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/opencompl/HOLFloat-Lean.git | 6207518be26dcfc9980a63727bd1440cdbc6bb7a | HOLFloat/Float_theorem.lean | float_greatest_e_exists | [99, 1] | [155, 12] | sorry | fmt : flformat
x : ℝ
fmt_val : format
FMT : is_valid_flformat fmt_val
hx : x ≠ 0
e1 : ℤ
hp : ↑fmt_val.r ^ e1 ≤ abs x
he1 : e1 ∈ { z | ↑fmt_val.r ^ z ≤ abs x }
⊢ BddAbove { z | ↑fmt_val.r ^ z ≤ abs x } | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
fmt : flformat
x : ℝ
fmt_val : format
FMT : is_valid_flformat fmt_val
hx : x ≠ 0
e1 : ℤ
hp : ↑fmt_val.r ^ e1 ≤ abs x
he1 : e1 ∈ { z | ↑fmt_val.r ^ z ≤ abs x }
⊢ BddAbove { z | ↑fmt_val.r ^ z ≤ abs x }
TACTIC:
|
https://github.com/opencompl/HOLFloat-Lean.git | 6207518be26dcfc9980a63727bd1440cdbc6bb7a | HOLFloat/Float_theorem.lean | float_greatest_m_exists | [165, 1] | [169, 8] | sorry | fmt : flformat
x : ℝ
m : ℤ
⊢ x ≠ 0 → greatest_m fmt x = ↑m → is_greatest_m fmt x m ∧ 1 ≤ m ∧ m < (↑fmt).r | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
fmt : flformat
x : ℝ
m : ℤ
⊢ x ≠ 0 → greatest_m fmt x = ↑m → is_greatest_m fmt x m ∧ 1 ≤ m ∧ m < (↑fmt).r
TACTIC:
|
https://github.com/opencompl/HOLFloat-Lean.git | 6207518be26dcfc9980a63727bd1440cdbc6bb7a | HOLFloat/Float_theorem.lean | is_greatest_e_exist_greatest_e | [174, 1] | [178, 8] | intro hx he | x : ℝ
fmt : flformat
e : ℤ
⊢ x ≠ 0 → is_greatest_e fmt x e → greatest_e fmt x = e | x : ℝ
fmt : flformat
e : ℤ
hx : x ≠ 0
he : is_greatest_e fmt x e
⊢ greatest_e fmt x = e | Please generate a tactic in lean4 to solve the state.
STATE:
x : ℝ
fmt : flformat
e : ℤ
⊢ x ≠ 0 → is_greatest_e fmt x e → greatest_e fmt x = e
TACTIC:
|
https://github.com/opencompl/HOLFloat-Lean.git | 6207518be26dcfc9980a63727bd1440cdbc6bb7a | HOLFloat/Float_theorem.lean | is_greatest_e_exist_greatest_e | [174, 1] | [178, 8] | simp_all only [is_greatest_e, greatest_e] | x : ℝ
fmt : flformat
e : ℤ
hx : x ≠ 0
he : is_greatest_e fmt x e
⊢ greatest_e fmt x = e | x : ℝ
fmt : flformat
e : ℤ
hx : x ≠ 0
he : ↑(↑fmt).r ^ e ≤ abs x ∧ ∀ (e' : ℤ), ↑(↑fmt).r ^ e' ≤ abs x → e' ≤ e
⊢ supₛ { z | ↑(↑fmt).r ^ z ≤ abs x } = e | Please generate a tactic in lean4 to solve the state.
