url stringclasses 147
values | commit stringclasses 147
values | file_path stringlengths 7 101 | full_name stringlengths 1 94 | start stringlengths 6 10 | end stringlengths 6 11 | tactic stringlengths 1 11.2k | state_before stringlengths 3 2.09M | state_after stringlengths 6 2.09M |
|---|---|---|---|---|---|---|---|---|
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Tactic/BoundTests.lean | test_sq | [54, 1] | [54, 62] | bound | a b c x y : ℝ
z : ℂ
n✝ : ℕ
n : x ≥ 0
h : x ≤ y
⊢ x ^ 2 ≤ y ^ 2 | no goals |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Tactic/BoundTests.lean | test_sq_ge | [55, 1] | [55, 65] | bound | a b c x y : ℝ
z : ℂ
n✝ : ℕ
n : x ≥ 0
h : x ≤ y
⊢ y ^ 2 ≥ x ^ 2 | no goals |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Tactic/BoundTests.lean | test_mul_left | [56, 1] | [56, 72] | bound | a b c x y : ℝ
z : ℂ
n✝ : ℕ
n : a ≥ 0
h : x ≤ y
⊢ a * x ≤ a * y | no goals |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Tactic/BoundTests.lean | test_mul_right | [57, 1] | [57, 73] | bound | a b c x y : ℝ
z : ℂ
n✝ : ℕ
n : a ≥ 0
h : x ≤ y
⊢ x * a ≤ y * a | no goals |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Tactic/BoundTests.lean | test_mul_both | [58, 1] | [58, 100] | bound | a b c x y : ℝ
z : ℂ
n : ℕ
bp : b ≥ 0
xp : x ≥ 0
ab : a ≤ b
xy : x ≤ y
⊢ a * x ≤ b * y | no goals |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Tactic/BoundTests.lean | test_abs_mul | [59, 1] | [59, 67] | bound | a b c x y : ℝ
z : ℂ
n : ℕ
h : x ≤ y
⊢ Complex.abs z * x ≤ Complex.abs z * y | no goals |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Tactic/BoundTests.lean | test_add_left | [60, 1] | [60, 60] | bound | a b c x y : ℝ
z : ℂ
n : ℕ
h : x ≤ y
⊢ a + x ≤ a + y | no goals |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Tactic/BoundTests.lean | test_add_right | [61, 1] | [61, 61] | bound | a b c x y : ℝ
z : ℂ
n : ℕ
h : x ≤ y
⊢ x + a ≤ y + a | no goals |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Tactic/BoundTests.lean | test_add_both | [62, 1] | [62, 74] | bound | a b c x y : ℝ
z : ℂ
n : ℕ
ab : a ≤ b
xy : x ≤ y
⊢ a + x ≤ b + y | no goals |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Tactic/BoundTests.lean | test_sub_left | [63, 1] | [63, 60] | bound | a b c x y : ℝ
z : ℂ
n : ℕ
h : x ≥ y
⊢ a - x ≤ a - y | no goals |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Tactic/BoundTests.lean | test_sub_right | [64, 1] | [64, 61] | bound | a b c x y : ℝ
z : ℂ
n : ℕ
h : x ≤ y
⊢ x - a ≤ y - a | no goals |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Tactic/BoundTests.lean | test_sub_both | [65, 1] | [65, 74] | bound | a b c x y : ℝ
z : ℂ
n : ℕ
ab : a ≤ b
xy : x ≥ y
⊢ a - x ≤ b - y | no goals |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Tactic/BoundTests.lean | test_sub_pos | [66, 1] | [66, 55] | bound | a b c x y : ℝ
z : ℂ
n : ℕ
h : x < y
⊢ y - x > 0 | no goals |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Tactic/BoundTests.lean | test_le_of_lt | [67, 1] | [67, 52] | bound | a b c x y : ℝ
z : ℂ
n : ℕ
h : x > 0
⊢ x ≥ 0 | no goals |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Tactic/BoundTests.lean | test_extra | [68, 1] | [68, 76] | bound [h n] | a b c x y : ℝ
z : ℂ
n : ℕ
f : ℕ → ℝ
h : ∀ (n : ℕ), f n ≥ 0
⊢ f n ≥ 0 | no goals |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Tactic/BoundTests.lean | test_1_4 | [69, 1] | [69, 41] | bound | a b c x y : ℝ
z : ℂ
n : ℕ
⊢ 1 < 4 | no goals |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Tactic/BoundTests.lean | test_2_4 | [70, 1] | [70, 41] | bound | a b c x y : ℝ
z : ℂ
n : ℕ
⊢ 2 < 4 | no goals |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Tactic/BoundTests.lean | test_div_left | [71, 1] | [71, 73] | bound | a b c x y : ℝ
z : ℂ
n : ℕ
hc : c ≥ 0
h : a ≤ b
⊢ a / c ≤ b / c | no goals |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Tactic/BoundTests.lean | test_div_right | [72, 1] | [72, 87] | bound | a b c x y : ℝ
z : ℂ
n : ℕ
ha : a ≥ 0
hc : c > 0
h : b ≥ c
⊢ a / b ≤ a / c | no goals |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Tactic/BoundTests.lean | test_coe | [73, 1] | [73, 65] | bound | a b c x✝ y✝ : ℝ
z : ℂ
n : ℕ
x y : ℝ≥0
h : x < y
⊢ ↑x < ↑y | no goals |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Tactic/BoundTests.lean | test_dist | [74, 1] | [74, 61] | bound | a b c x y : ℝ
z : ℂ
n : ℕ
⊢ dist a c ≤ dist a b + dist b c | no goals |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Tactic/BoundTests.lean | test_log | [75, 1] | [75, 78] | bound | a b c x✝ y✝ : ℝ
z : ℂ
n : ℕ
x y : ℝ
x0 : 0 < x
h : x ≤ y
⊢ x.log ≤ y.log | no goals |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Tactic/BoundTests.lean | test_le_max_of_le_left | [81, 1] | [81, 67] | bound | a b c : ℝ
n m : ℕ
h : a ≤ b
⊢ a ≤ max b c | no goals |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Tactic/BoundTests.lean | test_le_max_of_le_right | [82, 1] | [82, 68] | bound | a b c : ℝ
n m : ℕ
h : a ≤ c
⊢ a ≤ max b c | no goals |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Tactic/BoundTests.lean | test_lt_max_of_lt_left | [83, 1] | [83, 67] | bound | a b c : ℝ
n m : ℕ
h : a < b
⊢ a < max b c | no goals |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Tactic/BoundTests.lean | test_lt_max_of_lt_right | [84, 1] | [84, 68] | bound | a b c : ℝ
n m : ℕ
h : a < c
⊢ a < max b c | no goals |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Tactic/BoundTests.lean | test_min_le_of_left_le | [85, 1] | [85, 67] | bound | a b c : ℝ
