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stringclasses 147
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stringclasses 147
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stringlengths 7
101
| full_name
stringlengths 1
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| start
stringlengths 6
10
| end
stringlengths 6
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stringlengths 1
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stringlengths 3
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https://github.com/aronerben/lean4-playground.git | 5efced915ecee24cd723d28d00aa63f9c7ea0a9c | meetings/ex1.lean | sqrt17 | [11, 1] | [25, 39] | exact Real.sq_sqrt (by norm_num) | case h.mpr.inr
x : ℝ
hneg : x = -Real.sqrt 17
⊢ Real.sqrt 17 ^ 2 = 17 | no goals |
https://github.com/aronerben/lean4-playground.git | 5efced915ecee24cd723d28d00aa63f9c7ea0a9c | meetings/ex1.lean | sqrt17 | [11, 1] | [25, 39] | norm_num | x : ℝ
hneg : x = -Real.sqrt 17
⊢ 0 ≤ 17 | no goals |
https://github.com/aronerben/lean4-playground.git | 5efced915ecee24cd723d28d00aa63f9c7ea0a9c | meetings/ex1.lean | lt24 | [29, 1] | [63, 13] | ext x | ⊢ {x | |3 * x| < 24} = {-7, -6, -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, 6, 7} | case h
x : ℤ
⊢ x ∈ {x | |3 * x| < 24} ↔ x ∈ {-7, -6, -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, 6, 7} |
https://github.com/aronerben/lean4-playground.git | 5efced915ecee24cd723d28d00aa63f9c7ea0a9c | meetings/ex1.lean | lt24 | [29, 1] | [63, 13] | constructor | case h
x : ℤ
⊢ x ∈ {x | |3 * x| < 24} ↔ x ∈ {-7, -6, -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, 6, 7} | case h.mp
x : ℤ
⊢ x ∈ {x | |3 * x| < 24} → x ∈ {-7, -6, -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, 6, 7}
case h.mpr
x : ℤ
⊢ x ∈ {-7, -6, -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, 6, 7} → x ∈ {x | |3 * x| < 24} |
https://github.com/aronerben/lean4-playground.git | 5efced915ecee24cd723d28d00aa63f9c7ea0a9c | meetings/ex1.lean | lt24 | [29, 1] | [63, 13] | intro hlt | case h.mp
x : ℤ
⊢ x ∈ {x | |3 * x| < 24} → x ∈ {-7, -6, -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, 6, 7} | case h.mp
x : ℤ
hlt : x ∈ {x | |3 * x| < 24}
⊢ x ∈ {-7, -6, -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, 6, 7} |
https://github.com/aronerben/lean4-playground.git | 5efced915ecee24cd723d28d00aa63f9c7ea0a9c | meetings/ex1.lean | lt24 | [29, 1] | [63, 13] | simp only [Set.mem_setOf_eq] at hlt | case h.mp
x : ℤ
hlt : x ∈ {x | |3 * x| < 24}
⊢ x ∈ {-7, -6, -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, 6, 7} | case h.mp
x : ℤ
hlt : |3 * x| < 24
⊢ x ∈ {-7, -6, -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, 6, 7} |
https://github.com/aronerben/lean4-playground.git | 5efced915ecee24cd723d28d00aa63f9c7ea0a9c | meetings/ex1.lean | lt24 | [29, 1] | [63, 13] | rw [abs_lt] at hlt | case h.mp
x : ℤ
hlt : |3 * x| < 24
⊢ x ∈ {-7, -6, -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, 6, 7} | case h.mp
x : ℤ
hlt : -24 < 3 * x ∧ 3 * x < 24
⊢ x ∈ {-7, -6, -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, 6, 7} |
https://github.com/aronerben/lean4-playground.git | 5efced915ecee24cd723d28d00aa63f9c7ea0a9c | meetings/ex1.lean | lt24 | [29, 1] | [63, 13] | rcases hlt with ⟨hlt, hlt'⟩ | case h.mp
x : ℤ
hlt : -24 < 3 * x ∧ 3 * x < 24
⊢ x ∈ {-7, -6, -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, 6, 7} | case h.mp.intro
x : ℤ
hlt : -24 < 3 * x
hlt' : 3 * x < 24
⊢ x ∈ {-7, -6, -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, 6, 7} |
https://github.com/aronerben/lean4-playground.git | 5efced915ecee24cd723d28d00aa63f9c7ea0a9c | meetings/ex1.lean | lt24 | [29, 1] | [63, 13] | simp only [Set.mem_singleton_iff, Set.mem_insert_iff, or_self] | case h.mp.intro
x : ℤ
hlt : -24 < 3 * x
hlt' : 3 * x < 24
⊢ x ∈ {-7, -6, -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, 6, 7} | case h.mp.intro
x : ℤ
hlt : -24 < 3 * x
hlt' : 3 * x < 24
⊢ x = -7 ∨
x = -6 ∨ x = -5 ∨ x = -4 ∨ x = -3 ∨ x = -2 ∨ x = -1 ∨ x = 0 ∨ x = 1 ∨ x = 2 ∨ x = 3 ∨ x = 4 ∨ x = 5 ∨ x = 6 ∨ x = 7 |
https://github.com/aronerben/lean4-playground.git | 5efced915ecee24cd723d28d00aa63f9c7ea0a9c | meetings/ex1.lean | lt24 | [29, 1] | [63, 13] | by_contra hne | case h.mp.intro
x : ℤ
hlt : -24 < 3 * x
hlt' : 3 * x < 24
⊢ x = -7 ∨
x = -6 ∨ x = -5 ∨ x = -4 ∨ x = -3 ∨ x = -2 ∨ x = -1 ∨ x = 0 ∨ x = 1 ∨ x = 2 ∨ x = 3 ∨ x = 4 ∨ x = 5 ∨ x = 6 ∨ x = 7 | case h.mp.intro
x : ℤ
hlt : -24 < 3 * x
hlt' : 3 * x < 24
hne :
¬(x = -7 ∨
x = -6 ∨
x = -5 ∨ x = -4 ∨ x = -3 ∨ x = -2 ∨ x = -1 ∨ x = 0 ∨ x = 1 ∨ x = 2 ∨ x = 3 ∨ x = 4 ∨ x = 5 ∨ x = 6 ∨ x = 7)
⊢ False |
https://github.com/aronerben/lean4-playground.git | 5efced915ecee24cd723d28d00aa63f9c7ea0a9c | meetings/ex1.lean | lt24 | [29, 1] | [63, 13] | repeat rw [not_or] at hne | case h.mp.intro
x : ℤ
hlt : -24 < 3 * x
hlt' : 3 * x < 24
hne :
¬(x = -7 ∨
x = -6 ∨
x = -5 ∨ x = -4 ∨ x = -3 ∨ x = -2 ∨ x = -1 ∨ x = 0 ∨ x = 1 ∨ x = 2 ∨ x = 3 ∨ x = 4 ∨ x = 5 ∨ x = 6 ∨ x = 7)
⊢ False | case h.mp.intro
x : ℤ
hlt : -24 < 3 * x
hlt' : 3 * x < 24
hne :
¬x = -7 ∧
¬x = -6 ∧
¬x = -5 ∧
¬x = -4 ∧ ¬x = -3 ∧ ¬x = -2 ∧ ¬x = -1 ∧ ¬x = 0 ∧ ¬x = 1 ∧ ¬x = 2 ∧ ¬x = 3 ∧ ¬x = 4 ∧ ¬x = 5 ∧ ¬x = 6 ∧ ¬x = 7
⊢ False |