STATE:
x : ℝ
fmt : flformat
e : ℤ
hx : x ≠ 0
he : is_greatest_e fmt x e
⊢ greatest_e fmt x = e
TACTIC:
|
https://github.com/opencompl/HOLFloat-Lean.git | 6207518be26dcfc9980a63727bd1440cdbc6bb7a | HOLFloat/Float_theorem.lean | is_greatest_e_exist_greatest_e | [174, 1] | [178, 8] | sorry | x : ℝ
fmt : flformat
e : ℤ
hx : x ≠ 0
he : ↑(↑fmt).r ^ e ≤ abs x ∧ ∀ (e' : ℤ), ↑(↑fmt).r ^ e' ≤ abs x → e' ≤ e
⊢ supₛ { z | ↑(↑fmt).r ^ z ≤ abs x } = e | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
x : ℝ
fmt : flformat
e : ℤ
hx : x ≠ 0
he : ↑(↑fmt).r ^ e ≤ abs x ∧ ∀ (e' : ℤ), ↑(↑fmt).r ^ e' ≤ abs x → e' ≤ e
⊢ supₛ { z | ↑(↑fmt).r ^ z ≤ abs x } = e
TACTIC:
|
https://github.com/opencompl/HOLFloat-Lean.git | 6207518be26dcfc9980a63727bd1440cdbc6bb7a | HOLFloat/Float_theorem.lean | float_normalize_real | [182, 1] | [184, 8] | intro h | fmt : flformat
x : ℝ
⊢ x < 0 → x = greatest_m fmt x * ↑(↑fmt).r ^ greatest_e fmt x + greatest_r fmt x | fmt : flformat
x : ℝ
h : x < 0
⊢ x = greatest_m fmt x * ↑(↑fmt).r ^ greatest_e fmt x + greatest_r fmt x | Please generate a tactic in lean4 to solve the state.
STATE:
fmt : flformat
x : ℝ
⊢ x < 0 → x = greatest_m fmt x * ↑(↑fmt).r ^ greatest_e fmt x + greatest_r fmt x
TACTIC:
|
https://github.com/opencompl/HOLFloat-Lean.git | 6207518be26dcfc9980a63727bd1440cdbc6bb7a | HOLFloat/Float_theorem.lean | float_normalize_real | [182, 1] | [184, 8] | sorry | fmt : flformat
x : ℝ
h : x < 0
⊢ x = greatest_m fmt x * ↑(↑fmt).r ^ greatest_e fmt x + greatest_r fmt x | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
fmt : flformat
x : ℝ
h : x < 0
⊢ x = greatest_m fmt x * ↑(↑fmt).r ^ greatest_e fmt x + greatest_r fmt x
TACTIC:
|
https://github.com/opencompl/HOLFloat-Lean.git | 6207518be26dcfc9980a63727bd1440cdbc6bb7a | HOLFloat/Float_theorem.lean | float_pow_int_eq_le | [189, 1] | [199, 13] | intro hx hm he | r : ℤ
x : ℝ
m e : ℤ
⊢ x ≠ 0 → 1 ≤ m → abs x = ↑m * ↑r ^ e → ↑r ^ e ≤ abs x | r : ℤ
x : ℝ
m e : ℤ
hx : x ≠ 0
hm : 1 ≤ m
he : abs x = ↑m * ↑r ^ e
⊢ ↑r ^ e ≤ abs x | Please generate a tactic in lean4 to solve the state.
STATE:
r : ℤ
x : ℝ
m e : ℤ
⊢ x ≠ 0 → 1 ≤ m → abs x = ↑m * ↑r ^ e → ↑r ^ e ≤ abs x
TACTIC:
|
https://github.com/opencompl/HOLFloat-Lean.git | 6207518be26dcfc9980a63727bd1440cdbc6bb7a | HOLFloat/Float_theorem.lean | float_pow_int_eq_le | [189, 1] | [199, 13] | rw [he] | r : ℤ
x : ℝ
m e : ℤ
hx : x ≠ 0
hm : 1 ≤ m
he : abs x = ↑m * ↑r ^ e
⊢ ↑r ^ e ≤ abs x | r : ℤ
x : ℝ
m e : ℤ
hx : x ≠ 0
hm : 1 ≤ m
he : abs x = ↑m * ↑r ^ e
⊢ ↑r ^ e ≤ ↑m * ↑r ^ e | Please generate a tactic in lean4 to solve the state.