n m : ℕ
h : a ≤ c
⊢ min a b ≤ c | no goals |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Tactic/BoundTests.lean | test_min_le_of_right_le | [86, 1] | [86, 68] | bound | a b c : ℝ
n m : ℕ
h : b ≤ c
⊢ min a b ≤ c | no goals |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Tactic/BoundTests.lean | test_min_lt_of_left_lt | [87, 1] | [87, 67] | bound | a b c : ℝ
n m : ℕ
h : a < c
⊢ min a b < c | no goals |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Tactic/BoundTests.lean | test_min_lt_of_right_lt | [88, 1] | [88, 68] | bound | a b c : ℝ
n m : ℕ
h : b < c
⊢ min a b < c | no goals |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Tactic/BoundTests.lean | test_pow_le_pow_right | [89, 1] | [89, 77] | bound | a b c : ℝ
n m : ℕ
a1 : 1 ≤ a
h : m ≤ n
⊢ a ^ m ≤ a ^ n | no goals |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Tactic/BoundTests.lean | test_pow_le_pow_of_le_one | [90, 1] | [90, 94] | bound | a b c : ℝ
n m : ℕ
a0 : 0 ≤ a
a1 : a ≤ 1
h : n ≤ m
⊢ a ^ m ≤ a ^ n | no goals |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Tactic/BoundTests.lean | test_rpow_le_rpow_of_exponent_le | [91, 1] | [91, 88] | bound | a b c : ℝ
n m : ℕ
a1 : 1 ≤ a
h : b ≤ c
⊢ a ^ b ≤ a ^ c | no goals |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Tactic/BoundTests.lean | test_rpow_le_rpow_of_exponent_ge | [92, 1] | [92, 101] | bound | a b c : ℝ
n m : ℕ
a0 : 0 < a
a1 : a ≤ 1
h : c ≤ b
⊢ a ^ b ≤ a ^ c | no goals |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Tactic/BoundTests.lean | test_with_context | [96, 1] | [101, 8] | rw [Metric.isOpen_iff] at o | s : Set ℂ
o : IsOpen s
z : ℂ
h : z ∈ s
⊢ ∃ r, r > 0 | s : Set ℂ
o : ∀ x ∈ s, ∃ ε > 0, Metric.ball x ε ⊆ s
z : ℂ
h : z ∈ s
⊢ ∃ r, r > 0 |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Tactic/BoundTests.lean | test_with_context | [96, 1] | [101, 8] | rcases o z h with ⟨t, tp, bs⟩ | s : Set ℂ
o : ∀ x ∈ s, ∃ ε > 0, Metric.ball x ε ⊆ s
z : ℂ
h : z ∈ s
⊢ ∃ r, r > 0 | case intro.intro
s : Set ℂ
o : ∀ x ∈ s, ∃ ε > 0, Metric.ball x ε ⊆ s
z : ℂ
h : z ∈ s
t : ℝ
tp : t > 0
bs : Metric.ball z t ⊆ s
⊢ ∃ r, r > 0 |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Tactic/BoundTests.lean | test_with_context | [96, 1] | [101, 8] | exists t/2 | case intro.intro
s : Set ℂ
o : ∀ x ∈ s, ∃ ε > 0, Metric.ball x ε ⊆ s
z : ℂ
h : z ∈ s
t : ℝ
tp : t > 0
bs : Metric.ball z t ⊆ s
⊢ ∃ r, r > 0 | case intro.intro
s : Set ℂ
o : ∀ x ∈ s, ∃ ε > 0, Metric.ball x ε ⊆ s
z : ℂ
h : z ∈ s
t : ℝ
tp : t > 0
bs : Metric.ball z t ⊆ s
⊢ t / 2 > 0 |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Tactic/BoundTests.lean | test_with_context | [96, 1] | [101, 8] | clear o h bs z s | case intro.intro
s : Set ℂ
o : ∀ x ∈ s, ∃ ε > 0, Metric.ball x ε ⊆ s
z : ℂ
h : z ∈ s
t : ℝ
tp : t > 0
bs : Metric.ball z t ⊆ s
⊢ t / 2 > 0 | case intro.intro
t : ℝ
tp : t > 0
⊢ t / 2 > 0 |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Tactic/BoundTests.lean | test_with_context | [96, 1] | [101, 8] | bound | case intro.intro
t : ℝ
tp : t > 0
⊢ t / 2 > 0 | no goals |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Tactic/BoundTests.lean | test_try_elab | [104, 1] | [110, 50] | calc abs (f z) = abs (f w - (f w - f z)) := by ring_nf
_ ≤ abs (f w) + abs (f w - f z) := by bound
_ ≤ c * abs w + e := by bound [h w wr, sc wz] | f : ℂ → ℂ
z w : ℂ
s r c e : ℝ
sc : ∀ {w : ℂ}, Complex.abs (w - z) < s → Complex.abs (f w - f z) < e
wz : Complex.abs (w - z) < s
wr : Complex.abs w < r
h : ∀ (z : ℂ), Complex.abs z < r → Complex.abs (f z) ≤ c * Complex.abs z
⊢ Complex.abs (f z) ≤ c * Complex.abs w + e | no goals |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Tactic/BoundTests.lean | test_try_elab | [104, 1] | [110, 50] | ring_nf | f : ℂ → ℂ
z w : ℂ
s r c e : ℝ
sc : ∀ {w : ℂ}, Complex.abs (w - z) < s → Complex.abs (f w - f z) < e
wz : Complex.abs (w - z) < s
wr : Complex.abs w < r
h : ∀ (z : ℂ), Complex.abs z < r → Complex.abs (f z) ≤ c * Complex.abs z
⊢ Complex.abs (f z) = Complex.abs (f w - (f w - f z)) | no goals |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Tactic/BoundTests.lean | test_try_elab | [104, 1] | [110, 50] | bound | f : ℂ → ℂ
z w : ℂ
s r c e : ℝ
sc : ∀ {w : ℂ}, Complex.abs (w - z) < s → Complex.abs (f w - f z) < e
wz : Complex.abs (w - z) < s
wr : Complex.abs w < r
h : ∀ (z : ℂ), Complex.abs z < r → Complex.abs (f z) ≤ c * Complex.abs z
⊢ Complex.abs (f w - (f w - f z)) ≤ Complex.abs (f w) + Complex.abs (f w - f z) | no goals |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Tactic/BoundTests.lean | test_try_elab | [104, 1] | [110, 50] | bound [h w wr, sc wz] | f : ℂ → ℂ
z w : ℂ
s r c e : ℝ
sc : ∀ {w : ℂ}, Complex.abs (w - z) < s → Complex.abs (f w - f z) < e
wz : Complex.abs (w - z) < s
wr : Complex.abs w < r
h : ∀ (z : ℂ), Complex.abs z < r → Complex.abs (f z) ≤ c * Complex.abs z
⊢ Complex.abs (f w) + Complex.abs (f w - f z) ≤ c * Complex.abs w + e | no goals |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Tactic/BoundTests.lean | test_fun_inference | [113, 1] | [115, 8] | bound | α : Type
s : Finset α
f g : α → ℂ
⊢ ‖s.sum fun x => f x + g x‖ ≤ s.sum fun x => ‖f x + g x‖ | no goals |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Tactic/BoundTests.lean | test_whnf | [118, 1] | [119, 14] | bound [h.1] | x y : ℝ
h : x < y ∧ True
⊢ x ≤ y | no goals |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Tactic/BoundTests.lean | test_unknown_identifier | [122, 1] | [123, 24] | intro n | f : ℕ → ℝ
le : ∀ (n : ℕ), f n ≤ ↑n
