of_diffside dL aL eL hL cM bM fM gM dN cN aK bK eO fO hP gP pLM (para_symm pKN) pOP (by perma... | case neg.intro.intro.intro.intro
i : incidence_geometry
a b c d e f g h : point
L M K N O P : line
aL : online a L
dL : online d L
eL : online e L
hL : online h L
bM : online b M
cM : online c M
fM : online f M
gM : online g M
aK : online a K
bK : online b K
dN : online d N
cN : online c N
eO : online e O
fO : online f... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case neg.intro.intro.intro.intro
i : incidence_geometry
a b c d e f g h : point
L M K N O P : line
aL : online a L
dL : online d L
eL : online e L
hL : online h L
bM : online b M
cM : online c M
fM : online f M
gM : online g M
aK : online a K
bK : online b K
... |
https://github.com/ianjauslin-rutgers/pythagoras4.git | f97e5d2375d2e350b15d79e541520f8ba81600ec | Pythagoras/euclid_I_extras.lean | eq_of_parallelogram_of_eq_basis | [301, 1] | [334, 55] | exact eq_of_parallelogram_of_eq_basis_of_diffside aL dL eL hL bM cM fM gM aK bK dN cN eO fO hP gP pLM pKN pOP hlen cS eS (diffside_symm aPd) bc | case neg.intro.intro.intro.intro.inl
i : incidence_geometry
a b c d e f g h : point
L M K N O P : line
aL : online a L
dL : online d L
eL : online e L
hL : online h L
bM : online b M
cM : online c M
fM : online f M
gM : online g M
aK : online a K
bK : online b K
dN : online d N
cN : online c N
eO : online e O
fO : onli... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case neg.intro.intro.intro.intro.inl
i : incidence_geometry
a b c d e f g h : point
L M K N O P : line
aL : online a L
dL : online d L
eL : online e L
hL : online h L
bM : online b M
cM : online c M
fM : online f M
gM : online g M
aK : online a K
bK : online ... |
https://github.com/ianjauslin-rutgers/pythagoras4.git | f97e5d2375d2e350b15d79e541520f8ba81600ec | Pythagoras/euclid_I_extras.lean | eq_of_parallelogram_of_eq_basis | [301, 1] | [334, 55] | rw [← eq_of_parallelogram_of_eq_basis_of_diffside dL aL eL hL cM bM fM gM dN cN aK bK eO fO hP gP pLM (para_symm pKN) pOP (by perma) bQ eQ (diffside_symm aPd) bc.symm] | case neg.intro.intro.intro.intro.inr
i : incidence_geometry
a b c d e f g h : point
L M K N O P : line
aL : online a L
dL : online d L
eL : online e L
hL : online h L
bM : online b M
cM : online c M
fM : online f M
gM : online g M
aK : online a K
bK : online b K
dN : online d N
cN : online c N
eO : online e O
fO : onli... | case neg.intro.intro.intro.intro.inr
i : incidence_geometry
a b c d e f g h : point
L M K N O P : line
aL : online a L
dL : online d L
eL : online e L
hL : online h L
bM : online b M
cM : online c M
fM : online f M
gM : online g M
aK : online a K
bK : online b K
dN : online d N
cN : online c N
eO : online e O
fO : onli... | Please generate a tactic in lean4 to solve the state.
STATE:
case neg.intro.intro.intro.intro.inr
i : incidence_geometry
a b c d e f g h : point
L M K N O P : line
aL : online a L
dL : online d L
eL : online e L
hL : online h L
bM : online b M
cM : online c M
fM : online f M
gM : online g M
aK : online a K
bK : online ... |
https://github.com/ianjauslin-rutgers/pythagoras4.git | f97e5d2375d2e350b15d79e541520f8ba81600ec | Pythagoras/euclid_I_extras.lean | eq_of_parallelogram_of_eq_basis | [301, 1] | [334, 55] | perm [(area_of_parallelogram bcda).1] | case neg.intro.intro.intro.intro.inr
i : incidence_geometry
a b c d e f g h : point
L M K N O P : line
aL : online a L
dL : online d L
eL : online e L
hL : online h L
bM : online b M
cM : online c M
fM : online f M
gM : online g M
aK : online a K
bK : online b K
dN : online d N
cN : online c N
eO : online e O
fO : onli... | case neg.intro.intro.intro.intro.inr
i : incidence_geometry
a b c d e f g h : point
L M K N O P : line
aL : online a L
dL : online d L
eL : online e L
hL : online h L
bM : online b M
cM : online c M
fM : online f M
gM : online g M
aK : online a K
bK : online b K
dN : online d N
cN : online c N
eO : online e O
fO : onli... | Please generate a tactic in lean4 to solve the state.