https://github.com/aronerben/lean4-playground.git | 5efced915ecee24cd723d28d00aa63f9c7ea0a9c | meetings/ex1.lean | lt24 | [29, 1] | [63, 13] | rcases hne with ⟨m7, m6, m5, m4, m3, m2, m1, z, p1, p2, p3, p4, p5, p6, p7⟩ | case h.mp.intro
x : ℤ
hlt : -24 < 3 * x
hlt' : 3 * x < 24
hne :
¬x = -7 ∧
¬x = -6 ∧
¬x = -5 ∧
¬x = -4 ∧ ¬x = -3 ∧ ¬x = -2 ∧ ¬x = -1 ∧ ¬x = 0 ∧ ¬x = 1 ∧ ¬x = 2 ∧ ¬x = 3 ∧ ¬x = 4 ∧ ¬x = 5 ∧ ¬x = 6 ∧ ¬x = 7
⊢ False | case h.mp.intro.intro.intro.intro.intro.intro.intro.intro.intro.intro.intro.intro.intro.intro.intro
x : ℤ
hlt : -24 < 3 * x
hlt' : 3 * x < 24
m7 : ¬x = -7
m6 : ¬x = -6
m5 : ¬x = -5
m4 : ¬x = -4
m3 : ¬x = -3
m2 : ¬x = -2
m1 : ¬x = -1
z : ¬x = 0
p1 : ¬x = 1
p2 : ¬x = 2
p3 : ¬x = 3
p4 : ¬x = 4
p5 : ¬x = 5
p6 : ¬x = 6
p7 : ¬x = 7
⊢ False |
https://github.com/aronerben/lean4-playground.git | 5efced915ecee24cd723d28d00aa63f9c7ea0a9c | meetings/ex1.lean | lt24 | [29, 1] | [63, 13] | have threedvd : ((3 : ℤ) ∣ 24) := by
have : (24 : ℤ) = 3 * 8 := by ring_nf
rw [this]
simp only [dvd_mul_right] | case h.mp.intro.intro.intro.intro.intro.intro.intro.intro.intro.intro.intro.intro.intro.intro.intro
x : ℤ
hlt : -24 < 3 * x
hlt' : 3 * x < 24
m7 : ¬x = -7
m6 : ¬x = -6
m5 : ¬x = -5
m4 : ¬x = -4
m3 : ¬x = -3
m2 : ¬x = -2
m1 : ¬x = -1
z : ¬x = 0
p1 : ¬x = 1
p2 : ¬x = 2
p3 : ¬x = 3
p4 : ¬x = 4
p5 : ¬x = 5
p6 : ¬x = 6
p7 : ¬x = 7
⊢ False | case h.mp.intro.intro.intro.intro.intro.intro.intro.intro.intro.intro.intro.intro.intro.intro.intro
x : ℤ
hlt : -24 < 3 * x
hlt' : 3 * x < 24
m7 : ¬x = -7
m6 : ¬x = -6
m5 : ¬x = -5
m4 : ¬x = -4
m3 : ¬x = -3
m2 : ¬x = -2
m1 : ¬x = -1
z : ¬x = 0
p1 : ¬x = 1
p2 : ¬x = 2
p3 : ¬x = 3
p4 : ¬x = 4
p5 : ¬x = 5
p6 : ¬x = 6
p7 : ¬x = 7
threedvd : 3 ∣ 24
⊢ False |
https://github.com/aronerben/lean4-playground.git | 5efced915ecee24cd723d28d00aa63f9c7ea0a9c | meetings/ex1.lean | lt24 | [29, 1] | [63, 13] | rw [mul_comm, ←Int.lt_ediv_iff_mul_lt 3 (by simp) threedvd] at hlt' | case h.mp.intro.intro.intro.intro.intro.intro.intro.intro.intro.intro.intro.intro.intro.intro.intro
x : ℤ
hlt : -24 < 3 * x
hlt' : 3 * x < 24
m7 : ¬x = -7
m6 : ¬x = -6
m5 : ¬x = -5
m4 : ¬x = -4
m3 : ¬x = -3
m2 : ¬x = -2
m1 : ¬x = -1
z : ¬x = 0
p1 : ¬x = 1
p2 : ¬x = 2
p3 : ¬x = 3
p4 : ¬x = 4
p5 : ¬x = 5
p6 : ¬x = 6
p7 : ¬x = 7
threedvd : 3 ∣ 24
⊢ False | case h.mp.intro.intro.intro.intro.intro.intro.intro.intro.intro.intro.intro.intro.intro.intro.intro
x : ℤ
hlt : -24 < 3 * x
hlt' : x < 24 / 3
m7 : ¬x = -7
m6 : ¬x = -6
m5 : ¬x = -5
m4 : ¬x = -4
m3 : ¬x = -3
m2 : ¬x = -2
m1 : ¬x = -1
z : ¬x = 0
p1 : ¬x = 1
p2 : ¬x = 2
p3 : ¬x = 3
p4 : ¬x = 4
p5 : ¬x = 5
p6 : ¬x = 6
p7 : ¬x = 7
threedvd : 3 ∣ 24
⊢ False |
https://github.com/aronerben/lean4-playground.git | 5efced915ecee24cd723d28d00aa63f9c7ea0a9c | meetings/ex1.lean | lt24 | [29, 1] | [63, 13] | have lt8 : x < 8 := by
exact hlt' | case h.mp.intro.intro.intro.intro.intro.intro.intro.intro.intro.intro.intro.intro.intro.intro.intro
x : ℤ
hlt : -24 < 3 * x
hlt' : x < 24 / 3
m7 : ¬x = -7
m6 : ¬x = -6
m5 : ¬x = -5
m4 : ¬x = -4
m3 : ¬x = -3
m2 : ¬x = -2
m1 : ¬x = -1
z : ¬x = 0
p1 : ¬x = 1
p2 : ¬x = 2
p3 : ¬x = 3
p4 : ¬x = 4
p5 : ¬x = 5
p6 : ¬x = 6
p7 : ¬x = 7
threedvd : 3 ∣ 24
⊢ False | case h.mp.intro.intro.intro.intro.intro.intro.intro.intro.intro.intro.intro.intro.intro.intro.intro
x : ℤ
hlt : -24 < 3 * x
hlt' : x < 24 / 3
m7 : ¬x = -7
m6 : ¬x = -6
m5 : ¬x = -5
m4 : ¬x = -4
m3 : ¬x = -3
m2 : ¬x = -2
m1 : ¬x = -1
z : ¬x = 0
p1 : ¬x = 1
p2 : ¬x = 2
p3 : ¬x = 3
p4 : ¬x = 4
p5 : ¬x = 5
p6 : ¬x = 6
p7 : ¬x = 7
threedvd : 3 ∣ 24
lt8 : x < 8
⊢ False |
https://github.com/aronerben/lean4-playground.git | 5efced915ecee24cd723d28d00aa63f9c7ea0a9c | meetings/ex1.lean | lt24 | [29, 1] | [63, 13] | have gt8 : -8 < x := by
sorry | case h.mp.intro.intro.intro.intro.intro.intro.intro.intro.intro.intro.intro.intro.intro.intro.intro
x : ℤ
hlt : -24 < 3 * x
hlt' : x < 24 / 3
m7 : ¬x = -7
m6 : ¬x = -6
m5 : ¬x = -5
m4 : ¬x = -4
m3 : ¬x = -3
m2 : ¬x = -2
m1 : ¬x = -1
z : ¬x = 0
p1 : ¬x = 1
p2 : ¬x = 2
p3 : ¬x = 3
p4 : ¬x = 4
p5 : ¬x = 5
p6 : ¬x = 6
p7 : ¬x = 7
threedvd : 3 ∣ 24
lt8 : x < 8
⊢ False | case h.mp.intro.intro.intro.intro.intro.intro.intro.intro.intro.intro.intro.intro.intro.intro.intro
x : ℤ
hlt : -24 < 3 * x
hlt' : x < 24 / 3
m7 : ¬x = -7
m6 : ¬x = -6
m5 : ¬x = -5
m4 : ¬x = -4
m3 : ¬x = -3
m2 : ¬x = -2
m1 : ¬x = -1
z : ¬x = 0
p1 : ¬x = 1
p2 : ¬x = 2
p3 : ¬x = 3
p4 : ¬x = 4
p5 : ¬x = 5
p6 : ¬x = 6
p7 : ¬x = 7
threedvd : 3 ∣ 24
lt8 : x < 8
gt8 : -8 < x
⊢ False |
https://github.com/aronerben/lean4-playground.git | 5efced915ecee24cd723d28d00aa63f9c7ea0a9c | meetings/ex1.lean | lt24 | [29, 1] | [63, 13] | sorry | case h.mp.intro.intro.intro.intro.intro.intro.intro.intro.intro.intro.intro.intro.intro.intro.intro
x : ℤ
hlt : -24 < 3 * x
hlt' : x < 24 / 3
m7 : ¬x = -7
m6 : ¬x = -6
m5 : ¬x = -5
m4 : ¬x = -4
m3 : ¬x = -3
m2 : ¬x = -2
m1 : ¬x = -1
z : ¬x = 0
p1 : ¬x = 1
p2 : ¬x = 2
p3 : ¬x = 3
p4 : ¬x = 4
p5 : ¬x = 5
p6 : ¬x = 6
p7 : ¬x = 7
threedvd : 3 ∣ 24
lt8 : x < 8
gt8 : -8 < x
⊢ False | no goals |
https://github.com/aronerben/lean4-playground.git | 5efced915ecee24cd723d28d00aa63f9c7ea0a9c | meetings/ex1.lean | lt24 | [29, 1] | [63, 13] | rw [not_or] at hne | case h.mp.intro
x : ℤ
hlt : -24 < 3 * x
hlt' : 3 * x < 24
hne :
¬x = -7 ∧
¬x = -6 ∧
¬x = -5 ∧
¬x = -4 ∧ ¬x = -3 ∧ ¬x = -2 ∧ ¬x = -1 ∧ ¬x = 0 ∧ ¬x = 1 ∧ ¬x = 2 ∧ ¬x = 3 ∧ ¬x = 4 ∧ ¬x = 5 ∧ ¬(x = 6 ∨ x = 7)