⊢ ∀ (n : ℕ), f n ≤ ↑n | f : ℕ → ℝ
le : ∀ (n : ℕ), f n ≤ ↑n
n : ℕ
⊢ f n ≤ ↑n |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Tactic/BoundTests.lean | test_unknown_identifier | [122, 1] | [123, 24] | bound [le n] | f : ℕ → ℝ
le : ∀ (n : ℕ), f n ≤ ↑n
n : ℕ
⊢ f n ≤ ↑n | no goals |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Tactic/BoundTests.lean | le_sqr_add | [126, 1] | [132, 30] | calc Complex.abs (z^2 + c)
_ ≥ Complex.abs (z^2) - abs c := by bound
_ ≥ Complex.abs (z^2) - abs z := by bound
_ ≥ (abs z - 1) * abs z := by rw [mul_comm, mul_sub_one, ←pow_two, ←Complex.abs.map_pow]
_ ≥ 2 * abs z := by bound | c z : ℂ
cz : Complex.abs c ≤ Complex.abs z
z3 : 3 ≤ Complex.abs z
⊢ 2 * Complex.abs z ≤ Complex.abs (z ^ 2 + c) | no goals |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Tactic/BoundTests.lean | le_sqr_add | [126, 1] | [132, 30] | bound | c z : ℂ
cz : Complex.abs c ≤ Complex.abs z
z3 : 3 ≤ Complex.abs z
⊢ Complex.abs (z ^ 2 + c) ≥ Complex.abs (z ^ 2) - Complex.abs c | no goals |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Tactic/BoundTests.lean | le_sqr_add | [126, 1] | [132, 30] | bound | c z : ℂ
cz : Complex.abs c ≤ Complex.abs z
z3 : 3 ≤ Complex.abs z
⊢ Complex.abs (z ^ 2) - Complex.abs c ≥ Complex.abs (z ^ 2) - Complex.abs z | no goals |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Tactic/BoundTests.lean | le_sqr_add | [126, 1] | [132, 30] | rw [mul_comm, mul_sub_one, ←pow_two, ←Complex.abs.map_pow] | c z : ℂ
cz : Complex.abs c ≤ Complex.abs z
z3 : 3 ≤ Complex.abs z
⊢ Complex.abs (z ^ 2) - Complex.abs z ≥ (Complex.abs z - 1) * Complex.abs z | no goals |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Tactic/BoundTests.lean | le_sqr_add | [126, 1] | [132, 30] | bound | c z : ℂ
cz : Complex.abs c ≤ Complex.abs z
z3 : 3 ≤ Complex.abs z
⊢ (Complex.abs z - 1) * Complex.abs z ≥ 2 * Complex.abs z | no goals |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Render/Iterate.lean | iterate'_correct | [53, 1] | [91, 16] | induction' n with n h generalizing k z z' | c z : Box
rs : Floating
c' z' : ℂ
rs' : ℝ
cm : c' ∈ approx c
zm : z' ∈ approx z
rsn : rs ≠ nan
rsm : rs' ≤ rs.val
k n : ℕ
⊢ let i := iterate' c z rs k n;
let w' := (f' 2 c')^[i.n - k] z';
k ≤ i.n ∧ w' ∈ approx i.z ∧ (i.exit = Exit.large → rs' < Complex.abs w' ^ 2) | case zero
c : Box
rs : Floating
c' : ℂ
rs' : ℝ
cm : c' ∈ approx c
rsn : rs ≠ nan
rsm : rs' ≤ rs.val
z : Box
z' : ℂ
zm : z' ∈ approx z
k : ℕ
⊢ let i := iterate' c z rs k 0;
let w' := (f' 2 c')^[i.n - k] z';
k ≤ i.n ∧ w' ∈ approx i.z ∧ (i.exit = Exit.large → rs' < Complex.abs w' ^ 2)
case succ
c : Box
rs : Floating
... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Render/Iterate.lean | iterate'_correct | [53, 1] | [91, 16] | simpa only [iterate', le_refl, ge_iff_le, tsub_eq_zero_of_le, Function.iterate_zero, id_eq,
IsEmpty.forall_iff, and_true, true_and] | case zero
c : Box
rs : Floating
c' : ℂ
rs' : ℝ
cm : c' ∈ approx c
rsn : rs ≠ nan
rsm : rs' ≤ rs.val
z : Box
z' : ℂ
zm : z' ∈ approx z
k : ℕ
⊢ let i := iterate' c z rs k 0;
let w' := (f' 2 c')^[i.n - k] z';
k ≤ i.n ∧ w' ∈ approx i.z ∧ (i.exit = Exit.large → rs' < Complex.abs w' ^ 2) | no goals |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Render/Iterate.lean | iterate'_correct | [53, 1] | [91, 16] | simp only [iterate', Floating.val_lt_val] | case succ
c : Box
rs : Floating
c' : ℂ
rs' : ℝ
cm : c' ∈ approx c
rsn : rs ≠ nan
rsm : rs' ≤ rs.val
n : ℕ
h :
∀ {z : Box} {z' : ℂ},
z' ∈ approx z →
∀ (k : ℕ),
let i := iterate' c z rs k n;
let w' := (f' 2 c')^[i.n - k] z';
k ≤ i.n ∧ w' ∈ approx i.z ∧ (i.exit = Exit.large → rs' < Comp... | case succ
c : Box
rs : Floating
c' : ℂ
rs' : ℝ
cm : c' ∈ approx c
rsn : rs ≠ nan
rsm : rs' ≤ rs.val
n : ℕ
h :
∀ {z : Box} {z' : ℂ},
z' ∈ approx z →
∀ (k : ℕ),
let i := iterate' c z rs k n;
let w' := (f' 2 c')^[i.n - k] z';
k ≤ i.n ∧ w' ∈ approx i.z ∧ (i.exit = Exit.large → rs' < Comp... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Render/Iterate.lean | iterate'_correct | [53, 1] | [91, 16] | generalize hzr2 : z.re.sqr = zr2 | case succ
c : Box
rs : Floating
c' : ℂ
rs' : ℝ
cm : c' ∈ approx c
rsn : rs ≠ nan
rsm : rs' ≤ rs.val
n : ℕ
h :
∀ {z : Box} {z' : ℂ},
z' ∈ approx z →
∀ (k : ℕ),
let i := iterate' c z rs k n;
let w' := (f' 2 c')^[i.n - k] z';
k ≤ i.n ∧ w' ∈ approx i.z ∧ (i.exit = Exit.large → rs' < Comp... | case succ
c : Box
rs : Floating
c' : ℂ
rs' : ℝ
cm : c' ∈ approx c
rsn : rs ≠ nan
rsm : rs' ≤ rs.val
n : ℕ
h :
∀ {z : Box} {z' : ℂ},
z' ∈ approx z →
∀ (k : ℕ),
let i := iterate' c z rs k n;
let w' := (f' 2 c')^[i.n - k] z';
k ≤ i.n ∧ w' ∈ approx i.z ∧ (i.exit = Exit.large → rs' < Comp... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Render/Iterate.lean | iterate'_correct | [53, 1] | [91, 16] | generalize hzi2 : z.im.sqr = zi2 | case succ
c : Box
rs : Floating
c' : ℂ
rs' : ℝ
cm : c' ∈ approx c
rsn : rs ≠ nan
rsm : rs' ≤ rs.val
n : ℕ
h :
∀ {z : Box} {z' : ℂ},
z' ∈ approx z →
∀ (k : ℕ),
let i := iterate' c z rs k n;
let w' := (f' 2 c')^[i.n - k] z';
k ≤ i.n ∧ w' ∈ approx i.z ∧ (i.exit = Exit.large → rs' < Comp... | case succ
c : Box
rs : Floating
c' : ℂ
rs' : ℝ
cm : c' ∈ approx c
rsn : rs ≠ nan
rsm : rs' ≤ rs.val
n : ℕ
h :
∀ {z : Box} {z' : ℂ},
z' ∈ approx z →
∀ (k : ℕ),
let i := iterate' c z rs k n;
let w' := (f' 2 c')^[i.n - k] z';
k ≤ i.n ∧ w' ∈ approx i.z ∧ (i.exit = Exit.large → rs' < Comp... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Render/Iterate.lean | iterate'_correct | [53, 1] | [91, 16] | generalize hz2 : zr2.lo.add zi2.lo false = z2 | case succ