STATE:
case neg.intro.intro.intro.intro.inr
i : incidence_geometry
a b c d e f g h : point
L M K N O P : line
aL : online a L
dL : online d L
eL : online e L
hL : online h L
bM : online b M
cM : online c M
fM : online f M
gM : online g M
aK : online a K
bK : online ... |
https://github.com/ianjauslin-rutgers/pythagoras4.git | f97e5d2375d2e350b15d79e541520f8ba81600ec | Pythagoras/euclid_I_extras.lean | eq_of_parallelogram_of_eq_basis | [301, 1] | [334, 55] | rw [this] | case neg.intro.intro.intro.intro.inr
i : incidence_geometry
a b c d e f g h : point
L M K N O P : line
aL : online a L
dL : online d L
eL : online e L
hL : online h L
bM : online b M
cM : online c M
fM : online f M
gM : online g M
aK : online a K
bK : online b K
dN : online d N
cN : online c N
eO : online e O
fO : onli... | case neg.intro.intro.intro.intro.inr
i : incidence_geometry
a b c d e f g h : point
L M K N O P : line
aL : online a L
dL : online d L
eL : online e L
hL : online h L
bM : online b M
cM : online c M
fM : online f M
gM : online g M
aK : online a K
bK : online b K
dN : online d N
cN : online c N
eO : online e O
fO : onli... | Please generate a tactic in lean4 to solve the state.
STATE:
case neg.intro.intro.intro.intro.inr
i : incidence_geometry
a b c d e f g h : point
L M K N O P : line
aL : online a L
dL : online d L
eL : online e L
hL : online h L
bM : online b M
cM : online c M
fM : online f M
gM : online g M
aK : online a K
bK : online ... |
https://github.com/ianjauslin-rutgers/pythagoras4.git | f97e5d2375d2e350b15d79e541520f8ba81600ec | Pythagoras/euclid_I_extras.lean | eq_of_parallelogram_of_eq_basis | [301, 1] | [334, 55] | perm [(area_of_parallelogram bcda).2] | case neg.intro.intro.intro.intro.inr
i : incidence_geometry
a b c d e f g h : point
L M K N O P : line
aL : online a L
dL : online d L
eL : online e L
hL : online h L
bM : online b M
cM : online c M
fM : online f M
gM : online g M
aK : online a K
bK : online b K
dN : online d N
cN : online c N
eO : online e O
fO : onli... | case neg.intro.intro.intro.intro.inr
i : incidence_geometry
a b c d e f g h : point
L M K N O P : line
aL : online a L
dL : online d L
eL : online e L
hL : online h L
bM : online b M
cM : online c M
fM : online f M
gM : online g M
aK : online a K
bK : online b K
dN : online d N
cN : online c N
eO : online e O
fO : onli... | Please generate a tactic in lean4 to solve the state.
STATE:
case neg.intro.intro.intro.intro.inr
i : incidence_geometry
a b c d e f g h : point
L M K N O P : line
aL : online a L
dL : online d L
eL : online e L
hL : online h L
bM : online b M
cM : online c M
fM : online f M
gM : online g M
aK : online a K
bK : online ... |
https://github.com/ianjauslin-rutgers/pythagoras4.git | f97e5d2375d2e350b15d79e541520f8ba81600ec | Pythagoras/euclid_I_extras.lean | eq_of_parallelogram_of_eq_basis | [301, 1] | [334, 55] | rw [this] | case neg.intro.intro.intro.intro.inr
i : incidence_geometry
a b c d e f g h : point
L M K N O P : line
aL : online a L
dL : online d L
eL : online e L
hL : online h L
bM : online b M
cM : online c M
fM : online f M
gM : online g M
aK : online a K
bK : online b K
dN : online d N
cN : online c N
eO : online e O
fO : onli... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case neg.intro.intro.intro.intro.inr
i : incidence_geometry
a b c d e f g h : point
L M K N O P : line
aL : online a L
dL : online d L
eL : online e L
hL : online h L
bM : online b M
cM : online c M
fM : online f M
gM : online g M
aK : online a K
bK : online ... |
https://github.com/ianjauslin-rutgers/pythagoras4.git | f97e5d2375d2e350b15d79e541520f8ba81600ec | Pythagoras/euclid_I_extras.lean | eq_of_parallelogram_of_eq_basis | [301, 1] | [334, 55] | perma | i : incidence_geometry