⊢ False | case h.mp.intro
x : ℤ
hlt : -24 < 3 * x
hlt' : 3 * x < 24
hne :
¬x = -7 ∧
¬x = -6 ∧
¬x = -5 ∧
¬x = -4 ∧ ¬x = -3 ∧ ¬x = -2 ∧ ¬x = -1 ∧ ¬x = 0 ∧ ¬x = 1 ∧ ¬x = 2 ∧ ¬x = 3 ∧ ¬x = 4 ∧ ¬x = 5 ∧ ¬x = 6 ∧ ¬x = 7
⊢ False |
https://github.com/aronerben/lean4-playground.git | 5efced915ecee24cd723d28d00aa63f9c7ea0a9c | meetings/ex1.lean | lt24 | [29, 1] | [63, 13] | have : (24 : ℤ) = 3 * 8 := by ring_nf | x : ℤ
hlt : -24 < 3 * x
hlt' : 3 * x < 24
m7 : ¬x = -7
m6 : ¬x = -6
m5 : ¬x = -5
m4 : ¬x = -4
m3 : ¬x = -3
m2 : ¬x = -2
m1 : ¬x = -1
z : ¬x = 0
p1 : ¬x = 1
p2 : ¬x = 2
p3 : ¬x = 3
p4 : ¬x = 4
p5 : ¬x = 5
p6 : ¬x = 6
p7 : ¬x = 7
⊢ 3 ∣ 24 | x : ℤ
hlt : -24 < 3 * x
hlt' : 3 * x < 24
m7 : ¬x = -7
m6 : ¬x = -6
m5 : ¬x = -5
m4 : ¬x = -4
m3 : ¬x = -3
m2 : ¬x = -2
m1 : ¬x = -1
z : ¬x = 0
p1 : ¬x = 1
p2 : ¬x = 2
p3 : ¬x = 3
p4 : ¬x = 4
p5 : ¬x = 5
p6 : ¬x = 6
p7 : ¬x = 7
this : 24 = 3 * 8
⊢ 3 ∣ 24 |
https://github.com/aronerben/lean4-playground.git | 5efced915ecee24cd723d28d00aa63f9c7ea0a9c | meetings/ex1.lean | lt24 | [29, 1] | [63, 13] | rw [this] | x : ℤ
hlt : -24 < 3 * x
hlt' : 3 * x < 24
m7 : ¬x = -7
m6 : ¬x = -6
m5 : ¬x = -5
m4 : ¬x = -4
m3 : ¬x = -3
m2 : ¬x = -2
m1 : ¬x = -1
z : ¬x = 0
p1 : ¬x = 1
p2 : ¬x = 2
p3 : ¬x = 3
p4 : ¬x = 4
p5 : ¬x = 5
p6 : ¬x = 6
p7 : ¬x = 7
this : 24 = 3 * 8
⊢ 3 ∣ 24 | x : ℤ
hlt : -24 < 3 * x
hlt' : 3 * x < 24
m7 : ¬x = -7
m6 : ¬x = -6
m5 : ¬x = -5
m4 : ¬x = -4
m3 : ¬x = -3
m2 : ¬x = -2
m1 : ¬x = -1
z : ¬x = 0
p1 : ¬x = 1
p2 : ¬x = 2
p3 : ¬x = 3
p4 : ¬x = 4
p5 : ¬x = 5
p6 : ¬x = 6
p7 : ¬x = 7
this : 24 = 3 * 8
⊢ 3 ∣ 3 * 8 |
https://github.com/aronerben/lean4-playground.git | 5efced915ecee24cd723d28d00aa63f9c7ea0a9c | meetings/ex1.lean | lt24 | [29, 1] | [63, 13] | simp only [dvd_mul_right] | x : ℤ
hlt : -24 < 3 * x
hlt' : 3 * x < 24
m7 : ¬x = -7
m6 : ¬x = -6
m5 : ¬x = -5
m4 : ¬x = -4
m3 : ¬x = -3
m2 : ¬x = -2
m1 : ¬x = -1
z : ¬x = 0
p1 : ¬x = 1
p2 : ¬x = 2
p3 : ¬x = 3
p4 : ¬x = 4
p5 : ¬x = 5
p6 : ¬x = 6
p7 : ¬x = 7
this : 24 = 3 * 8
⊢ 3 ∣ 3 * 8 | no goals |
https://github.com/aronerben/lean4-playground.git | 5efced915ecee24cd723d28d00aa63f9c7ea0a9c | meetings/ex1.lean | lt24 | [29, 1] | [63, 13] | ring_nf | x : ℤ
hlt : -24 < 3 * x
hlt' : 3 * x < 24
m7 : ¬x = -7
m6 : ¬x = -6
m5 : ¬x = -5
m4 : ¬x = -4
m3 : ¬x = -3
m2 : ¬x = -2
m1 : ¬x = -1
z : ¬x = 0
p1 : ¬x = 1
p2 : ¬x = 2
p3 : ¬x = 3
p4 : ¬x = 4
p5 : ¬x = 5
p6 : ¬x = 6
p7 : ¬x = 7
⊢ 24 = 3 * 8 | no goals |
https://github.com/aronerben/lean4-playground.git | 5efced915ecee24cd723d28d00aa63f9c7ea0a9c | meetings/ex1.lean | lt24 | [29, 1] | [63, 13] | simp | x : ℤ
hlt : -24 < 3 * x
hlt' : x * 3 < 24
m7 : ¬x = -7
m6 : ¬x = -6
m5 : ¬x = -5
m4 : ¬x = -4
m3 : ¬x = -3
m2 : ¬x = -2
m1 : ¬x = -1
z : ¬x = 0
p1 : ¬x = 1
p2 : ¬x = 2
p3 : ¬x = 3
p4 : ¬x = 4
p5 : ¬x = 5
p6 : ¬x = 6
p7 : ¬x = 7
threedvd : 3 ∣ 24
⊢ 0 < 3 | no goals |
https://github.com/aronerben/lean4-playground.git | 5efced915ecee24cd723d28d00aa63f9c7ea0a9c | meetings/ex1.lean | lt24 | [29, 1] | [63, 13] | exact hlt' | x : ℤ
hlt : -24 < 3 * x
hlt' : x < 24 / 3
m7 : ¬x = -7
m6 : ¬x = -6
m5 : ¬x = -5
m4 : ¬x = -4
m3 : ¬x = -3
m2 : ¬x = -2
m1 : ¬x = -1
z : ¬x = 0
p1 : ¬x = 1
p2 : ¬x = 2
p3 : ¬x = 3
p4 : ¬x = 4
p5 : ¬x = 5
p6 : ¬x = 6
p7 : ¬x = 7
threedvd : 3 ∣ 24
⊢ x < 8 | no goals |
https://github.com/aronerben/lean4-playground.git | 5efced915ecee24cd723d28d00aa63f9c7ea0a9c | meetings/ex1.lean | lt24 | [29, 1] | [63, 13] | sorry | x : ℤ
hlt : -24 < 3 * x
hlt' : x < 24 / 3
m7 : ¬x = -7
m6 : ¬x = -6
m5 : ¬x = -5
m4 : ¬x = -4
m3 : ¬x = -3
m2 : ¬x = -2
m1 : ¬x = -1
z : ¬x = 0
p1 : ¬x = 1
p2 : ¬x = 2
p3 : ¬x = 3
p4 : ¬x = 4
p5 : ¬x = 5
p6 : ¬x = 6
p7 : ¬x = 7
threedvd : 3 ∣ 24
lt8 : x < 8
⊢ -8 < x | no goals |
https://github.com/aronerben/lean4-playground.git | 5efced915ecee24cd723d28d00aa63f9c7ea0a9c | meetings/ex1.lean | lt24 | [29, 1] | [63, 13] | intro hor | case h.mpr
x : ℤ
⊢ x ∈ {-7, -6, -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, 6, 7} → x ∈ {x | |3 * x| < 24} | case h.mpr
x : ℤ
hor : x ∈ {-7, -6, -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, 6, 7}
⊢ x ∈ {x | |3 * x| < 24} |
https://github.com/aronerben/lean4-playground.git | 5efced915ecee24cd723d28d00aa63f9c7ea0a9c | meetings/ex1.lean | lt24 | [29, 1] | [63, 13] | simp only [Set.mem_singleton_iff, Set.mem_insert_iff, or_self] at hor | case h.mpr
x : ℤ
hor : x ∈ {-7, -6, -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, 6, 7}
⊢ x ∈ {x | |3 * x| < 24} | case h.mpr
x : ℤ
hor :
x = -7 ∨
x = -6 ∨ x = -5 ∨ x = -4 ∨ x = -3 ∨ x = -2 ∨ x = -1 ∨ x = 0 ∨ x = 1 ∨ x = 2 ∨ x = 3 ∨ x = 4 ∨ x = 5 ∨ x = 6 ∨ x = 7
⊢ x ∈ {x | |3 * x| < 24} |
https://github.com/aronerben/lean4-playground.git | 5efced915ecee24cd723d28d00aa63f9c7ea0a9c | meetings/ex1.lean | lt24 | [29, 1] | [63, 13] | simp only [Set.mem_setOf_eq] | case h.mpr
x : ℤ
hor :
x = -7 ∨
x = -6 ∨ x = -5 ∨ x = -4 ∨ x = -3 ∨ x = -2 ∨ x = -1 ∨ x = 0 ∨ x = 1 ∨ x = 2 ∨ x = 3 ∨ x = 4 ∨ x = 5 ∨ x = 6 ∨ x = 7
⊢ x ∈ {x | |3 * x| < 24} | case h.mpr
x : ℤ
hor :
x = -7 ∨
x = -6 ∨ x = -5 ∨ x = -4 ∨ x = -3 ∨ x = -2 ∨ x = -1 ∨ x = 0 ∨ x = 1 ∨ x = 2 ∨ x = 3 ∨ x = 4 ∨ x = 5 ∨ x = 6 ∨ x = 7
⊢ |3 * x| < 24 |
https://github.com/aronerben/lean4-playground.git | 5efced915ecee24cd723d28d00aa63f9c7ea0a9c | meetings/ex1.lean | lt24 | [29, 1] | [63, 13] | rcases hor with (rfl | rfl | rfl | rfl | rfl | rfl | rfl | rfl | rfl | rfl | rfl | rfl | rfl | rfl | rfl | rfl) | case h.mpr