c : Box
rs : Floating
c' : ℂ
rs' : ℝ
cm : c' ∈ approx c
rsn : rs ≠ nan
rsm : rs' ≤ rs.val
n : ℕ
h :
∀ {z : Box} {z' : ℂ},
z' ∈ approx z →
∀ (k : ℕ),
let i := iterate' c z rs k n;
let w' := (f' 2 c')^[i.n - k] z';
k ≤ i.n ∧ w' ∈ approx i.z ∧ (i.exit = Exit.large → rs' < Comp... | case succ
c : Box
rs : Floating
c' : ℂ
rs' : ℝ
cm : c' ∈ approx c
rsn : rs ≠ nan
rsm : rs' ≤ rs.val
n : ℕ
h :
∀ {z : Box} {z' : ℂ},
z' ∈ approx z →
∀ (k : ℕ),
let i := iterate' c z rs k n;
let w' := (f' 2 c')^[i.n - k] z';
k ≤ i.n ∧ w' ∈ approx i.z ∧ (i.exit = Exit.large → rs' < Comp... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Render/Iterate.lean | iterate'_correct | [53, 1] | [91, 16] | generalize hw : (⟨zr2 - zi2, (z.re * z.im).scaleB 1⟩ : Box) + c = w | case succ
c : Box
rs : Floating
c' : ℂ
rs' : ℝ
cm : c' ∈ approx c
rsn : rs ≠ nan
rsm : rs' ≤ rs.val
n : ℕ
h :
∀ {z : Box} {z' : ℂ},
z' ∈ approx z →
∀ (k : ℕ),
let i := iterate' c z rs k n;
let w' := (f' 2 c')^[i.n - k] z';
k ≤ i.n ∧ w' ∈ approx i.z ∧ (i.exit = Exit.large → rs' < Comp... | case succ
c : Box
rs : Floating
c' : ℂ
rs' : ℝ
cm : c' ∈ approx c
rsn : rs ≠ nan
rsm : rs' ≤ rs.val
n : ℕ
h :
∀ {z : Box} {z' : ℂ},
z' ∈ approx z →
∀ (k : ℕ),
let i := iterate' c z rs k n;
let w' := (f' 2 c')^[i.n - k] z';
k ≤ i.n ∧ w' ∈ approx i.z ∧ (i.exit = Exit.large → rs' < Comp... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Render/Iterate.lean | iterate'_correct | [53, 1] | [91, 16] | have we : w = z.sqr + c := by rw [←hw, Box.sqr, hzr2, hzi2] | case succ
c : Box
rs : Floating
c' : ℂ
rs' : ℝ
cm : c' ∈ approx c
rsn : rs ≠ nan
rsm : rs' ≤ rs.val
n : ℕ
h :
∀ {z : Box} {z' : ℂ},
z' ∈ approx z →
∀ (k : ℕ),
let i := iterate' c z rs k n;
let w' := (f' 2 c')^[i.n - k] z';
k ≤ i.n ∧ w' ∈ approx i.z ∧ (i.exit = Exit.large → rs' < Comp... | case succ
c : Box
rs : Floating
c' : ℂ
rs' : ℝ
cm : c' ∈ approx c
rsn : rs ≠ nan
rsm : rs' ≤ rs.val
n : ℕ
h :
∀ {z : Box} {z' : ℂ},
z' ∈ approx z →
∀ (k : ℕ),
let i := iterate' c z rs k n;
let w' := (f' 2 c')^[i.n - k] z';
k ≤ i.n ∧ w' ∈ approx i.z ∧ (i.exit = Exit.large → rs' < Comp... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Render/Iterate.lean | iterate'_correct | [53, 1] | [91, 16] | have wa : f' 2 c' z' ∈ approx w := by rw [we, f']; mono | case succ
c : Box
rs : Floating
c' : ℂ
rs' : ℝ
cm : c' ∈ approx c
rsn : rs ≠ nan
rsm : rs' ≤ rs.val
n : ℕ
h :
∀ {z : Box} {z' : ℂ},
z' ∈ approx z →
∀ (k : ℕ),
let i := iterate' c z rs k n;
let w' := (f' 2 c')^[i.n - k] z';
k ≤ i.n ∧ w' ∈ approx i.z ∧ (i.exit = Exit.large → rs' < Comp... | case succ
c : Box
rs : Floating
c' : ℂ
rs' : ℝ
cm : c' ∈ approx c
rsn : rs ≠ nan
rsm : rs' ≤ rs.val
n : ℕ
h :
∀ {z : Box} {z' : ℂ},
z' ∈ approx z →
∀ (k : ℕ),
let i := iterate' c z rs k n;
let w' := (f' 2 c')^[i.n - k] z';
k ≤ i.n ∧ w' ∈ approx i.z ∧ (i.exit = Exit.large → rs' < Comp... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Render/Iterate.lean | iterate'_correct | [53, 1] | [91, 16] | generalize hw' : f' 2 c' z' = w' at wa | case succ
c : Box
rs : Floating
c' : ℂ
rs' : ℝ
cm : c' ∈ approx c
rsn : rs ≠ nan
rsm : rs' ≤ rs.val
n : ℕ
h :
∀ {z : Box} {z' : ℂ},
z' ∈ approx z →
∀ (k : ℕ),
let i := iterate' c z rs k n;
let w' := (f' 2 c')^[i.n - k] z';
k ≤ i.n ∧ w' ∈ approx i.z ∧ (i.exit = Exit.large → rs' < Comp... | case succ
c : Box
rs : Floating
c' : ℂ
rs' : ℝ
cm : c' ∈ approx c
rsn : rs ≠ nan
rsm : rs' ≤ rs.val
n : ℕ
h :
∀ {z : Box} {z' : ℂ},
z' ∈ approx z →
∀ (k : ℕ),
let i := iterate' c z rs k n;
let w' := (f' 2 c')^[i.n - k] z';
k ≤ i.n ∧ w' ∈ approx i.z ∧ (i.exit = Exit.large → rs' < Comp... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Render/Iterate.lean | iterate'_correct | [53, 1] | [91, 16] | by_cases z2n : z2 = nan | case succ
c : Box
rs : Floating
c' : ℂ
rs' : ℝ
cm : c' ∈ approx c
rsn : rs ≠ nan
rsm : rs' ≤ rs.val
n : ℕ
h :
∀ {z : Box} {z' : ℂ},
z' ∈ approx z →
∀ (k : ℕ),
let i := iterate' c z rs k n;
let w' := (f' 2 c')^[i.n - k] z';
k ≤ i.n ∧ w' ∈ approx i.z ∧ (i.exit = Exit.large → rs' < Comp... | case pos
c : Box
rs : Floating
c' : ℂ
rs' : ℝ
cm : c' ∈ approx c
rsn : rs ≠ nan
rsm : rs' ≤ rs.val
n : ℕ
h :
∀ {z : Box} {z' : ℂ},
z' ∈ approx z →
∀ (k : ℕ),
let i := iterate' c z rs k n;
let w' := (f' 2 c')^[i.n - k] z';
k ≤ i.n ∧ w' ∈ approx i.z ∧ (i.exit = Exit.large → rs' < Compl... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Render/Iterate.lean | iterate'_correct | [53, 1] | [91, 16] | by_cases rz : rs.val < z2.val | case neg
c : Box
rs : Floating
c' : ℂ
rs' : ℝ
cm : c' ∈ approx c
rsn : rs ≠ nan
rsm : rs' ≤ rs.val
n : ℕ
h :
∀ {z : Box} {z' : ℂ},
z' ∈ approx z →
∀ (k : ℕ),
let i := iterate' c z rs k n;
let w' := (f' 2 c')^[i.n - k] z';
k ≤ i.n ∧ w' ∈ approx i.z ∧ (i.exit = Exit.large → rs' < Compl... | case pos
c : Box
rs : Floating
c' : ℂ
rs' : ℝ
cm : c' ∈ approx c
rsn : rs ≠ nan
rsm : rs' ≤ rs.val
n : ℕ
h :
∀ {z : Box} {z' : ℂ},
z' ∈ approx z →
∀ (k : ℕ),
let i := iterate' c z rs k n;
let w' := (f' 2 c')^[i.n - k] z';
k ≤ i.n ∧ w' ∈ approx i.z ∧ (i.exit = Exit.large → rs' < Compl... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Render/Iterate.lean | iterate'_correct | [53, 1] | [91, 16] | rw [←hw, Box.sqr, hzr2, hzi2] | c : Box
rs : Floating
c' : ℂ
rs' : ℝ
cm : c' ∈ approx c
rsn : rs ≠ nan
rsm : rs' ≤ rs.val
n : ℕ
h :
∀ {z : Box} {z' : ℂ},
z' ∈ approx z →
∀ (k : ℕ),
let i := iterate' c z rs k n;
let w' := (f' 2 c')^[i.n - k] z';