a b c d e f g h : point
L M K N O P : line
aL : online a L
dL : online d L
eL : online e L
hL : online h L
bM : online b M
cM : online c M
fM : online f M
gM : online g M
aK : online a K
bK : online b K
dN : online d N
cN : online c N
eO : online e O
fO : online f O
hP : online h P
gP : online g ... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
i : incidence_geometry
a b c d e f g h : point
L M K N O P : line
aL : online a L
dL : online d L
eL : online e L
hL : online h L
bM : online b M
cM : online c M
fM : online f M
gM : online g M
aK : online a K
bK : online b K
dN : online d N
cN : online c N
e... |
https://github.com/ianjauslin-rutgers/pythagoras4.git | f97e5d2375d2e350b15d79e541520f8ba81600ec | Pythagoras/euclid_I_extras.lean | eq_area_of_eq_base | [339, 1] | [374, 11] | by_cases bc: b = c | i : incidence_geometry
a b c d e f : point
L M : line
aM : online a M
bL : online b L
cL : online c L
dM : online d M
eL : online e L
fL : online f L
pLM : para L M
hlen : length b c = length e f
⊢ area a b c = area d e f | case pos
i : incidence_geometry
a b c d e f : point
L M : line
aM : online a M
bL : online b L
cL : online c L
dM : online d M
eL : online e L
fL : online f L
pLM : para L M
hlen : length b c = length e f
bc : b = c
⊢ area a b c = area d e f
case neg
i : incidence_geometry
a b c d e f : point
L M : line
aM : online a ... | Please generate a tactic in lean4 to solve the state.
STATE:
i : incidence_geometry
a b c d e f : point
L M : line
aM : online a M
bL : online b L
cL : online c L
dM : online d M
eL : online e L
fL : online f L
pLM : para L M
hlen : length b c = length e f
⊢ area a b c = area d e f
TACTIC:
|
https://github.com/ianjauslin-rutgers/pythagoras4.git | f97e5d2375d2e350b15d79e541520f8ba81600ec | Pythagoras/euclid_I_extras.lean | eq_area_of_eq_base | [339, 1] | [374, 11] | have ef : e ≠ f := ne_of_ne_len bc hlen | case neg
i : incidence_geometry
a b c d e f : point
L M : line
aM : online a M
bL : online b L
cL : online c L
dM : online d M
eL : online e L
fL : online f L
pLM : para L M
hlen : length b c = length e f
bc : ¬b = c
⊢ area a b c = area d e f | case neg
i : incidence_geometry
a b c d e f : point
L M : line
aM : online a M
bL : online b L
cL : online c L
dM : online d M
eL : online e L
fL : online f L
pLM : para L M
hlen : length b c = length e f
bc : ¬b = c
ef : e ≠ f
⊢ area a b c = area d e f | Please generate a tactic in lean4 to solve the state.
STATE:
case neg
i : incidence_geometry
a b c d e f : point
L M : line
aM : online a M
bL : online b L
cL : online c L
dM : online d M
eL : online e L
fL : online f L
pLM : para L M
hlen : length b c = length e f
bc : ¬b = c
⊢ area a b c = area d e f
TACTIC:
|
https://github.com/ianjauslin-rutgers/pythagoras4.git | f97e5d2375d2e350b15d79e541520f8ba81600ec | Pythagoras/euclid_I_extras.lean | eq_area_of_eq_base | [339, 1] | [374, 11] | obtain ⟨ K, aK, cK ⟩ := line_of_pts a c | case neg
i : incidence_geometry
a b c d e f : point
L M : line
aM : online a M
bL : online b L
cL : online c L
dM : online d M
eL : online e L
fL : online f L
pLM : para L M
hlen : length b c = length e f
bc : ¬b = c
ef : e ≠ f
⊢ area a b c = area d e f | case neg.intro.intro
i : incidence_geometry
a b c d e f : point
L M : line
aM : online a M
bL : online b L
cL : online c L
dM : online d M
eL : online e L
fL : online f L
pLM : para L M
hlen : length b c = length e f
bc : ¬b = c
ef : e ≠ f
K : line
aK : online a K
cK : online c K
⊢ area a b c = area d e f | Please generate a tactic in lean4 to solve the state.