STATE:
r : ℤ
x : ℝ
m e : ℤ
hx : x ≠ 0
hm : 1 ≤ m
he : abs x = ↑m * ↑r ^ e
⊢ ↑r ^ e ≤ abs x
TACTIC:
|
https://github.com/opencompl/HOLFloat-Lean.git | 6207518be26dcfc9980a63727bd1440cdbc6bb7a | HOLFloat/Float_theorem.lean | float_pow_int_eq_le | [189, 1] | [199, 13] | apply float_real_le_1_le | r : ℤ
x : ℝ
m e : ℤ
hx : x ≠ 0
hm : 1 ≤ m
he : abs x = ↑m * ↑r ^ e
⊢ ↑r ^ e ≤ ↑m * ↑r ^ e | case a
r : ℤ
x : ℝ
m e : ℤ
hx : x ≠ 0
hm : 1 ≤ m
he : abs x = ↑m * ↑r ^ e
⊢ 0 < ↑r ^ e
case a
r : ℤ
x : ℝ
m e : ℤ
hx : x ≠ 0
hm : 1 ≤ m
he : abs x = ↑m * ↑r ^ e
⊢ 1 ≤ m | Please generate a tactic in lean4 to solve the state.
STATE:
r : ℤ
x : ℝ
m e : ℤ
hx : x ≠ 0
hm : 1 ≤ m
he : abs x = ↑m * ↑r ^ e
⊢ ↑r ^ e ≤ ↑m * ↑r ^ e
TACTIC:
|
https://github.com/opencompl/HOLFloat-Lean.git | 6207518be26dcfc9980a63727bd1440cdbc6bb7a | HOLFloat/Float_theorem.lean | float_pow_int_eq_le | [189, 1] | [199, 13] | case a =>
norm_cast
suffices abs x > 0 by simp_all only [lt_self_iff_false, ne_eq, Int.cast_lt_zero, Int.one_lt_zero_le_iff, Int.cast_eq_zero, gt_iff_lt, Int.cast_pos, zero_add, zero_lt_mul_left]
simp; exact hx | r : ℤ
x : ℝ
m e : ℤ
hx : x ≠ 0
hm : 1 ≤ m
he : abs x = ↑m * ↑r ^ e
⊢ 0 < ↑r ^ e | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
r : ℤ
x : ℝ
m e : ℤ
hx : x ≠ 0
hm : 1 ≤ m
he : abs x = ↑m * ↑r ^ e
⊢ 0 < ↑r ^ e
TACTIC:
|
https://github.com/opencompl/HOLFloat-Lean.git | 6207518be26dcfc9980a63727bd1440cdbc6bb7a | HOLFloat/Float_theorem.lean | float_pow_int_eq_le | [189, 1] | [199, 13] | case a =>
exact hm | r : ℤ
x : ℝ
m e : ℤ
hx : x ≠ 0
hm : 1 ≤ m
he : abs x = ↑m * ↑r ^ e
⊢ 1 ≤ m | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
r : ℤ
x : ℝ
m e : ℤ
hx : x ≠ 0
hm : 1 ≤ m
he : abs x = ↑m * ↑r ^ e
⊢ 1 ≤ m
TACTIC:
|
https://github.com/opencompl/HOLFloat-Lean.git | 6207518be26dcfc9980a63727bd1440cdbc6bb7a | HOLFloat/Float_theorem.lean | float_pow_int_eq_le | [189, 1] | [199, 13] | suffices abs x > 0 by simp_all only [lt_self_iff_false, ne_eq, Int.cast_lt_zero, Int.one_lt_zero_le_iff, Int.cast_eq_zero, gt_iff_lt, Int.cast_pos, zero_add, zero_lt_mul_left] | r : ℤ
x : ℝ
m e : ℤ
hx : x ≠ 0
hm : 1 ≤ m
he : abs x = ↑m * ↑r ^ e
⊢ 0 < ↑r ^ e | r : ℤ
x : ℝ
m e : ℤ
hx : x ≠ 0
hm : 1 ≤ m
he : abs x = ↑m * ↑r ^ e
⊢ abs x > 0 | Please generate a tactic in lean4 to solve the state.