k ≤ i.n ∧ w' ∈ approx i.z ∧ (i.exit = Exit.large → rs' < Complex.abs w'... | no goals |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Render/Iterate.lean | iterate'_correct | [53, 1] | [91, 16] | rw [we, f'] | c : Box
rs : Floating
c' : ℂ
rs' : ℝ
cm : c' ∈ approx c
rsn : rs ≠ nan
rsm : rs' ≤ rs.val
n : ℕ
h :
∀ {z : Box} {z' : ℂ},
z' ∈ approx z →
∀ (k : ℕ),
let i := iterate' c z rs k n;
let w' := (f' 2 c')^[i.n - k] z';
k ≤ i.n ∧ w' ∈ approx i.z ∧ (i.exit = Exit.large → rs' < Complex.abs w'... | c : Box
rs : Floating
c' : ℂ
rs' : ℝ
cm : c' ∈ approx c
rsn : rs ≠ nan
rsm : rs' ≤ rs.val
n : ℕ
h :
∀ {z : Box} {z' : ℂ},
z' ∈ approx z →
∀ (k : ℕ),
let i := iterate' c z rs k n;
let w' := (f' 2 c')^[i.n - k] z';
k ≤ i.n ∧ w' ∈ approx i.z ∧ (i.exit = Exit.large → rs' < Complex.abs w'... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Render/Iterate.lean | iterate'_correct | [53, 1] | [91, 16] | mono | c : Box
rs : Floating
c' : ℂ
rs' : ℝ
cm : c' ∈ approx c
rsn : rs ≠ nan
rsm : rs' ≤ rs.val
n : ℕ
h :
∀ {z : Box} {z' : ℂ},
z' ∈ approx z →
∀ (k : ℕ),
let i := iterate' c z rs k n;
let w' := (f' 2 c')^[i.n - k] z';
k ≤ i.n ∧ w' ∈ approx i.z ∧ (i.exit = Exit.large → rs' < Complex.abs w'... | no goals |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Render/Iterate.lean | iterate'_correct | [53, 1] | [91, 16] | simpa only [z2n, ite_true, le_refl, ge_iff_le, tsub_eq_zero_of_le, Function.iterate_zero,
id_eq, IsEmpty.forall_iff, and_true, true_and] | case pos
c : Box
rs : Floating
c' : ℂ
rs' : ℝ
cm : c' ∈ approx c
rsn : rs ≠ nan
rsm : rs' ≤ rs.val
n : ℕ
h :
∀ {z : Box} {z' : ℂ},
z' ∈ approx z →
∀ (k : ℕ),
let i := iterate' c z rs k n;
let w' := (f' 2 c')^[i.n - k] z';
k ≤ i.n ∧ w' ∈ approx i.z ∧ (i.exit = Exit.large → rs' < Compl... | no goals |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Render/Iterate.lean | iterate'_correct | [53, 1] | [91, 16] | simp only [z2n, rz, ite_true, le_refl, ge_iff_le, tsub_eq_zero_of_le, Function.iterate_zero,
id_eq, zm, forall_true_left, true_and, Complex.abs_def,
Real.sq_sqrt (Complex.normSq_nonneg _), if_false] | case pos
c : Box
rs : Floating
c' : ℂ
rs' : ℝ
cm : c' ∈ approx c
rsn : rs ≠ nan
rsm : rs' ≤ rs.val
n : ℕ
h :
∀ {z : Box} {z' : ℂ},
z' ∈ approx z →
∀ (k : ℕ),
let i := iterate' c z rs k n;
let w' := (f' 2 c')^[i.n - k] z';
k ≤ i.n ∧ w' ∈ approx i.z ∧ (i.exit = Exit.large → rs' < Compl... | case pos
c : Box
rs : Floating
c' : ℂ
rs' : ℝ
cm : c' ∈ approx c
rsn : rs ≠ nan
rsm : rs' ≤ rs.val
n : ℕ
h :
∀ {z : Box} {z' : ℂ},
z' ∈ approx z →
∀ (k : ℕ),
let i := iterate' c z rs k n;
let w' := (f' 2 c')^[i.n - k] z';
k ≤ i.n ∧ w' ∈ approx i.z ∧ (i.exit = Exit.large → rs' < Compl... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Render/Iterate.lean | iterate'_correct | [53, 1] | [91, 16] | refine lt_of_le_of_lt rsm (lt_of_lt_of_le rz ?_) | case pos
c : Box
rs : Floating
c' : ℂ
rs' : ℝ
cm : c' ∈ approx c
rsn : rs ≠ nan
rsm : rs' ≤ rs.val
n : ℕ
h :
∀ {z : Box} {z' : ℂ},
z' ∈ approx z →
∀ (k : ℕ),
let i := iterate' c z rs k n;
let w' := (f' 2 c')^[i.n - k] z';
k ≤ i.n ∧ w' ∈ approx i.z ∧ (i.exit = Exit.large → rs' < Compl... | case pos
c : Box
rs : Floating
c' : ℂ
rs' : ℝ
cm : c' ∈ approx c
rsn : rs ≠ nan
rsm : rs' ≤ rs.val
n : ℕ
h :
∀ {z : Box} {z' : ℂ},
z' ∈ approx z →
∀ (k : ℕ),
let i := iterate' c z rs k n;
let w' := (f' 2 c')^[i.n - k] z';
k ≤ i.n ∧ w' ∈ approx i.z ∧ (i.exit = Exit.large → rs' < Compl... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Render/Iterate.lean | iterate'_correct | [53, 1] | [91, 16] | simp only [Complex.normSq_apply, ←sq, ←hz2, ←hzr2, ←hzi2] at z2n ⊢ | case pos
c : Box
rs : Floating
c' : ℂ
rs' : ℝ
cm : c' ∈ approx c
rsn : rs ≠ nan
rsm : rs' ≤ rs.val
n : ℕ
h :
∀ {z : Box} {z' : ℂ},
z' ∈ approx z →
∀ (k : ℕ),
let i := iterate' c z rs k n;
let w' := (f' 2 c')^[i.n - k] z';
k ≤ i.n ∧ w' ∈ approx i.z ∧ (i.exit = Exit.large → rs' < Compl... | case pos
c : Box
rs : Floating
c' : ℂ
rs' : ℝ
cm : c' ∈ approx c
rsn : rs ≠ nan
rsm : rs' ≤ rs.val
n : ℕ
h :
∀ {z : Box} {z' : ℂ},
z' ∈ approx z →
∀ (k : ℕ),
let i := iterate' c z rs k n;
let w' := (f' 2 c')^[i.n - k] z';
k ≤ i.n ∧ w' ∈ approx i.z ∧ (i.exit = Exit.large → rs' < Compl... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Render/Iterate.lean | iterate'_correct | [53, 1] | [91, 16] | rcases Floating.ne_nan_of_add z2n with ⟨nr, ni⟩ | case pos
c : Box
rs : Floating
c' : ℂ
rs' : ℝ
cm : c' ∈ approx c
rsn : rs ≠ nan
rsm : rs' ≤ rs.val
n : ℕ
h :
∀ {z : Box} {z' : ℂ},
z' ∈ approx z →
∀ (k : ℕ),
let i := iterate' c z rs k n;
let w' := (f' 2 c')^[i.n - k] z';
k ≤ i.n ∧ w' ∈ approx i.z ∧ (i.exit = Exit.large → rs' < Compl... | case pos.intro
c : Box
rs : Floating
c' : ℂ
rs' : ℝ
cm : c' ∈ approx c
rsn : rs ≠ nan
rsm : rs' ≤ rs.val
n : ℕ
h :
∀ {z : Box} {z' : ℂ},
z' ∈ approx z →
∀ (k : ℕ),
let i := iterate' c z rs k n;
let w' := (f' 2 c')^[i.n - k] z';
k ≤ i.n ∧ w' ∈ approx i.z ∧ (i.exit = Exit.large → rs' <... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Render/Iterate.lean | iterate'_correct | [53, 1] | [91, 16] | simp only [ne_eq, Interval.lo_eq_nan] at nr ni | case pos.intro
c : Box
rs : Floating
c' : ℂ
rs' : ℝ
cm : c' ∈ approx c
rsn : rs ≠ nan
rsm : rs' ≤ rs.val
n : ℕ
h :
∀ {z : Box} {z' : ℂ},
z' ∈ approx z →
∀ (k : ℕ),
let i := iterate' c z rs k n;
let w' := (f' 2 c')^[i.n - k] z';
k ≤ i.n ∧ w' ∈ approx i.z ∧ (i.exit = Exit.large → rs' <... | case pos.intro
c : Box
rs : Floating
c' : ℂ
rs' : ℝ
cm : c' ∈ approx c
rsn : rs ≠ nan
rsm : rs' ≤ rs.val
n : ℕ
h :
∀ {z : Box} {z' : ℂ},