STATE:
case neg
i : incidence_geometry
a b c d e f : point
L M : line
aM : online a M
bL : online b L
cL : online c L
dM : online d M
eL : online e L
fL : online f L
pLM : para L M
hlen : length b c = length e f
bc : ¬b = c
ef : e ≠ f
⊢ area a b c = area d e f
TACTI... |
https://github.com/ianjauslin-rutgers/pythagoras4.git | f97e5d2375d2e350b15d79e541520f8ba81600ec | Pythagoras/euclid_I_extras.lean | eq_area_of_eq_base | [339, 1] | [374, 11] | obtain ⟨ N, dN, eN ⟩ := line_of_pts d e | case neg.intro.intro
i : incidence_geometry
a b c d e f : point
L M : line
aM : online a M
bL : online b L
cL : online c L
dM : online d M
eL : online e L
fL : online f L
pLM : para L M
hlen : length b c = length e f
bc : ¬b = c
ef : e ≠ f
K : line
aK : online a K
cK : online c K
⊢ area a b c = area d e f | case neg.intro.intro.intro.intro
i : incidence_geometry
a b c d e f : point
L M : line
aM : online a M
bL : online b L
cL : online c L
dM : online d M
eL : online e L
fL : online f L
pLM : para L M
hlen : length b c = length e f
bc : ¬b = c
ef : e ≠ f
K : line
aK : online a K
cK : online c K
N : line
dN : online d N
eN... | Please generate a tactic in lean4 to solve the state.
STATE:
case neg.intro.intro
i : incidence_geometry
a b c d e f : point
L M : line
aM : online a M
bL : online b L
cL : online c L
dM : online d M
eL : online e L
fL : online f L
pLM : para L M
hlen : length b c = length e f
bc : ¬b = c
ef : e ≠ f
K : line
aK : onlin... |
https://github.com/ianjauslin-rutgers/pythagoras4.git | f97e5d2375d2e350b15d79e541520f8ba81600ec | Pythagoras/euclid_I_extras.lean | eq_area_of_eq_base | [339, 1] | [374, 11] | have aL := offline_of_para aM (para_symm pLM) | case neg.intro.intro.intro.intro
i : incidence_geometry
a b c d e f : point
L M : line
aM : online a M
bL : online b L
cL : online c L
dM : online d M
eL : online e L
fL : online f L
pLM : para L M
hlen : length b c = length e f
bc : ¬b = c
ef : e ≠ f
K : line
aK : online a K
cK : online c K
N : line
dN : online d N
eN... | case neg.intro.intro.intro.intro
i : incidence_geometry
a b c d e f : point
L M : line
aM : online a M
bL : online b L
cL : online c L
dM : online d M
eL : online e L
fL : online f L
pLM : para L M
hlen : length b c = length e f
bc : ¬b = c
ef : e ≠ f
K : line
aK : online a K
cK : online c K
N : line
dN : online d N
eN... | Please generate a tactic in lean4 to solve the state.
STATE:
case neg.intro.intro.intro.intro
i : incidence_geometry
a b c d e f : point
L M : line
aM : online a M
bL : online b L
cL : online c L
dM : online d M
eL : online e L
fL : online f L
pLM : para L M
hlen : length b c = length e f
bc : ¬b = c
ef : e ≠ f
K : lin... |
https://github.com/ianjauslin-rutgers/pythagoras4.git | f97e5d2375d2e350b15d79e541520f8ba81600ec | Pythagoras/euclid_I_extras.lean | eq_area_of_eq_base | [339, 1] | [374, 11] | have := not_online_of_triangle aK cK cL bL aL (fun cb => bc cb.symm) | case neg.intro.intro.intro.intro
i : incidence_geometry
a b c d e f : point
L M : line
aM : online a M
bL : online b L
cL : online c L
dM : online d M
eL : online e L
fL : online f L
pLM : para L M
hlen : length b c = length e f
bc : ¬b = c
ef : e ≠ f
K : line
aK : online a K
cK : online c K
N : line
dN : online d N
eN... | case neg.intro.intro.intro.intro
i : incidence_geometry
a b c d e f : point
L M : line
aM : online a M
bL : online b L
cL : online c L
dM : online d M
eL : online e L
fL : online f L
pLM : para L M
hlen : length b c = length e f
bc : ¬b = c
ef : e ≠ f
K : line
aK : online a K
cK : online c K
N : line
dN : online d N
eN... | Please generate a tactic in lean4 to solve the state.