x : ℤ
hor :
x = -7 ∨
x = -6 ∨ x = -5 ∨ x = -4 ∨ x = -3 ∨ x = -2 ∨ x = -1 ∨ x = 0 ∨ x = 1 ∨ x = 2 ∨ x = 3 ∨ x = 4 ∨ x = 5 ∨ x = 6 ∨ x = 7
⊢ |3 * x| < 24 | case h.mpr.inl
⊢ |3 * -7| < 24
case h.mpr.inr.inl
⊢ |3 * -6| < 24
case h.mpr.inr.inr.inl
⊢ |3 * -5| < 24
case h.mpr.inr.inr.inr.inl
⊢ |3 * -4| < 24
case h.mpr.inr.inr.inr.inr.inl
⊢ |3 * -3| < 24
case h.mpr.inr.inr.inr.inr.inr.inl
⊢ |3 * -2| < 24
case h.mpr.inr.inr.inr.inr.inr.inr.inl
⊢ |3 * -1| < 24
case h.mpr.inr.inr.inr.inr.inr.inr.inr.inl
⊢ |3 * 0| < 24
case h.mpr.inr.inr.inr.inr.inr.inr.inr.inr.inl
⊢ |3 * 1| < 24
case h.mpr.inr.inr.inr.inr.inr.inr.inr.inr.inr.inl
⊢ |3 * 2| < 24
case h.mpr.inr.inr.inr.inr.inr.inr.inr.inr.inr.inr.inl
⊢ |3 * 3| < 24
case h.mpr.inr.inr.inr.inr.inr.inr.inr.inr.inr.inr.inr.inl
⊢ |3 * 4| < 24
case h.mpr.inr.inr.inr.inr.inr.inr.inr.inr.inr.inr.inr.inr.inl
⊢ |3 * 5| < 24
case h.mpr.inr.inr.inr.inr.inr.inr.inr.inr.inr.inr.inr.inr.inr.inl
⊢ |3 * 6| < 24
case h.mpr.inr.inr.inr.inr.inr.inr.inr.inr.inr.inr.inr.inr.inr.inr.refl
⊢ |3 * 7| < 24 |
https://github.com/aronerben/lean4-playground.git | 5efced915ecee24cd723d28d00aa63f9c7ea0a9c | meetings/ex1.lean | lt24 | [29, 1] | [63, 13] | ring_nf | case h.mpr.inr.inr.inr.inr.inr.inr.inr.inr.inr.inr.inr.inr.inr.inr.refl
⊢ |3 * 7| < 24 | case h.mpr.inr.inr.inr.inr.inr.inr.inr.inr.inr.inr.inr.inr.inr.inr.refl
⊢ |21| < 24 |
https://github.com/aronerben/lean4-playground.git | 5efced915ecee24cd723d28d00aa63f9c7ea0a9c | meetings/ex1.lean | lt24 | [29, 1] | [63, 13] | simp only [abs_neg, abs_lt] | case h.mpr.inr.inr.inr.inr.inr.inr.inr.inr.inr.inr.inr.inr.inr.inr.refl
⊢ |21| < 24 | case h.mpr.inr.inr.inr.inr.inr.inr.inr.inr.inr.inr.inr.inr.inr.inr.refl
⊢ -24 < 21 ∧ 21 < 24 |
https://github.com/aronerben/lean4-playground.git | 5efced915ecee24cd723d28d00aa63f9c7ea0a9c | meetings/ex1.lean | lt24 | [29, 1] | [63, 13] | constructor | case h.mpr.inr.inr.inr.inr.inr.inr.inr.inr.inr.inr.inr.inr.inr.inr.refl
⊢ -24 < 21 ∧ 21 < 24 | case h.mpr.inr.inr.inr.inr.inr.inr.inr.inr.inr.inr.inr.inr.inr.inr.refl.left
⊢ -24 < 21
case h.mpr.inr.inr.inr.inr.inr.inr.inr.inr.inr.inr.inr.inr.inr.inr.refl.right
⊢ 21 < 24 |
https://github.com/aronerben/lean4-playground.git | 5efced915ecee24cd723d28d00aa63f9c7ea0a9c | meetings/ex1.lean | lt24 | [29, 1] | [63, 13] | norm_num | case h.mpr.inr.inr.inr.inr.inr.inr.inr.inr.inr.inr.inr.inr.inr.inr.refl.left
⊢ -24 < 21 | no goals |
https://github.com/aronerben/lean4-playground.git | 5efced915ecee24cd723d28d00aa63f9c7ea0a9c | meetings/ex1.lean | lt24 | [29, 1] | [63, 13] | norm_num | case h.mpr.inr.inr.inr.inr.inr.inr.inr.inr.inr.inr.inr.inr.inr.inr.refl.right
⊢ 21 < 24 | no goals |
https://github.com/aronerben/lean4-playground.git | 5efced915ecee24cd723d28d00aa63f9c7ea0a9c | meetings/ex1.lean | circle_area_subset_square_area | [70, 1] | [82, 41] | intros p hmem | ⊢ {p | p.1 ^ 2 + p.2 ^ 2 < 1} ⊆ Set.Icc (-1) 1 ×ˢ Set.Icc (-1) 1 | p : ℝ × ℝ
hmem : p ∈ {p | p.1 ^ 2 + p.2 ^ 2 < 1}
⊢ p ∈ Set.Icc (-1) 1 ×ˢ Set.Icc (-1) 1 |
https://github.com/aronerben/lean4-playground.git | 5efced915ecee24cd723d28d00aa63f9c7ea0a9c | meetings/ex1.lean | circle_area_subset_square_area | [70, 1] | [82, 41] | simp at * | p : ℝ × ℝ
hmem : p ∈ {p | p.1 ^ 2 + p.2 ^ 2 < 1}
⊢ p ∈ Set.Icc (-1) 1 ×ˢ Set.Icc (-1) 1 | p : ℝ × ℝ
hmem : p.1 ^ 2 + p.2 ^ 2 < 1
⊢ (-1, -1) ≤ p ∧ p ≤ (1, 1) |
https://github.com/aronerben/lean4-playground.git | 5efced915ecee24cd723d28d00aa63f9c7ea0a9c | meetings/ex1.lean | circle_area_subset_square_area | [70, 1] | [82, 41] | simp only [sq_le_one_iff_abs_le_one, abs_le] at h | p : ℝ × ℝ
hmem : p.1 ^ 2 + p.2 ^ 2 < 1
h : p.1 ^ 2 ≤ 1 ∧ p.2 ^ 2 ≤ 1
⊢ (-1, -1) ≤ p ∧ p ≤ (1, 1) | p : ℝ × ℝ
hmem : p.1 ^ 2 + p.2 ^ 2 < 1
h : (-1 ≤ p.1 ∧ p.1 ≤ 1) ∧ -1 ≤ p.2 ∧ p.2 ≤ 1
⊢ (-1, -1) ≤ p ∧ p ≤ (1, 1) |
https://github.com/aronerben/lean4-playground.git | 5efced915ecee24cd723d28d00aa63f9c7ea0a9c | meetings/ex1.lean | circle_area_subset_square_area | [70, 1] | [82, 41] | exact ⟨⟨h.1.1, h.2.1⟩, ⟨h.1.2, h.2.2⟩⟩ | p : ℝ × ℝ
hmem : p.1 ^ 2 + p.2 ^ 2 < 1
h : (-1 ≤ p.1 ∧ p.1 ≤ 1) ∧ -1 ≤ p.2 ∧ p.2 ≤ 1
⊢ (-1, -1) ≤ p ∧ p ≤ (1, 1) | no goals |
https://github.com/aronerben/lean4-playground.git | 5efced915ecee24cd723d28d00aa63f9c7ea0a9c | meetings/ex1.lean | circle_area_subset_square_area | [70, 1] | [82, 41] | have p1nonneg := sq_nonneg (p.1) | p : ℝ × ℝ
hmem : p.1 ^ 2 + p.2 ^ 2 < 1
⊢ p.1 ^ 2 ≤ 1 ∧ p.2 ^ 2 ≤ 1 | p : ℝ × ℝ
hmem : p.1 ^ 2 + p.2 ^ 2 < 1
p1nonneg : 0 ≤ p.1 ^ 2
⊢ p.1 ^ 2 ≤ 1 ∧ p.2 ^ 2 ≤ 1 |
https://github.com/aronerben/lean4-playground.git | 5efced915ecee24cd723d28d00aa63f9c7ea0a9c | meetings/ex1.lean | circle_area_subset_square_area | [70, 1] | [82, 41] | have p2nonneg := sq_nonneg (p.2) | p : ℝ × ℝ
hmem : p.1 ^ 2 + p.2 ^ 2 < 1
p1nonneg : 0 ≤ p.1 ^ 2
⊢ p.1 ^ 2 ≤ 1 ∧ p.2 ^ 2 ≤ 1 | p : ℝ × ℝ
hmem : p.1 ^ 2 + p.2 ^ 2 < 1
p1nonneg : 0 ≤ p.1 ^ 2
p2nonneg : 0 ≤ p.2 ^ 2
⊢ p.1 ^ 2 ≤ 1 ∧ p.2 ^ 2 ≤ 1 |
https://github.com/aronerben/lean4-playground.git | 5efced915ecee24cd723d28d00aa63f9c7ea0a9c | meetings/ex1.lean | circle_area_subset_square_area | [70, 1] | [82, 41] | constructor | p : ℝ × ℝ
hmem : p.1 ^ 2 + p.2 ^ 2 < 1
p1nonneg : 0 ≤ p.1 ^ 2
p2nonneg : 0 ≤ p.2 ^ 2