z' ∈ approx z →
∀ (k : ℕ),
let i := iterate' c z rs k n;
let w' := (f' 2 c')^[i.n - k] z';
k ≤ i.n ∧ w' ∈ approx i.z ∧ (i.exit = Exit.large → rs' <... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Render/Iterate.lean | iterate'_correct | [53, 1] | [91, 16] | refine le_trans (Floating.add_le z2n) (add_le_add ?_ ?_) | case pos.intro
c : Box
rs : Floating
c' : ℂ
rs' : ℝ
cm : c' ∈ approx c
rsn : rs ≠ nan
rsm : rs' ≤ rs.val
n : ℕ
h :
∀ {z : Box} {z' : ℂ},
z' ∈ approx z →
∀ (k : ℕ),
let i := iterate' c z rs k n;
let w' := (f' 2 c')^[i.n - k] z';
k ≤ i.n ∧ w' ∈ approx i.z ∧ (i.exit = Exit.large → rs' <... | case pos.intro.refine_1
c : Box
rs : Floating
c' : ℂ
rs' : ℝ
cm : c' ∈ approx c
rsn : rs ≠ nan
rsm : rs' ≤ rs.val
n : ℕ
h :
∀ {z : Box} {z' : ℂ},
z' ∈ approx z →
∀ (k : ℕ),
let i := iterate' c z rs k n;
let w' := (f' 2 c')^[i.n - k] z';
k ≤ i.n ∧ w' ∈ approx i.z ∧ (i.exit = Exit.larg... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Render/Iterate.lean | iterate'_correct | [53, 1] | [91, 16] | apply Interval.lo_le nr | case pos.intro.refine_1
c : Box
rs : Floating
c' : ℂ
rs' : ℝ
cm : c' ∈ approx c
rsn : rs ≠ nan
rsm : rs' ≤ rs.val
n : ℕ
h :
∀ {z : Box} {z' : ℂ},
z' ∈ approx z →
∀ (k : ℕ),
let i := iterate' c z rs k n;
let w' := (f' 2 c')^[i.n - k] z';
k ≤ i.n ∧ w' ∈ approx i.z ∧ (i.exit = Exit.larg... | case pos.intro.refine_1
c : Box
rs : Floating
c' : ℂ
rs' : ℝ
cm : c' ∈ approx c
rsn : rs ≠ nan
rsm : rs' ≤ rs.val
n : ℕ
h :
∀ {z : Box} {z' : ℂ},
z' ∈ approx z →
∀ (k : ℕ),
let i := iterate' c z rs k n;
let w' := (f' 2 c')^[i.n - k] z';
k ≤ i.n ∧ w' ∈ approx i.z ∧ (i.exit = Exit.larg... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Render/Iterate.lean | iterate'_correct | [53, 1] | [91, 16] | mono | case pos.intro.refine_1
c : Box
rs : Floating
c' : ℂ
rs' : ℝ
cm : c' ∈ approx c
rsn : rs ≠ nan
rsm : rs' ≤ rs.val
n : ℕ
h :
∀ {z : Box} {z' : ℂ},
z' ∈ approx z →
∀ (k : ℕ),
let i := iterate' c z rs k n;
let w' := (f' 2 c')^[i.n - k] z';
k ≤ i.n ∧ w' ∈ approx i.z ∧ (i.exit = Exit.larg... | no goals |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Render/Iterate.lean | iterate'_correct | [53, 1] | [91, 16] | apply Interval.lo_le ni | case pos.intro.refine_2
c : Box
rs : Floating
c' : ℂ
rs' : ℝ
cm : c' ∈ approx c
rsn : rs ≠ nan
rsm : rs' ≤ rs.val
n : ℕ
h :
∀ {z : Box} {z' : ℂ},
z' ∈ approx z →
∀ (k : ℕ),
let i := iterate' c z rs k n;
let w' := (f' 2 c')^[i.n - k] z';
k ≤ i.n ∧ w' ∈ approx i.z ∧ (i.exit = Exit.larg... | case pos.intro.refine_2
c : Box
rs : Floating
c' : ℂ
rs' : ℝ
cm : c' ∈ approx c
rsn : rs ≠ nan
rsm : rs' ≤ rs.val
n : ℕ
h :
∀ {z : Box} {z' : ℂ},
z' ∈ approx z →
∀ (k : ℕ),
let i := iterate' c z rs k n;
let w' := (f' 2 c')^[i.n - k] z';
k ≤ i.n ∧ w' ∈ approx i.z ∧ (i.exit = Exit.larg... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Render/Iterate.lean | iterate'_correct | [53, 1] | [91, 16] | mono | case pos.intro.refine_2
c : Box
rs : Floating
c' : ℂ
rs' : ℝ
cm : c' ∈ approx c
rsn : rs ≠ nan
rsm : rs' ≤ rs.val
n : ℕ
h :
∀ {z : Box} {z' : ℂ},
z' ∈ approx z →
∀ (k : ℕ),
let i := iterate' c z rs k n;
let w' := (f' 2 c')^[i.n - k] z';
k ≤ i.n ∧ w' ∈ approx i.z ∧ (i.exit = Exit.larg... | no goals |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Render/Iterate.lean | iterate'_correct | [53, 1] | [91, 16] | simp only [rz, ite_false, z2n] | case neg
c : Box
rs : Floating
c' : ℂ
rs' : ℝ
cm : c' ∈ approx c
rsn : rs ≠ nan
rsm : rs' ≤ rs.val
n : ℕ
h :
∀ {z : Box} {z' : ℂ},
z' ∈ approx z →
∀ (k : ℕ),
let i := iterate' c z rs k n;
let w' := (f' 2 c')^[i.n - k] z';
k ≤ i.n ∧ w' ∈ approx i.z ∧ (i.exit = Exit.large → rs' < Compl... | case neg
c : Box
rs : Floating
c' : ℂ
rs' : ℝ
cm : c' ∈ approx c
rsn : rs ≠ nan
rsm : rs' ≤ rs.val
n : ℕ
h :
∀ {z : Box} {z' : ℂ},
z' ∈ approx z →
∀ (k : ℕ),
let i := iterate' c z rs k n;
let w' := (f' 2 c')^[i.n - k] z';
k ≤ i.n ∧ w' ∈ approx i.z ∧ (i.exit = Exit.large → rs' < Compl... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Render/Iterate.lean | iterate'_correct | [53, 1] | [91, 16] | generalize hi : iterate' c w rs (k + 1) n = i | case neg
c : Box
rs : Floating
c' : ℂ
rs' : ℝ
cm : c' ∈ approx c
rsn : rs ≠ nan
rsm : rs' ≤ rs.val
n : ℕ
h :
∀ {z : Box} {z' : ℂ},
z' ∈ approx z →
∀ (k : ℕ),
let i := iterate' c z rs k n;
let w' := (f' 2 c')^[i.n - k] z';
k ≤ i.n ∧ w' ∈ approx i.z ∧ (i.exit = Exit.large → rs' < Compl... | case neg
c : Box
rs : Floating
c' : ℂ
rs' : ℝ
cm : c' ∈ approx c
rsn : rs ≠ nan
rsm : rs' ≤ rs.val
n : ℕ
h :
∀ {z : Box} {z' : ℂ},
z' ∈ approx z →
∀ (k : ℕ),
let i := iterate' c z rs k n;
let w' := (f' 2 c')^[i.n - k] z';
k ≤ i.n ∧ w' ∈ approx i.z ∧ (i.exit = Exit.large → rs' < Compl... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Render/Iterate.lean | iterate'_correct | [53, 1] | [91, 16] | specialize h wa (k+1) | case neg
c : Box
rs : Floating
c' : ℂ
rs' : ℝ
cm : c' ∈ approx c
rsn : rs ≠ nan
rsm : rs' ≤ rs.val
n : ℕ
h :
∀ {z : Box} {z' : ℂ},
z' ∈ approx z →
∀ (k : ℕ),
let i := iterate' c z rs k n;
let w' := (f' 2 c')^[i.n - k] z';
k ≤ i.n ∧ w' ∈ approx i.z ∧ (i.exit = Exit.large → rs' < Compl... | case neg
c : Box
rs : Floating
c' : ℂ
rs' : ℝ
cm : c' ∈ approx c
rsn : rs ≠ nan
rsm : rs' ≤ rs.val
n : ℕ
z : Box
z' : ℂ
zm : z' ∈ approx z
k : ℕ
zr2 : Interval
hzr2 : z.re.sqr = zr2
zi2 : Interval
hzi2 : z.im.sqr = zi2
z2 : Floating
hz2 : zr2.lo.add zi2.lo false = z2
w : Box
hw : { re := zr2 - zi2, im := (z.re * z.im).... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Render/Iterate.lean | iterate'_correct | [53, 1] | [91, 16] | simp only [hi] at h | case neg