STATE:
case neg.intro.intro.intro.intro
i : incidence_geometry
a b c d e f : point
L M : line
aM : online a M
bL : online b L
cL : online c L
dM : online d M
eL : online e L
fL : online f L
pLM : para L M
hlen : length b c = length e f
bc : ¬b = c
ef : e ≠ f
K : lin... |
https://github.com/ianjauslin-rutgers/pythagoras4.git | f97e5d2375d2e350b15d79e541520f8ba81600ec | Pythagoras/euclid_I_extras.lean | eq_area_of_eq_base | [339, 1] | [374, 11] | obtain ⟨ g, O, gM, hgO, bO, pKO ⟩ := parallel_projection bL pLM (not_para_of_online_online cK cL) this | case neg.intro.intro.intro.intro
i : incidence_geometry
a b c d e f : point
L M : line
aM : online a M
bL : online b L
cL : online c L
dM : online d M
eL : online e L
fL : online f L
pLM : para L M
hlen : length b c = length e f
bc : ¬b = c
ef : e ≠ f
K : line
aK : online a K
cK : online c K
N : line
dN : online d N
eN... | case neg.intro.intro.intro.intro.intro.intro.intro.intro.intro
i : incidence_geometry
a b c d e f : point
L M : line
aM : online a M
bL : online b L
cL : online c L
dM : online d M
eL : online e L
fL : online f L
pLM : para L M
hlen : length b c = length e f
bc : ¬b = c
ef : e ≠ f
K : line
aK : online a K
cK : online c... | Please generate a tactic in lean4 to solve the state.
STATE:
case neg.intro.intro.intro.intro
i : incidence_geometry
a b c d e f : point
L M : line
aM : online a M
bL : online b L
cL : online c L
dM : online d M
eL : online e L
fL : online f L
pLM : para L M
hlen : length b c = length e f
bc : ¬b = c
ef : e ≠ f
K : lin... |
https://github.com/ianjauslin-rutgers/pythagoras4.git | f97e5d2375d2e350b15d79e541520f8ba81600ec | Pythagoras/euclid_I_extras.lean | eq_area_of_eq_base | [339, 1] | [374, 11] | have dL := offline_of_para dM (para_symm pLM) | case neg.intro.intro.intro.intro.intro.intro.intro.intro.intro
i : incidence_geometry
a b c d e f : point
L M : line
aM : online a M
bL : online b L
cL : online c L
dM : online d M
eL : online e L
fL : online f L
pLM : para L M
hlen : length b c = length e f
bc : ¬b = c
ef : e ≠ f
K : line
aK : online a K
cK : online c... | case neg.intro.intro.intro.intro.intro.intro.intro.intro.intro
i : incidence_geometry
a b c d e f : point
L M : line
aM : online a M
bL : online b L
cL : online c L
dM : online d M
eL : online e L
fL : online f L
pLM : para L M
hlen : length b c = length e f
bc : ¬b = c
ef : e ≠ f
K : line
aK : online a K
cK : online c... | Please generate a tactic in lean4 to solve the state.
STATE:
case neg.intro.intro.intro.intro.intro.intro.intro.intro.intro
i : incidence_geometry
a b c d e f : point
L M : line
aM : online a M
bL : online b L
cL : online c L
dM : online d M
eL : online e L
fL : online f L
pLM : para L M
hlen : length b c = length e f
... |
https://github.com/ianjauslin-rutgers/pythagoras4.git | f97e5d2375d2e350b15d79e541520f8ba81600ec | Pythagoras/euclid_I_extras.lean | eq_area_of_eq_base | [339, 1] | [374, 11] | have := not_online_of_triangle dN eN eL fL dL ef | case neg.intro.intro.intro.intro.intro.intro.intro.intro.intro
i : incidence_geometry
a b c d e f : point
L M : line
aM : online a M
bL : online b L
cL : online c L
dM : online d M
eL : online e L
fL : online f L
pLM : para L M
hlen : length b c = length e f
bc : ¬b = c
ef : e ≠ f
K : line
aK : online a K
cK : online c... | case neg.intro.intro.intro.intro.intro.intro.intro.intro.intro
i : incidence_geometry
a b c d e f : point
L M : line
aM : online a M
bL : online b L
cL : online c L
dM : online d M
eL : online e L
fL : online f L
pLM : para L M
hlen : length b c = length e f
bc : ¬b = c
ef : e ≠ f
K : line
aK : online a K
cK : online c... | Please generate a tactic in lean4 to solve the state.