⊢ p.1 ^ 2 ≤ 1 ∧ p.2 ^ 2 ≤ 1 | case left
p : ℝ × ℝ
hmem : p.1 ^ 2 + p.2 ^ 2 < 1
p1nonneg : 0 ≤ p.1 ^ 2
p2nonneg : 0 ≤ p.2 ^ 2
⊢ p.1 ^ 2 ≤ 1
case right
p : ℝ × ℝ
hmem : p.1 ^ 2 + p.2 ^ 2 < 1
p1nonneg : 0 ≤ p.1 ^ 2
p2nonneg : 0 ≤ p.2 ^ 2
⊢ p.2 ^ 2 ≤ 1 |
https://github.com/aronerben/lean4-playground.git | 5efced915ecee24cd723d28d00aa63f9c7ea0a9c | meetings/ex1.lean | circle_area_subset_square_area | [70, 1] | [82, 41] | linarith | case left
p : ℝ × ℝ
hmem : p.1 ^ 2 + p.2 ^ 2 < 1
p1nonneg : 0 ≤ p.1 ^ 2
p2nonneg : 0 ≤ p.2 ^ 2
⊢ p.1 ^ 2 ≤ 1 | no goals |
https://github.com/aronerben/lean4-playground.git | 5efced915ecee24cd723d28d00aa63f9c7ea0a9c | meetings/ex1.lean | circle_area_subset_square_area | [70, 1] | [82, 41] | linarith | case right
p : ℝ × ℝ
hmem : p.1 ^ 2 + p.2 ^ 2 < 1
p1nonneg : 0 ≤ p.1 ^ 2
p2nonneg : 0 ≤ p.2 ^ 2
⊢ p.2 ^ 2 ≤ 1 | no goals |
https://github.com/aronerben/lean4-playground.git | 5efced915ecee24cd723d28d00aa63f9c7ea0a9c | meetings/ex1.lean | square_area_not_subset_circle_area | [85, 1] | [94, 11] | intro sub | ⊢ ¬Set.Icc (-1) 1 ×ˢ Set.Icc (-1) 1 ⊆ {p | p.1 ^ 2 + p.2 ^ 2 < 1} | sub : Set.Icc (-1) 1 ×ˢ Set.Icc (-1) 1 ⊆ {p | p.1 ^ 2 + p.2 ^ 2 < 1}
⊢ False |
https://github.com/aronerben/lean4-playground.git | 5efced915ecee24cd723d28d00aa63f9c7ea0a9c | meetings/ex1.lean | square_area_not_subset_circle_area | [85, 1] | [94, 11] | simp at * | sub : Set.Icc (-1) 1 ×ˢ Set.Icc (-1) 1 ⊆ {p | p.1 ^ 2 + p.2 ^ 2 < 1}
⊢ False | sub : Set.Icc (-1, -1) (1, 1) ⊆ {p | p.1 ^ 2 + p.2 ^ 2 < 1}
⊢ False |
https://github.com/aronerben/lean4-playground.git | 5efced915ecee24cd723d28d00aa63f9c7ea0a9c | meetings/ex1.lean | square_area_not_subset_circle_area | [85, 1] | [94, 11] | have hel : ((-1, -1) : ℝ × ℝ) ∈ Set.Icc (-1, -1) (1, 1) := by
simp | sub : Set.Icc (-1, -1) (1, 1) ⊆ {p | p.1 ^ 2 + p.2 ^ 2 < 1}
⊢ False | sub : Set.Icc (-1, -1) (1, 1) ⊆ {p | p.1 ^ 2 + p.2 ^ 2 < 1}
hel : (-1, -1) ∈ Set.Icc (-1, -1) (1, 1)
⊢ False |
https://github.com/aronerben/lean4-playground.git | 5efced915ecee24cd723d28d00aa63f9c7ea0a9c | meetings/ex1.lean | square_area_not_subset_circle_area | [85, 1] | [94, 11] | specialize sub hel | sub : Set.Icc (-1, -1) (1, 1) ⊆ {p | p.1 ^ 2 + p.2 ^ 2 < 1}
hel : (-1, -1) ∈ Set.Icc (-1, -1) (1, 1)
⊢ False | hel : (-1, -1) ∈ Set.Icc (-1, -1) (1, 1)
sub : (-1, -1) ∈ {p | p.1 ^ 2 + p.2 ^ 2 < 1}
⊢ False |
https://github.com/aronerben/lean4-playground.git | 5efced915ecee24cd723d28d00aa63f9c7ea0a9c | meetings/ex1.lean | square_area_not_subset_circle_area | [85, 1] | [94, 11] | simp at sub | hel : (-1, -1) ∈ Set.Icc (-1, -1) (1, 1)
sub : (-1, -1) ∈ {p | p.1 ^ 2 + p.2 ^ 2 < 1}
⊢ False | hel : (-1, -1) ∈ Set.Icc (-1, -1) (1, 1)
sub : 1 < 0
⊢ False |
https://github.com/aronerben/lean4-playground.git | 5efced915ecee24cd723d28d00aa63f9c7ea0a9c | meetings/ex1.lean | square_area_not_subset_circle_area | [85, 1] | [94, 11] | linarith | hel : (-1, -1) ∈ Set.Icc (-1, -1) (1, 1)
sub : 1 < 0
⊢ False | no goals |
https://github.com/aronerben/lean4-playground.git | 5efced915ecee24cd723d28d00aa63f9c7ea0a9c | meetings/ex1.lean | square_area_not_subset_circle_area | [85, 1] | [94, 11] | simp | sub : Set.Icc (-1, -1) (1, 1) ⊆ {p | p.1 ^ 2 + p.2 ^ 2 < 1}
⊢ (-1, -1) ∈ Set.Icc (-1, -1) (1, 1) | no goals |
https://github.com/aronerben/lean4-playground.git | 5efced915ecee24cd723d28d00aa63f9c7ea0a9c | meetings/ex1.lean | nat_subset_real | [108, 1] | [112, 27] | intro n _ | ⊢ heterogeneous_subset Set.univ Set.univ | n : ℕ
a✝ : n ∈ Set.univ
⊢ Coe.coe n ∈ Set.univ |
https://github.com/aronerben/lean4-playground.git | 5efced915ecee24cd723d28d00aa63f9c7ea0a9c | meetings/ex1.lean | nat_subset_real | [108, 1] | [112, 27] | simp only [Set.mem_univ] | n : ℕ
a✝ : n ∈ Set.univ
⊢ Coe.coe n ∈ Set.univ | no goals |
https://github.com/aronerben/lean4-playground.git | 5efced915ecee24cd723d28d00aa63f9c7ea0a9c | meetings/ex1.lean | union_even_up_to | [119, 1] | [131, 18] | simp | ⊢ ⋃ j ∈ Set.univ, even_up_to j = {m | Even m} | ⊢ ⋃ j, even_up_to j = {m | Even m} |
https://github.com/aronerben/lean4-playground.git | 5efced915ecee24cd723d28d00aa63f9c7ea0a9c | meetings/ex1.lean | union_even_up_to | [119, 1] | [131, 18] | simp_rw [even_up_to, Set.ext_iff] | ⊢ ⋃ j, even_up_to j = {m | Even m} | ⊢ ∀ (x : ℕ), x ∈ ⋃ j, {m | m ≤ 2 * j ∧ Even m} ↔ x ∈ {m | Even m} |
https://github.com/aronerben/lean4-playground.git | 5efced915ecee24cd723d28d00aa63f9c7ea0a9c | meetings/ex1.lean | union_even_up_to | [119, 1] | [131, 18] | intro x | ⊢ ∀ (x : ℕ), x ∈ ⋃ j, {m | m ≤ 2 * j ∧ Even m} ↔ x ∈ {m | Even m} | x : ℕ
⊢ x ∈ ⋃ j, {m | m ≤ 2 * j ∧ Even m} ↔ x ∈ {m | Even m} |
https://github.com/aronerben/lean4-playground.git | 5efced915ecee24cd723d28d00aa63f9c7ea0a9c | meetings/ex1.lean | union_even_up_to | [119, 1] | [131, 18] | constructor | x : ℕ
⊢ x ∈ ⋃ j, {m | m ≤ 2 * j ∧ Even m} ↔ x ∈ {m | Even m} | case mp
x : ℕ
⊢ x ∈ ⋃ j, {m | m ≤ 2 * j ∧ Even m} → x ∈ {m | Even m}
case mpr
x : ℕ
⊢ x ∈ {m | Even m} → x ∈ ⋃ j, {m | m ≤ 2 * j ∧ Even m} |
https://github.com/aronerben/lean4-playground.git | 5efced915ecee24cd723d28d00aa63f9c7ea0a9c | meetings/ex1.lean | union_even_up_to | [119, 1] | [131, 18] | simp | case mp
x : ℕ
⊢ x ∈ ⋃ j, {m | m ≤ 2 * j ∧ Even m} → x ∈ {m | Even m} | no goals |
https://github.com/aronerben/lean4-playground.git | 5efced915ecee24cd723d28d00aa63f9c7ea0a9c | meetings/ex1.lean | union_even_up_to | [119, 1] | [131, 18] | simp | case mpr