c : Box
rs : Floating
c' : ℂ
rs' : ℝ
cm : c' ∈ approx c
rsn : rs ≠ nan
rsm : rs' ≤ rs.val
n : ℕ
z : Box
z' : ℂ
zm : z' ∈ approx z
k : ℕ
zr2 : Interval
hzr2 : z.re.sqr = zr2
zi2 : Interval
hzi2 : z.im.sqr = zi2
z2 : Floating
hz2 : zr2.lo.add zi2.lo false = z2
w : Box
hw : { re := zr2 - zi2, im := (z.re * z.im).... | case neg
c : Box
rs : Floating
c' : ℂ
rs' : ℝ
cm : c' ∈ approx c
rsn : rs ≠ nan
rsm : rs' ≤ rs.val
n : ℕ
z : Box
z' : ℂ
zm : z' ∈ approx z
k : ℕ
zr2 : Interval
hzr2 : z.re.sqr = zr2
zi2 : Interval
hzi2 : z.im.sqr = zi2
z2 : Floating
hz2 : zr2.lo.add zi2.lo false = z2
w : Box
hw : { re := zr2 - zi2, im := (z.re * z.im).... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Render/Iterate.lean | iterate'_correct | [53, 1] | [91, 16] | refine ⟨by omega, ?_⟩ | case neg
c : Box
rs : Floating
c' : ℂ
rs' : ℝ
cm : c' ∈ approx c
rsn : rs ≠ nan
rsm : rs' ≤ rs.val
n : ℕ
z : Box
z' : ℂ
zm : z' ∈ approx z
k : ℕ
zr2 : Interval
hzr2 : z.re.sqr = zr2
zi2 : Interval
hzi2 : z.im.sqr = zi2
z2 : Floating
hz2 : zr2.lo.add zi2.lo false = z2
w : Box
hw : { re := zr2 - zi2, im := (z.re * z.im).... | case neg
c : Box
rs : Floating
c' : ℂ
rs' : ℝ
cm : c' ∈ approx c
rsn : rs ≠ nan
rsm : rs' ≤ rs.val
n : ℕ
z : Box
z' : ℂ
zm : z' ∈ approx z
k : ℕ
zr2 : Interval
hzr2 : z.re.sqr = zr2
zi2 : Interval
hzi2 : z.im.sqr = zi2
z2 : Floating
hz2 : zr2.lo.add zi2.lo false = z2
w : Box
hw : { re := zr2 - zi2, im := (z.re * z.im).... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Render/Iterate.lean | iterate'_correct | [53, 1] | [91, 16] | have ie : i.n - k = (i.n - (k + 1)) + 1 := by omega | case neg
c : Box
rs : Floating
c' : ℂ
rs' : ℝ
cm : c' ∈ approx c
rsn : rs ≠ nan
rsm : rs' ≤ rs.val
n : ℕ
z : Box
z' : ℂ
zm : z' ∈ approx z
k : ℕ
zr2 : Interval
hzr2 : z.re.sqr = zr2
zi2 : Interval
hzi2 : z.im.sqr = zi2
z2 : Floating
hz2 : zr2.lo.add zi2.lo false = z2
w : Box
hw : { re := zr2 - zi2, im := (z.re * z.im).... | case neg
c : Box
rs : Floating
c' : ℂ
rs' : ℝ
cm : c' ∈ approx c
rsn : rs ≠ nan
rsm : rs' ≤ rs.val
n : ℕ
z : Box
z' : ℂ
zm : z' ∈ approx z
k : ℕ
zr2 : Interval
hzr2 : z.re.sqr = zr2
zi2 : Interval
hzi2 : z.im.sqr = zi2
z2 : Floating
hz2 : zr2.lo.add zi2.lo false = z2
w : Box
hw : { re := zr2 - zi2, im := (z.re * z.im).... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Render/Iterate.lean | iterate'_correct | [53, 1] | [91, 16] | rw [ie, Function.iterate_succ_apply, hw'] | case neg
c : Box
rs : Floating
c' : ℂ
rs' : ℝ
cm : c' ∈ approx c
rsn : rs ≠ nan
rsm : rs' ≤ rs.val
n : ℕ
z : Box
z' : ℂ
zm : z' ∈ approx z
k : ℕ
zr2 : Interval
hzr2 : z.re.sqr = zr2
zi2 : Interval
hzi2 : z.im.sqr = zi2
z2 : Floating
hz2 : zr2.lo.add zi2.lo false = z2
w : Box
hw : { re := zr2 - zi2, im := (z.re * z.im).... | case neg
c : Box
rs : Floating
c' : ℂ
rs' : ℝ
cm : c' ∈ approx c
rsn : rs ≠ nan
rsm : rs' ≤ rs.val
n : ℕ
z : Box
z' : ℂ
zm : z' ∈ approx z
k : ℕ
zr2 : Interval
hzr2 : z.re.sqr = zr2
zi2 : Interval
hzi2 : z.im.sqr = zi2
z2 : Floating
hz2 : zr2.lo.add zi2.lo false = z2
w : Box
hw : { re := zr2 - zi2, im := (z.re * z.im).... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Render/Iterate.lean | iterate'_correct | [53, 1] | [91, 16] | exact h.2 | case neg
c : Box
rs : Floating
c' : ℂ
rs' : ℝ
cm : c' ∈ approx c
rsn : rs ≠ nan
rsm : rs' ≤ rs.val
n : ℕ
z : Box
z' : ℂ
zm : z' ∈ approx z
k : ℕ
zr2 : Interval
hzr2 : z.re.sqr = zr2
zi2 : Interval
hzi2 : z.im.sqr = zi2
z2 : Floating
hz2 : zr2.lo.add zi2.lo false = z2
w : Box
hw : { re := zr2 - zi2, im := (z.re * z.im).... | no goals |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Render/Iterate.lean | iterate'_correct | [53, 1] | [91, 16] | omega | c : Box
rs : Floating
c' : ℂ
rs' : ℝ
cm : c' ∈ approx c
rsn : rs ≠ nan
rsm : rs' ≤ rs.val
n : ℕ
z : Box
z' : ℂ
zm : z' ∈ approx z
k : ℕ
zr2 : Interval
hzr2 : z.re.sqr = zr2
zi2 : Interval
hzi2 : z.im.sqr = zi2
z2 : Floating
hz2 : zr2.lo.add zi2.lo false = z2
w : Box
hw : { re := zr2 - zi2, im := (z.re * z.im).scaleB 1 ... | no goals |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Render/Iterate.lean | iterate'_correct | [53, 1] | [91, 16] | omega | c : Box
rs : Floating
c' : ℂ
rs' : ℝ
cm : c' ∈ approx c
rsn : rs ≠ nan
rsm : rs' ≤ rs.val
n : ℕ
z : Box
z' : ℂ
zm : z' ∈ approx z
k : ℕ
zr2 : Interval
hzr2 : z.re.sqr = zr2
zi2 : Interval
hzi2 : z.im.sqr = zi2
z2 : Floating
hz2 : zr2.lo.add zi2.lo false = z2
w : Box
hw : { re := zr2 - zi2, im := (z.re * z.im).scaleB 1 ... | no goals |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Render/Iterate.lean | mem_approx_iterate | [93, 1] | [101, 59] | rw [iterate] | c z : Box
rs : Floating
c' z' : ℂ
cm : c' ∈ approx c
zm : z' ∈ approx z
n : ℕ
⊢ (f' 2 c')^[(iterate c z rs n).n] z' ∈ approx (iterate c z rs n).z | c z : Box
rs : Floating
c' z' : ℂ
cm : c' ∈ approx c
zm : z' ∈ approx z
n : ℕ
⊢ (f' 2 c')^[(if rs = nan then { z := z, n := 0, exit := Exit.nan } else iterate' c z rs 0 n).n] z' ∈
approx (if rs = nan then { z := z, n := 0, exit := Exit.nan } else iterate' c z rs 0 n).z |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Render/Iterate.lean | mem_approx_iterate | [93, 1] | [101, 59] | by_cases rsn : rs = nan | c z : Box
rs : Floating
c' z' : ℂ
cm : c' ∈ approx c
zm : z' ∈ approx z
n : ℕ
⊢ (f' 2 c')^[(if rs = nan then { z := z, n := 0, exit := Exit.nan } else iterate' c z rs 0 n).n] z' ∈
approx (if rs = nan then { z := z, n := 0, exit := Exit.nan } else iterate' c z rs 0 n).z | case pos