STATE:
case neg.intro.intro.intro.intro.intro.intro.intro.intro.intro
i : incidence_geometry
a b c d e f : point
L M : line
aM : online a M
bL : online b L
cL : online c L
dM : online d M
eL : online e L
fL : online f L
pLM : para L M
hlen : length b c = length e f
... |
https://github.com/ianjauslin-rutgers/pythagoras4.git | f97e5d2375d2e350b15d79e541520f8ba81600ec | Pythagoras/euclid_I_extras.lean | eq_area_of_eq_base | [339, 1] | [374, 11] | obtain ⟨ h, P, hhM, hP, hfP, pNP ⟩ := parallel_projection fL pLM (not_para_of_online_online eN eL) this | case neg.intro.intro.intro.intro.intro.intro.intro.intro.intro
i : incidence_geometry
a b c d e f : point
L M : line
aM : online a M
bL : online b L
cL : online c L
dM : online d M
eL : online e L
fL : online f L
pLM : para L M
hlen : length b c = length e f
bc : ¬b = c
ef : e ≠ f
K : line
aK : online a K
cK : online c... | case neg.intro.intro.intro.intro.intro.intro.intro.intro.intro.intro.intro.intro.intro.intro
i : incidence_geometry
a b c d e f : point
L M : line
aM : online a M
bL : online b L
cL : online c L
dM : online d M
eL : online e L
fL : online f L
pLM : para L M
hlen : length b c = length e f
bc : ¬b = c
ef : e ≠ f
K : line... | Please generate a tactic in lean4 to solve the state.
STATE:
case neg.intro.intro.intro.intro.intro.intro.intro.intro.intro
i : incidence_geometry
a b c d e f : point
L M : line
aM : online a M
bL : online b L
cL : online c L
dM : online d M
eL : online e L
fL : online f L
pLM : para L M
hlen : length b c = length e f
... |
https://github.com/ianjauslin-rutgers/pythagoras4.git | f97e5d2375d2e350b15d79e541520f8ba81600ec | Pythagoras/euclid_I_extras.lean | eq_area_of_eq_base | [339, 1] | [374, 11] | perm [eq_of_parallelogram_of_eq_basis gM aM dM hhM bL cL eL fL hgO bO aK cK dN eN hP hfP (by perma) (by perma) pNP hlen] | case neg.intro.intro.intro.intro.intro.intro.intro.intro.intro.intro.intro.intro.intro.intro
i : incidence_geometry
a b c d e f : point
L M : line
aM : online a M
bL : online b L
cL : online c L
dM : online d M
eL : online e L
fL : online f L
pLM : para L M
hlen : length b c = length e f
bc : ¬b = c
ef : e ≠ f
K : line... | case neg.intro.intro.intro.intro.intro.intro.intro.intro.intro.intro.intro.intro.intro.intro
i : incidence_geometry
a b c d e f : point
L M : line
aM : online a M
bL : online b L
cL : online c L
dM : online d M
eL : online e L
fL : online f L
pLM : para L M
hlen : length b c = length e f
bc : ¬b = c
ef : e ≠ f
K : line... | Please generate a tactic in lean4 to solve the state.
STATE:
case neg.intro.intro.intro.intro.intro.intro.intro.intro.intro.intro.intro.intro.intro.intro
i : incidence_geometry
a b c d e f : point
L M : line
aM : online a M
bL : online b L
cL : online c L
dM : online d M
eL : online e L
fL : online f L
pLM : para L M
h... |
https://github.com/ianjauslin-rutgers/pythagoras4.git | f97e5d2375d2e350b15d79e541520f8ba81600ec | Pythagoras/euclid_I_extras.lean | eq_area_of_eq_base | [339, 1] | [374, 11] | have bcag: paragram b c a g L K M O:= by splitAll <;> perma only [para] | case neg.intro.intro.intro.intro.intro.intro.intro.intro.intro.intro.intro.intro.intro.intro
i : incidence_geometry
a b c d e f : point
L M : line
aM : online a M
bL : online b L
cL : online c L
dM : online d M
eL : online e L
fL : online f L
pLM : para L M
hlen : length b c = length e f
bc : ¬b = c
ef : e ≠ f
K : line... | case neg.intro.intro.intro.intro.intro.intro.intro.intro.intro.intro.intro.intro.intro.intro
i : incidence_geometry
a b c d e f : point
L M : line
aM : online a M
bL : online b L
cL : online c L
dM : online d M
eL : online e L
fL : online f L
pLM : para L M
hlen : length b c = length e f
bc : ¬b = c
ef : e ≠ f
K : line... | Please generate a tactic in lean4 to solve the state.