x : ℕ
⊢ x ∈ {m | Even m} → x ∈ ⋃ j, {m | m ≤ 2 * j ∧ Even m} | case mpr
x : ℕ
⊢ Even x → (∃ x_1, x ≤ 2 * x_1) ∧ Even x |
https://github.com/aronerben/lean4-playground.git | 5efced915ecee24cd723d28d00aa63f9c7ea0a9c | meetings/ex1.lean | union_even_up_to | [119, 1] | [131, 18] | intro heven | case mpr
x : ℕ
⊢ Even x → (∃ x_1, x ≤ 2 * x_1) ∧ Even x | case mpr
x : ℕ
heven : Even x
⊢ (∃ x_1, x ≤ 2 * x_1) ∧ Even x |
https://github.com/aronerben/lean4-playground.git | 5efced915ecee24cd723d28d00aa63f9c7ea0a9c | meetings/ex1.lean | union_even_up_to | [119, 1] | [131, 18] | constructor | case mpr
x : ℕ
heven : Even x
⊢ (∃ x_1, x ≤ 2 * x_1) ∧ Even x | case mpr.left
x : ℕ
heven : Even x
⊢ ∃ x_1, x ≤ 2 * x_1
case mpr.right
x : ℕ
heven : Even x
⊢ Even x |
https://github.com/aronerben/lean4-playground.git | 5efced915ecee24cd723d28d00aa63f9c7ea0a9c | meetings/ex1.lean | union_even_up_to | [119, 1] | [131, 18] | use x | case mpr.left
x : ℕ
heven : Even x
⊢ ∃ x_1, x ≤ 2 * x_1 | case h
x : ℕ
heven : Even x
⊢ x ≤ 2 * x |
https://github.com/aronerben/lean4-playground.git | 5efced915ecee24cd723d28d00aa63f9c7ea0a9c | meetings/ex1.lean | union_even_up_to | [119, 1] | [131, 18] | linarith | case h
x : ℕ
heven : Even x
⊢ x ≤ 2 * x | no goals |
https://github.com/aronerben/lean4-playground.git | 5efced915ecee24cd723d28d00aa63f9c7ea0a9c | meetings/ex1.lean | union_even_up_to | [119, 1] | [131, 18] | exact heven | case mpr.right
x : ℕ
heven : Even x
⊢ Even x | no goals |
https://github.com/aronerben/lean4-playground.git | 5efced915ecee24cd723d28d00aa63f9c7ea0a9c | meetings/ex1.lean | inter_even_up_to | [134, 1] | [153, 11] | simp | ⊢ ⋂ j ∈ Set.univ, even_up_to j = Set.singleton 0 | ⊢ ⋂ j, even_up_to j = Set.singleton 0 |
https://github.com/aronerben/lean4-playground.git | 5efced915ecee24cd723d28d00aa63f9c7ea0a9c | meetings/ex1.lean | inter_even_up_to | [134, 1] | [153, 11] | simp_rw [even_up_to, Set.ext_iff] | ⊢ ⋂ j, even_up_to j = Set.singleton 0 | ⊢ ∀ (x : ℕ), x ∈ ⋂ j, {m | m ≤ 2 * j ∧ Even m} ↔ x ∈ Set.singleton 0 |
https://github.com/aronerben/lean4-playground.git | 5efced915ecee24cd723d28d00aa63f9c7ea0a9c | meetings/ex1.lean | inter_even_up_to | [134, 1] | [153, 11] | intro x | ⊢ ∀ (x : ℕ), x ∈ ⋂ j, {m | m ≤ 2 * j ∧ Even m} ↔ x ∈ Set.singleton 0 | x : ℕ
⊢ x ∈ ⋂ j, {m | m ≤ 2 * j ∧ Even m} ↔ x ∈ Set.singleton 0 |
https://github.com/aronerben/lean4-playground.git | 5efced915ecee24cd723d28d00aa63f9c7ea0a9c | meetings/ex1.lean | inter_even_up_to | [134, 1] | [153, 11] | constructor | x : ℕ
⊢ x ∈ ⋂ j, {m | m ≤ 2 * j ∧ Even m} ↔ x ∈ Set.singleton 0 | case mp
x : ℕ
⊢ x ∈ ⋂ j, {m | m ≤ 2 * j ∧ Even m} → x ∈ Set.singleton 0
case mpr
x : ℕ
⊢ x ∈ Set.singleton 0 → x ∈ ⋂ j, {m | m ≤ 2 * j ∧ Even m} |
https://github.com/aronerben/lean4-playground.git | 5efced915ecee24cd723d28d00aa63f9c7ea0a9c | meetings/ex1.lean | inter_even_up_to | [134, 1] | [153, 11] | simp | case mp
x : ℕ
⊢ x ∈ ⋂ j, {m | m ≤ 2 * j ∧ Even m} → x ∈ Set.singleton 0 | case mp
x : ℕ
⊢ (∀ (i : ℕ), x ≤ 2 * i ∧ Even x) → x ∈ Set.singleton 0 |
https://github.com/aronerben/lean4-playground.git | 5efced915ecee24cd723d28d00aa63f9c7ea0a9c | meetings/ex1.lean | inter_even_up_to | [134, 1] | [153, 11] | intro imp | case mp
x : ℕ
⊢ (∀ (i : ℕ), x ≤ 2 * i ∧ Even x) → x ∈ Set.singleton 0 | case mp
x : ℕ
imp : ∀ (i : ℕ), x ≤ 2 * i ∧ Even x
⊢ x ∈ Set.singleton 0 |
https://github.com/aronerben/lean4-playground.git | 5efced915ecee24cd723d28d00aa63f9c7ea0a9c | meetings/ex1.lean | inter_even_up_to | [134, 1] | [153, 11] | specialize imp 0 | case mp
x : ℕ
imp : ∀ (i : ℕ), x ≤ 2 * i ∧ Even x
⊢ x ∈ Set.singleton 0 | case mp
x : ℕ
imp : x ≤ 2 * 0 ∧ Even x
⊢ x ∈ Set.singleton 0 |
https://github.com/aronerben/lean4-playground.git | 5efced915ecee24cd723d28d00aa63f9c7ea0a9c | meetings/ex1.lean | inter_even_up_to | [134, 1] | [153, 11] | simp at imp | case mp
x : ℕ
imp : x ≤ 2 * 0 ∧ Even x
⊢ x ∈ Set.singleton 0 | case mp
x : ℕ
imp : x = 0 ∧ Even x
⊢ x ∈ Set.singleton 0 |
https://github.com/aronerben/lean4-playground.git | 5efced915ecee24cd723d28d00aa63f9c7ea0a9c | meetings/ex1.lean | inter_even_up_to | [134, 1] | [153, 11] | rcases imp with ⟨hle, _⟩ | case mp
x : ℕ
imp : x = 0 ∧ Even x
⊢ x ∈ Set.singleton 0 | case mp.intro
x : ℕ
hle : x = 0
right✝ : Even x
⊢ x ∈ Set.singleton 0 |
https://github.com/aronerben/lean4-playground.git | 5efced915ecee24cd723d28d00aa63f9c7ea0a9c | meetings/ex1.lean | inter_even_up_to | [134, 1] | [153, 11] | exact Set.mem_singleton_of_eq hle | case mp.intro
x : ℕ
hle : x = 0
right✝ : Even x
⊢ x ∈ Set.singleton 0 | no goals |
https://github.com/aronerben/lean4-playground.git | 5efced915ecee24cd723d28d00aa63f9c7ea0a9c | meetings/ex1.lean | inter_even_up_to | [134, 1] | [153, 11] | simp | case mpr
x : ℕ
⊢ x ∈ Set.singleton 0 → x ∈ ⋂ j, {m | m ≤ 2 * j ∧ Even m} | case mpr
x : ℕ
⊢ x ∈ Set.singleton 0 → ∀ (i : ℕ), x ≤ 2 * i ∧ Even x |
https://github.com/aronerben/lean4-playground.git | 5efced915ecee24cd723d28d00aa63f9c7ea0a9c | meetings/ex1.lean | inter_even_up_to | [134, 1] | [153, 11] | intros mem i | case mpr
x : ℕ
⊢ x ∈ Set.singleton 0 → ∀ (i : ℕ), x ≤ 2 * i ∧ Even x | case mpr
x : ℕ
mem : x ∈ Set.singleton 0
i : ℕ
⊢ x ≤ 2 * i ∧ Even x |