c z : Box
rs : Floating
c' z' : ℂ
cm : c' ∈ approx c
zm : z' ∈ approx z
n : ℕ
rsn : rs = nan
⊢ (f' 2 c')^[(if rs = nan then { z := z, n := 0, exit := Exit.nan } else iterate' c z rs 0 n).n] z' ∈
approx (if rs = nan then { z := z, n := 0, exit := Exit.nan } else iterate' c z rs 0 n).z
case neg
c z : Box
rs... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Render/Iterate.lean | mem_approx_iterate | [93, 1] | [101, 59] | simpa only [rsn, ite_true, Function.iterate_zero, id_eq] | case pos
c z : Box
rs : Floating
c' z' : ℂ
cm : c' ∈ approx c
zm : z' ∈ approx z
n : ℕ
rsn : rs = nan
⊢ (f' 2 c')^[(if rs = nan then { z := z, n := 0, exit := Exit.nan } else iterate' c z rs 0 n).n] z' ∈
approx (if rs = nan then { z := z, n := 0, exit := Exit.nan } else iterate' c z rs 0 n).z | no goals |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Render/Iterate.lean | mem_approx_iterate | [93, 1] | [101, 59] | simp only [rsn, ite_false] | case neg
c z : Box
rs : Floating
c' z' : ℂ
cm : c' ∈ approx c
zm : z' ∈ approx z
n : ℕ
rsn : ¬rs = nan
⊢ (f' 2 c')^[(if rs = nan then { z := z, n := 0, exit := Exit.nan } else iterate' c z rs 0 n).n] z' ∈
approx (if rs = nan then { z := z, n := 0, exit := Exit.nan } else iterate' c z rs 0 n).z | case neg
c z : Box
rs : Floating
c' z' : ℂ
cm : c' ∈ approx c
zm : z' ∈ approx z
n : ℕ
rsn : ¬rs = nan
⊢ (f' 2 c')^[(iterate' c z rs 0 n).n] z' ∈ approx (iterate' c z rs 0 n).z |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Render/Iterate.lean | mem_approx_iterate | [93, 1] | [101, 59] | exact (iterate'_correct cm zm rsn (le_refl _) 0 n).2.1 | case neg
c z : Box
rs : Floating
c' z' : ℂ
cm : c' ∈ approx c
zm : z' ∈ approx z
n : ℕ
rsn : ¬rs = nan
⊢ (f' 2 c')^[(iterate' c z rs 0 n).n] z' ∈ approx (iterate' c z rs 0 n).z | no goals |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Render/Iterate.lean | iterate_large | [103, 1] | [111, 95] | rw [iterate] at l ⊢ | c z : Box
rs : Floating
n : ℕ
c' z' : ℂ
cm : c' ∈ approx c
zm : z' ∈ approx z
l : (iterate c z rs n).exit = Exit.large
⊢ rs.val < Complex.abs ((f' 2 c')^[(iterate c z rs n).n] z') ^ 2 | c z : Box
rs : Floating
n : ℕ
c' z' : ℂ
cm : c' ∈ approx c
zm : z' ∈ approx z
l : (if rs = nan then { z := z, n := 0, exit := Exit.nan } else iterate' c z rs 0 n).exit = Exit.large
⊢ rs.val <
Complex.abs ((f' 2 c')^[(if rs = nan then { z := z, n := 0, exit := Exit.nan } else iterate' c z rs 0 n).n] z') ^ 2 |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Render/Iterate.lean | iterate_large | [103, 1] | [111, 95] | by_cases rsn : rs = nan | c z : Box
rs : Floating
n : ℕ
c' z' : ℂ
cm : c' ∈ approx c
zm : z' ∈ approx z
l : (if rs = nan then { z := z, n := 0, exit := Exit.nan } else iterate' c z rs 0 n).exit = Exit.large
⊢ rs.val <
Complex.abs ((f' 2 c')^[(if rs = nan then { z := z, n := 0, exit := Exit.nan } else iterate' c z rs 0 n).n] z') ^ 2 | case pos
c z : Box
rs : Floating
n : ℕ
c' z' : ℂ
cm : c' ∈ approx c
zm : z' ∈ approx z
l : (if rs = nan then { z := z, n := 0, exit := Exit.nan } else iterate' c z rs 0 n).exit = Exit.large
rsn : rs = nan
⊢ rs.val <
Complex.abs ((f' 2 c')^[(if rs = nan then { z := z, n := 0, exit := Exit.nan } else iterate' c z rs ... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Render/Iterate.lean | iterate_large | [103, 1] | [111, 95] | simp only [rsn, ↓reduceIte] at l | case pos
c z : Box
rs : Floating
n : ℕ
c' z' : ℂ
cm : c' ∈ approx c
zm : z' ∈ approx z
l : (if rs = nan then { z := z, n := 0, exit := Exit.nan } else iterate' c z rs 0 n).exit = Exit.large
rsn : rs = nan
⊢ rs.val <
Complex.abs ((f' 2 c')^[(if rs = nan then { z := z, n := 0, exit := Exit.nan } else iterate' c z rs ... | no goals |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Render/Iterate.lean | iterate_large | [103, 1] | [111, 95] | simp only [rsn, ite_false] at l ⊢ | case neg
c z : Box
rs : Floating
n : ℕ
c' z' : ℂ
cm : c' ∈ approx c
zm : z' ∈ approx z
l : (if rs = nan then { z := z, n := 0, exit := Exit.nan } else iterate' c z rs 0 n).exit = Exit.large
rsn : ¬rs = nan
⊢ rs.val <
Complex.abs ((f' 2 c')^[(if rs = nan then { z := z, n := 0, exit := Exit.nan } else iterate' c z rs... | case neg
c z : Box
rs : Floating
n : ℕ
c' z' : ℂ
cm : c' ∈ approx c
zm : z' ∈ approx z
rsn : ¬rs = nan
l : (iterate' c z rs 0 n).exit = Exit.large
⊢ rs.val < Complex.abs ((f' 2 c')^[(iterate' c z rs 0 n).n] z') ^ 2 |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Render/Iterate.lean | iterate_large | [103, 1] | [111, 95] | simpa only [not_lt, Nat.sub_zero] using (iterate'_correct cm zm rsn (le_refl _) 0 n).2.2 l | case neg
c z : Box
rs : Floating
n : ℕ
c' z' : ℂ
cm : c' ∈ approx c
zm : z' ∈ approx z
rsn : ¬rs = nan
l : (iterate' c z rs 0 n).exit = Exit.large
⊢ rs.val < Complex.abs ((f' 2 c')^[(iterate' c z rs 0 n).n] z') ^ 2 | no goals |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Render/Iterate.lean | iterate_nan | [113, 1] | [115, 60] | rw [iterate] | c z : Box
n : ℕ
⊢ (iterate c z nan n).exit = Exit.nan | c z : Box
n : ℕ
⊢ (if nan = nan then { z := z, n := 0, exit := Exit.nan } else iterate' c z nan 0 n).exit = Exit.nan |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Render/Iterate.lean | iterate_nan | [113, 1] | [115, 60] | simp only [ite_true, Function.iterate_zero] | c z : Box
n : ℕ
⊢ (if nan = nan then { z := z, n := 0, exit := Exit.nan } else iterate' c z nan 0 n).exit = Exit.nan | no goals |
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