STATE:
case neg.intro.intro.intro.intro.intro.intro.intro.intro.intro.intro.intro.intro.intro.intro
i : incidence_geometry
a b c d e f : point
L M : line
aM : online a M
bL : online b L
cL : online c L
dM : online d M
eL : online e L
fL : online f L
pLM : para L M
h... |
https://github.com/ianjauslin-rutgers/pythagoras4.git | f97e5d2375d2e350b15d79e541520f8ba81600ec | Pythagoras/euclid_I_extras.lean | eq_area_of_eq_base | [339, 1] | [374, 11] | have fedh: paragram f e d h L N M P:= by splitAll <;> perma only [para] | case neg.intro.intro.intro.intro.intro.intro.intro.intro.intro.intro.intro.intro.intro.intro
i : incidence_geometry
a b c d e f : point
L M : line
aM : online a M
bL : online b L
cL : online c L
dM : online d M
eL : online e L
fL : online f L
pLM : para L M
hlen : length b c = length e f
bc : ¬b = c
ef : e ≠ f
K : line... | case neg.intro.intro.intro.intro.intro.intro.intro.intro.intro.intro.intro.intro.intro.intro
i : incidence_geometry
a b c d e f : point
L M : line
aM : online a M
bL : online b L
cL : online c L
dM : online d M
eL : online e L
fL : online f L
pLM : para L M
hlen : length b c = length e f
bc : ¬b = c
ef : e ≠ f
K : line... | Please generate a tactic in lean4 to solve the state.
STATE:
case neg.intro.intro.intro.intro.intro.intro.intro.intro.intro.intro.intro.intro.intro.intro
i : incidence_geometry
a b c d e f : point
L M : line
aM : online a M
bL : online b L
cL : online c L
dM : online d M
eL : online e L
fL : online f L
pLM : para L M
h... |
https://github.com/ianjauslin-rutgers/pythagoras4.git | f97e5d2375d2e350b15d79e541520f8ba81600ec | Pythagoras/euclid_I_extras.lean | eq_area_of_eq_base | [339, 1] | [374, 11] | have: area b c g + area a c g = 2 * area a b c := by perma [(area_of_parallelogram bcag).2] | case neg.intro.intro.intro.intro.intro.intro.intro.intro.intro.intro.intro.intro.intro.intro
i : incidence_geometry
a b c d e f : point
L M : line
aM : online a M
bL : online b L
cL : online c L
dM : online d M
eL : online e L
fL : online f L
pLM : para L M
hlen : length b c = length e f
bc : ¬b = c
ef : e ≠ f
K : line... | case neg.intro.intro.intro.intro.intro.intro.intro.intro.intro.intro.intro.intro.intro.intro
i : incidence_geometry
a b c d e f : point
L M : line
aM : online a M
bL : online b L
cL : online c L
dM : online d M
eL : online e L
fL : online f L
pLM : para L M
hlen : length b c = length e f
bc : ¬b = c
ef : e ≠ f
K : line... | Please generate a tactic in lean4 to solve the state.
STATE:
case neg.intro.intro.intro.intro.intro.intro.intro.intro.intro.intro.intro.intro.intro.intro
i : incidence_geometry
a b c d e f : point
L M : line
aM : online a M
bL : online b L
cL : online c L
dM : online d M
eL : online e L
fL : online f L
pLM : para L M
h... |
https://github.com/ianjauslin-rutgers/pythagoras4.git | f97e5d2375d2e350b15d79e541520f8ba81600ec | Pythagoras/euclid_I_extras.lean | eq_area_of_eq_base | [339, 1] | [374, 11] | have: area d e f = area d f h := by linperm [(area_of_parallelogram fedh).1] | case neg.intro.intro.intro.intro.intro.intro.intro.intro.intro.intro.intro.intro.intro.intro
i : incidence_geometry
a b c d e f : point
L M : line
aM : online a M
bL : online b L
cL : online c L
dM : online d M
eL : online e L
fL : online f L
pLM : para L M
hlen : length b c = length e f
bc : ¬b = c
ef : e ≠ f
K : line... | case neg.intro.intro.intro.intro.intro.intro.intro.intro.intro.intro.intro.intro.intro.intro
i : incidence_geometry
a b c d e f : point
L M : line
aM : online a M
bL : online b L
cL : online c L
dM : online d M
eL : online e L
fL : online f L
pLM : para L M
hlen : length b c = length e f
bc : ¬b = c
ef : e ≠ f
K : line... | Please generate a tactic in lean4 to solve the state.