https://github.com/aronerben/lean4-playground.git | 5efced915ecee24cd723d28d00aa63f9c7ea0a9c | meetings/ex1.lean | inter_even_up_to | [134, 1] | [153, 11] | have mem' := Set.eq_of_mem_singleton mem | case mpr
x : ℕ
mem : x ∈ Set.singleton 0
i : ℕ
⊢ x ≤ 2 * i ∧ Even x | case mpr
x : ℕ
mem : x ∈ Set.singleton 0
i : ℕ
mem' : x = 0
⊢ x ≤ 2 * i ∧ Even x |
https://github.com/aronerben/lean4-playground.git | 5efced915ecee24cd723d28d00aa63f9c7ea0a9c | meetings/ex1.lean | inter_even_up_to | [134, 1] | [153, 11] | constructor | case mpr
x : ℕ
mem : x ∈ Set.singleton 0
i : ℕ
mem' : x = 0
⊢ x ≤ 2 * i ∧ Even x | case mpr.left
x : ℕ
mem : x ∈ Set.singleton 0
i : ℕ
mem' : x = 0
⊢ x ≤ 2 * i
case mpr.right
x : ℕ
mem : x ∈ Set.singleton 0
i : ℕ
mem' : x = 0
⊢ Even x |
https://github.com/aronerben/lean4-playground.git | 5efced915ecee24cd723d28d00aa63f9c7ea0a9c | meetings/ex1.lean | inter_even_up_to | [134, 1] | [153, 11] | rw [mem'] | case mpr.left
x : ℕ
mem : x ∈ Set.singleton 0
i : ℕ
mem' : x = 0
⊢ x ≤ 2 * i | case mpr.left
x : ℕ
mem : x ∈ Set.singleton 0
i : ℕ
mem' : x = 0
⊢ 0 ≤ 2 * i |
https://github.com/aronerben/lean4-playground.git | 5efced915ecee24cd723d28d00aa63f9c7ea0a9c | meetings/ex1.lean | inter_even_up_to | [134, 1] | [153, 11] | linarith | case mpr.left
x : ℕ
mem : x ∈ Set.singleton 0
i : ℕ
mem' : x = 0
⊢ 0 ≤ 2 * i | no goals |
https://github.com/aronerben/lean4-playground.git | 5efced915ecee24cd723d28d00aa63f9c7ea0a9c | meetings/ex1.lean | inter_even_up_to | [134, 1] | [153, 11] | rw [mem'] | case mpr.right
x : ℕ
mem : x ∈ Set.singleton 0
i : ℕ
mem' : x = 0
⊢ Even x | case mpr.right
x : ℕ
mem : x ∈ Set.singleton 0
i : ℕ
mem' : x = 0
⊢ Even 0 |
https://github.com/aronerben/lean4-playground.git | 5efced915ecee24cd723d28d00aa63f9c7ea0a9c | meetings/ex1.lean | inter_even_up_to | [134, 1] | [153, 11] | simp | case mpr.right
x : ℕ
mem : x ∈ Set.singleton 0
i : ℕ
mem' : x = 0
⊢ Even 0 | no goals |
https://github.com/aronerben/lean4-playground.git | 5efced915ecee24cd723d28d00aa63f9c7ea0a9c | meetings/ex1.lean | inter_rectangles | [168, 1] | [193, 18] | simp only [ge_iff_le, zero_le_one, not_true, gt_iff_lt, Set.mem_Icc] | ⊢ ⋂ α ∈ Set.Icc 0 1, rectangle α = Set.singleton (1, 0) | ⊢ ⋂ α, ⋂ (_ : 0 ≤ α ∧ α ≤ 1), rectangle α = Set.singleton (1, 0) |
https://github.com/aronerben/lean4-playground.git | 5efced915ecee24cd723d28d00aa63f9c7ea0a9c | meetings/ex1.lean | inter_rectangles | [168, 1] | [193, 18] | simp_rw [rectangle, Set.ext_iff] | ⊢ ⋂ α, ⋂ (_ : 0 ≤ α ∧ α ≤ 1), rectangle α = Set.singleton (1, 0) | ⊢ ∀ (x : ℝ × ℝ), x ∈ ⋂ α, ⋂ (_ : 0 ≤ α ∧ α ≤ 1), Set.Icc α 1 ×ˢ Set.Icc 0 α ↔ x ∈ Set.singleton (1, 0) |
https://github.com/aronerben/lean4-playground.git | 5efced915ecee24cd723d28d00aa63f9c7ea0a9c | meetings/ex1.lean | inter_rectangles | [168, 1] | [193, 18] | intro x | ⊢ ∀ (x : ℝ × ℝ), x ∈ ⋂ α, ⋂ (_ : 0 ≤ α ∧ α ≤ 1), Set.Icc α 1 ×ˢ Set.Icc 0 α ↔ x ∈ Set.singleton (1, 0) | x : ℝ × ℝ
⊢ x ∈ ⋂ α, ⋂ (_ : 0 ≤ α ∧ α ≤ 1), Set.Icc α 1 ×ˢ Set.Icc 0 α ↔ x ∈ Set.singleton (1, 0) |
https://github.com/aronerben/lean4-playground.git | 5efced915ecee24cd723d28d00aa63f9c7ea0a9c | meetings/ex1.lean | inter_rectangles | [168, 1] | [193, 18] | simp only [ge_iff_le, not_le, gt_iff_lt, Set.Icc_prod_Icc, Prod.mk_le_mk, not_and, Prod.mk_lt_mk, Set.mem_iInter, Set.mem_Icc, and_imp] | x : ℝ × ℝ
⊢ x ∈ ⋂ α, ⋂ (_ : 0 ≤ α ∧ α ≤ 1), Set.Icc α 1 ×ˢ Set.Icc 0 α ↔ x ∈ Set.singleton (1, 0) | x : ℝ × ℝ
⊢ (∀ (i : ℝ), 0 ≤ i → i ≤ 1 → (i, 0) ≤ x ∧ x ≤ (1, i)) ↔ x ∈ Set.singleton (1, 0) |
https://github.com/aronerben/lean4-playground.git | 5efced915ecee24cd723d28d00aa63f9c7ea0a9c | meetings/ex1.lean | inter_rectangles | [168, 1] | [193, 18] | constructor | x : ℝ × ℝ
⊢ (∀ (i : ℝ), 0 ≤ i → i ≤ 1 → (i, 0) ≤ x ∧ x ≤ (1, i)) ↔ x ∈ Set.singleton (1, 0) | case mp
x : ℝ × ℝ
⊢ (∀ (i : ℝ), 0 ≤ i → i ≤ 1 → (i, 0) ≤ x ∧ x ≤ (1, i)) → x ∈ Set.singleton (1, 0)
case mpr
x : ℝ × ℝ
⊢ x ∈ Set.singleton (1, 0) → ∀ (i : ℝ), 0 ≤ i → i ≤ 1 → (i, 0) ≤ x ∧ x ≤ (1, i) |
https://github.com/aronerben/lean4-playground.git | 5efced915ecee24cd723d28d00aa63f9c7ea0a9c | meetings/ex1.lean | inter_rectangles | [168, 1] | [193, 18] | intro imp | case mp
x : ℝ × ℝ
⊢ (∀ (i : ℝ), 0 ≤ i → i ≤ 1 → (i, 0) ≤ x ∧ x ≤ (1, i)) → x ∈ Set.singleton (1, 0) | case mp
x : ℝ × ℝ
imp : ∀ (i : ℝ), 0 ≤ i → i ≤ 1 → (i, 0) ≤ x ∧ x ≤ (1, i)
⊢ x ∈ Set.singleton (1, 0) |
https://github.com/aronerben/lean4-playground.git | 5efced915ecee24cd723d28d00aa63f9c7ea0a9c | meetings/ex1.lean | inter_rectangles | [168, 1] | [193, 18] | have h1 := imp 0 | case mp
x : ℝ × ℝ
imp : ∀ (i : ℝ), 0 ≤ i → i ≤ 1 → (i, 0) ≤ x ∧ x ≤ (1, i)
⊢ x ∈ Set.singleton (1, 0) | case mp
x : ℝ × ℝ
imp : ∀ (i : ℝ), 0 ≤ i → i ≤ 1 → (i, 0) ≤ x ∧ x ≤ (1, i)
h1 : 0 ≤ 0 → 0 ≤ 1 → (0, 0) ≤ x ∧ x ≤ (1, 0)
⊢ x ∈ Set.singleton (1, 0) |
https://github.com/aronerben/lean4-playground.git | 5efced915ecee24cd723d28d00aa63f9c7ea0a9c | meetings/ex1.lean | inter_rectangles | [168, 1] | [193, 18] | have h2 := imp 1 | case mp
x : ℝ × ℝ
imp : ∀ (i : ℝ), 0 ≤ i → i ≤ 1 → (i, 0) ≤ x ∧ x ≤ (1, i)
h1 : 0 ≤ 0 → 0 ≤ 1 → (0, 0) ≤ x ∧ x ≤ (1, 0)
⊢ x ∈ Set.singleton (1, 0) | case mp
x : ℝ × ℝ
imp : ∀ (i : ℝ), 0 ≤ i → i ≤ 1 → (i, 0) ≤ x ∧ x ≤ (1, i)
h1 : 0 ≤ 0 → 0 ≤ 1 → (0, 0) ≤ x ∧ x ≤ (1, 0)
h2 : 0 ≤ 1 → 1 ≤ 1 → (1, 0) ≤ x ∧ x ≤ (1, 1)
⊢ x ∈ Set.singleton (1, 0) |