STATE:
case neg.intro.intro.intro.intro.intro.intro.intro.intro.intro.intro.intro.intro.intro.intro
i : incidence_geometry
a b c d e f : point
L M : line
aM : online a M
bL : online b L
cL : online c L
dM : online d M
eL : online e L
fL : online f L
pLM : para L M
h... |
https://github.com/ianjauslin-rutgers/pythagoras4.git | f97e5d2375d2e350b15d79e541520f8ba81600ec | Pythagoras/euclid_I_extras.lean | eq_area_of_eq_base | [339, 1] | [374, 11] | linarith | case neg.intro.intro.intro.intro.intro.intro.intro.intro.intro.intro.intro.intro.intro.intro
i : incidence_geometry
a b c d e f : point
L M : line
aM : online a M
bL : online b L
cL : online c L
dM : online d M
eL : online e L
fL : online f L
pLM : para L M
hlen : length b c = length e f
bc : ¬b = c
ef : e ≠ f
K : line... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case neg.intro.intro.intro.intro.intro.intro.intro.intro.intro.intro.intro.intro.intro.intro
i : incidence_geometry
a b c d e f : point
L M : line
aM : online a M
bL : online b L
cL : online c L
dM : online d M
eL : online e L
fL : online f L
pLM : para L M
h... |
https://github.com/ianjauslin-rutgers/pythagoras4.git | f97e5d2375d2e350b15d79e541520f8ba81600ec | Pythagoras/euclid_I_extras.lean | eq_area_of_eq_base | [339, 1] | [374, 11] | have ef: e = f := (same_len_pts_coincide_iff hlen).mp bc | case pos
i : incidence_geometry
a b c d e f : point
L M : line
aM : online a M
bL : online b L
cL : online c L
dM : online d M
eL : online e L
fL : online f L
pLM : para L M
hlen : length b c = length e f
bc : b = c
⊢ area a b c = area d e f | case pos
i : incidence_geometry
a b c d e f : point
L M : line
aM : online a M
bL : online b L
cL : online c L
dM : online d M
eL : online e L
fL : online f L
pLM : para L M
hlen : length b c = length e f
bc : b = c
ef : e = f
⊢ area a b c = area d e f | Please generate a tactic in lean4 to solve the state.
STATE:
case pos
i : incidence_geometry
a b c d e f : point
L M : line
aM : online a M
bL : online b L
cL : online c L
dM : online d M
eL : online e L
fL : online f L
pLM : para L M
hlen : length b c = length e f
bc : b = c
⊢ area a b c = area d e f
TACTIC:
|
https://github.com/ianjauslin-rutgers/pythagoras4.git | f97e5d2375d2e350b15d79e541520f8ba81600ec | Pythagoras/euclid_I_extras.lean | eq_area_of_eq_base | [339, 1] | [374, 11] | rw [area_of_eq a b c (by tauto), area_of_eq d e f (by tauto)] | case pos
i : incidence_geometry
a b c d e f : point
L M : line
aM : online a M
bL : online b L
cL : online c L
dM : online d M
eL : online e L
fL : online f L
pLM : para L M
hlen : length b c = length e f
bc : b = c
ef : e = f
⊢ area a b c = area d e f | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case pos
i : incidence_geometry
a b c d e f : point
L M : line
aM : online a M
bL : online b L
cL : online c L
dM : online d M
eL : online e L
fL : online f L
pLM : para L M
hlen : length b c = length e f
bc : b = c
ef : e = f
⊢ area a b c = area d e f
TACTIC... |
https://github.com/ianjauslin-rutgers/pythagoras4.git | f97e5d2375d2e350b15d79e541520f8ba81600ec | Pythagoras/euclid_I_extras.lean | eq_area_of_eq_base | [339, 1] | [374, 11] | tauto | i : incidence_geometry
a b c d e f : point
L M : line
aM : online a M
bL : online b L
cL : online c L
dM : online d M
eL : online e L
fL : online f L
pLM : para L M
hlen : length b c = length e f
bc : b = c
ef : e = f
⊢ a = b ∨ a = c ∨ b = c | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
i : incidence_geometry
a b c d e f : point
L M : line
aM : online a M
bL : online b L
cL : online c L
dM : online d M
eL : online e L
fL : online f L
pLM : para L M
hlen : length b c = length e f
bc : b = c
ef : e = f
⊢ a = b ∨ a = c ∨ b = c
TACTIC:
|
https://github.com/ianjauslin-rutgers/pythagoras4.git | f97e5d2375d2e350b15d79e541520f8ba81600ec | Pythagoras/euclid_I_extras.lean | eq_area_of_eq_base | [339, 1] | [374, 11] | tauto | i : incidence_geometry
a b c d e f : point
L M : line
aM : online a M
bL : online b L
cL : online c L
dM : online d M
eL : online e L
fL : online f L
pLM : para L M
hlen : length b c = length e f
bc : b = c
ef : e = f
⊢ d = e ∨ d = f ∨ e = f | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
i : incidence_geometry
a b c d e f : point
L M : line
aM : online a M
bL : online b L
cL : online c L
dM : online d M
eL : online e L
fL : online f L
pLM : para L M
hlen : length b c = length e f
bc : b = c
ef : e = f
⊢ d = e ∨ d = f ∨ e = f
TACTIC:
|
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.