https://github.com/aronerben/lean4-playground.git | 5efced915ecee24cd723d28d00aa63f9c7ea0a9c | meetings/ex1.lean | inter_rectangles | [168, 1] | [193, 18] | simp [Prod.le_def] at * | case mp
x : ℝ × ℝ
imp : ∀ (i : ℝ), 0 ≤ i → i ≤ 1 → (i, 0) ≤ x ∧ x ≤ (1, i)
h1 : 0 ≤ 0 → 0 ≤ 1 → (0, 0) ≤ x ∧ x ≤ (1, 0)
h2 : 0 ≤ 1 → 1 ≤ 1 → (1, 0) ≤ x ∧ x ≤ (1, 1)
⊢ x ∈ Set.singleton (1, 0) | case mp
x : ℝ × ℝ
imp : ∀ (i : ℝ), 0 ≤ i → i ≤ 1 → (i ≤ x.1 ∧ 0 ≤ x.2) ∧ x.1 ≤ 1 ∧ x.2 ≤ i
h1 : (0 ≤ x.1 ∧ 0 ≤ x.2) ∧ x.1 ≤ 1 ∧ x.2 ≤ 0
h2 : (1 ≤ x.1 ∧ 0 ≤ x.2) ∧ x.1 ≤ 1 ∧ x.2 ≤ 1
⊢ x ∈ Set.singleton (1, 0) |
https://github.com/aronerben/lean4-playground.git | 5efced915ecee24cd723d28d00aa63f9c7ea0a9c | meetings/ex1.lean | inter_rectangles | [168, 1] | [193, 18] | have hx1 : x.1 = 1 := by
linarith | case mp
x : ℝ × ℝ
imp : ∀ (i : ℝ), 0 ≤ i → i ≤ 1 → (i ≤ x.1 ∧ 0 ≤ x.2) ∧ x.1 ≤ 1 ∧ x.2 ≤ i
h1 : (0 ≤ x.1 ∧ 0 ≤ x.2) ∧ x.1 ≤ 1 ∧ x.2 ≤ 0
h2 : (1 ≤ x.1 ∧ 0 ≤ x.2) ∧ x.1 ≤ 1 ∧ x.2 ≤ 1
⊢ x ∈ Set.singleton (1, 0) | case mp
x : ℝ × ℝ
imp : ∀ (i : ℝ), 0 ≤ i → i ≤ 1 → (i ≤ x.1 ∧ 0 ≤ x.2) ∧ x.1 ≤ 1 ∧ x.2 ≤ i
h1 : (0 ≤ x.1 ∧ 0 ≤ x.2) ∧ x.1 ≤ 1 ∧ x.2 ≤ 0
h2 : (1 ≤ x.1 ∧ 0 ≤ x.2) ∧ x.1 ≤ 1 ∧ x.2 ≤ 1
hx1 : x.1 = 1
⊢ x ∈ Set.singleton (1, 0) |
https://github.com/aronerben/lean4-playground.git | 5efced915ecee24cd723d28d00aa63f9c7ea0a9c | meetings/ex1.lean | inter_rectangles | [168, 1] | [193, 18] | have hx2 : x.2 = 0 := by
linarith | case mp
x : ℝ × ℝ
imp : ∀ (i : ℝ), 0 ≤ i → i ≤ 1 → (i ≤ x.1 ∧ 0 ≤ x.2) ∧ x.1 ≤ 1 ∧ x.2 ≤ i
h1 : (0 ≤ x.1 ∧ 0 ≤ x.2) ∧ x.1 ≤ 1 ∧ x.2 ≤ 0
h2 : (1 ≤ x.1 ∧ 0 ≤ x.2) ∧ x.1 ≤ 1 ∧ x.2 ≤ 1
hx1 : x.1 = 1
⊢ x ∈ Set.singleton (1, 0) | case mp
x : ℝ × ℝ
imp : ∀ (i : ℝ), 0 ≤ i → i ≤ 1 → (i ≤ x.1 ∧ 0 ≤ x.2) ∧ x.1 ≤ 1 ∧ x.2 ≤ i
h1 : (0 ≤ x.1 ∧ 0 ≤ x.2) ∧ x.1 ≤ 1 ∧ x.2 ≤ 0
h2 : (1 ≤ x.1 ∧ 0 ≤ x.2) ∧ x.1 ≤ 1 ∧ x.2 ≤ 1
hx1 : x.1 = 1
hx2 : x.2 = 0
⊢ x ∈ Set.singleton (1, 0) |
https://github.com/aronerben/lean4-playground.git | 5efced915ecee24cd723d28d00aa63f9c7ea0a9c | meetings/ex1.lean | inter_rectangles | [168, 1] | [193, 18] | exact Set.mem_singleton_of_eq (Prod.ext hx1 hx2) | case mp
x : ℝ × ℝ
imp : ∀ (i : ℝ), 0 ≤ i → i ≤ 1 → (i ≤ x.1 ∧ 0 ≤ x.2) ∧ x.1 ≤ 1 ∧ x.2 ≤ i
h1 : (0 ≤ x.1 ∧ 0 ≤ x.2) ∧ x.1 ≤ 1 ∧ x.2 ≤ 0
h2 : (1 ≤ x.1 ∧ 0 ≤ x.2) ∧ x.1 ≤ 1 ∧ x.2 ≤ 1
hx1 : x.1 = 1
hx2 : x.2 = 0
⊢ x ∈ Set.singleton (1, 0) | no goals |
https://github.com/aronerben/lean4-playground.git | 5efced915ecee24cd723d28d00aa63f9c7ea0a9c | meetings/ex1.lean | inter_rectangles | [168, 1] | [193, 18] | linarith | x : ℝ × ℝ
imp : ∀ (i : ℝ), 0 ≤ i → i ≤ 1 → (i ≤ x.1 ∧ 0 ≤ x.2) ∧ x.1 ≤ 1 ∧ x.2 ≤ i
h1 : (0 ≤ x.1 ∧ 0 ≤ x.2) ∧ x.1 ≤ 1 ∧ x.2 ≤ 0
h2 : (1 ≤ x.1 ∧ 0 ≤ x.2) ∧ x.1 ≤ 1 ∧ x.2 ≤ 1
⊢ x.1 = 1 | no goals |
https://github.com/aronerben/lean4-playground.git | 5efced915ecee24cd723d28d00aa63f9c7ea0a9c | meetings/ex1.lean | inter_rectangles | [168, 1] | [193, 18] | linarith | x : ℝ × ℝ
imp : ∀ (i : ℝ), 0 ≤ i → i ≤ 1 → (i ≤ x.1 ∧ 0 ≤ x.2) ∧ x.1 ≤ 1 ∧ x.2 ≤ i
h1 : (0 ≤ x.1 ∧ 0 ≤ x.2) ∧ x.1 ≤ 1 ∧ x.2 ≤ 0
h2 : (1 ≤ x.1 ∧ 0 ≤ x.2) ∧ x.1 ≤ 1 ∧ x.2 ≤ 1
hx1 : x.1 = 1
⊢ x.2 = 0 | no goals |
https://github.com/aronerben/lean4-playground.git | 5efced915ecee24cd723d28d00aa63f9c7ea0a9c | meetings/ex1.lean | inter_rectangles | [168, 1] | [193, 18] | intros mem i hle0i hlei1 | case mpr
x : ℝ × ℝ
⊢ x ∈ Set.singleton (1, 0) → ∀ (i : ℝ), 0 ≤ i → i ≤ 1 → (i, 0) ≤ x ∧ x ≤ (1, i) | case mpr
x : ℝ × ℝ
mem : x ∈ Set.singleton (1, 0)
i : ℝ
hle0i : 0 ≤ i
hlei1 : i ≤ 1
⊢ (i, 0) ≤ x ∧ x ≤ (1, i) |
https://github.com/aronerben/lean4-playground.git | 5efced915ecee24cd723d28d00aa63f9c7ea0a9c | meetings/ex1.lean | inter_rectangles | [168, 1] | [193, 18] | have mem' := Set.eq_of_mem_singleton mem | case mpr
x : ℝ × ℝ
mem : x ∈ Set.singleton (1, 0)
i : ℝ
hle0i : 0 ≤ i
hlei1 : i ≤ 1
⊢ (i, 0) ≤ x ∧ x ≤ (1, i) | case mpr
x : ℝ × ℝ
mem : x ∈ Set.singleton (1, 0)
i : ℝ
hle0i : 0 ≤ i
hlei1 : i ≤ 1
mem' : x = (1, 0)
⊢ (i, 0) ≤ x ∧ x ≤ (1, i) |
https://github.com/aronerben/lean4-playground.git | 5efced915ecee24cd723d28d00aa63f9c7ea0a9c | meetings/ex1.lean | inter_rectangles | [168, 1] | [193, 18] | constructor | case mpr
x : ℝ × ℝ
mem : x ∈ Set.singleton (1, 0)
i : ℝ
hle0i : 0 ≤ i
hlei1 : i ≤ 1
mem' : x = (1, 0)
⊢ (i, 0) ≤ x ∧ x ≤ (1, i) | case mpr.left
x : ℝ × ℝ
mem : x ∈ Set.singleton (1, 0)
i : ℝ
hle0i : 0 ≤ i
hlei1 : i ≤ 1
mem' : x = (1, 0)
⊢ (i, 0) ≤ x
case mpr.right
x : ℝ × ℝ
mem : x ∈ Set.singleton (1, 0)
i : ℝ
hle0i : 0 ≤ i
hlei1 : i ≤ 1
mem' : x = (1, 0)
⊢ x ≤ (1, i) |
https://github.com/aronerben/lean4-playground.git | 5efced915ecee24cd723d28d00aa63f9c7ea0a9c | meetings/ex1.lean | inter_rectangles | [168, 1] | [193, 18] | rw [mem'] | case mpr.left
x : ℝ × ℝ
mem : x ∈ Set.singleton (1, 0)
i : ℝ
hle0i : 0 ≤ i
hlei1 : i ≤ 1
mem' : x = (1, 0)
⊢ (i, 0) ≤ x | case mpr.left
x : ℝ × ℝ
mem : x ∈ Set.singleton (1, 0)
i : ℝ
hle0i : 0 ≤ i
hlei1 : i ≤ 1
mem' : x = (1, 0)
⊢ (i, 0) ≤ (1, 0) |
https://github.com/aronerben/lean4-playground.git | 5efced915ecee24cd723d28d00aa63f9c7ea0a9c | meetings/ex1.lean | inter_rectangles | [168, 1] | [193, 18] | simp [Prod.le_def] | case mpr.left
x : ℝ × ℝ
mem : x ∈ Set.singleton (1, 0)
i : ℝ
hle0i : 0 ≤ i
hlei1 : i ≤ 1
mem' : x = (1, 0)
⊢ (i, 0) ≤ (1, 0) | case mpr.left
x : ℝ × ℝ
mem : x ∈ Set.singleton (1, 0)
i : ℝ
hle0i : 0 ≤ i
hlei1 : i ≤ 1
mem' : x = (1, 0)
⊢ i ≤ 1 |
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