STATE:
r : ℤ
x : ℝ
m e : ℤ
hx : x ≠ 0
hm : 1 ≤ m
he : abs x = ↑m * ↑r ^ e
⊢ 0 < ↑r ^ e
TACTIC:
|
https://github.com/opencompl/HOLFloat-Lean.git | 6207518be26dcfc9980a63727bd1440cdbc6bb7a | HOLFloat/Float_theorem.lean | float_pow_int_eq_le | [189, 1] | [199, 13] | simp | r : ℤ
x : ℝ
m e : ℤ
hx : x ≠ 0
hm : 1 ≤ m
he : abs x = ↑m * ↑r ^ e
⊢ abs x > 0 | r : ℤ
x : ℝ
m e : ℤ
hx : x ≠ 0
hm : 1 ≤ m
he : abs x = ↑m * ↑r ^ e
⊢ ¬x = 0 | Please generate a tactic in lean4 to solve the state.
STATE:
r : ℤ
x : ℝ
m e : ℤ
hx : x ≠ 0
hm : 1 ≤ m
he : abs x = ↑m * ↑r ^ e
⊢ abs x > 0
TACTIC:
|
https://github.com/opencompl/HOLFloat-Lean.git | 6207518be26dcfc9980a63727bd1440cdbc6bb7a | HOLFloat/Float_theorem.lean | float_pow_int_eq_le | [189, 1] | [199, 13] | exact hx | r : ℤ
x : ℝ
m e : ℤ
hx : x ≠ 0
hm : 1 ≤ m
he : abs x = ↑m * ↑r ^ e
⊢ ¬x = 0 | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
r : ℤ
x : ℝ
m e : ℤ
hx : x ≠ 0
hm : 1 ≤ m
he : abs x = ↑m * ↑r ^ e
⊢ ¬x = 0
TACTIC:
|
https://github.com/opencompl/HOLFloat-Lean.git | 6207518be26dcfc9980a63727bd1440cdbc6bb7a | HOLFloat/Float_theorem.lean | float_pow_int_eq_le | [189, 1] | [199, 13] | simp_all only [lt_self_iff_false, ne_eq, Int.cast_lt_zero, Int.one_lt_zero_le_iff, Int.cast_eq_zero, gt_iff_lt, Int.cast_pos, zero_add, zero_lt_mul_left] | r : ℤ
x : ℝ
m e : ℤ
hx : x ≠ 0
hm : 1 ≤ m
he : abs x = ↑m * ↑r ^ e
this : abs x > 0
⊢ 0 < ↑r ^ e | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
r : ℤ
x : ℝ
m e : ℤ
hx : x ≠ 0
hm : 1 ≤ m
he : abs x = ↑m * ↑r ^ e
this : abs x > 0
⊢ 0 < ↑r ^ e
TACTIC:
|
https://github.com/opencompl/HOLFloat-Lean.git | 6207518be26dcfc9980a63727bd1440cdbc6bb7a | HOLFloat/Float_theorem.lean | float_pow_int_eq_le | [189, 1] | [199, 13] | exact hm | r : ℤ
x : ℝ
m e : ℤ
hx : x ≠ 0
hm : 1 ≤ m
he : abs x = ↑m * ↑r ^ e
⊢ 1 ≤ m | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
r : ℤ
x : ℝ
m e : ℤ
hx : x ≠ 0
hm : 1 ≤ m
he : abs x = ↑m * ↑r ^ e
⊢ 1 ≤ m
TACTIC:
|
https://github.com/opencompl/HOLFloat-Lean.git | 6207518be26dcfc9980a63727bd1440cdbc6bb7a | HOLFloat/Float_theorem.lean | float_eq_ipow | [201, 1] | [227, 10] | intros hx hm hr he | fmt : flformat
x : ℝ
e : ℤ
m : ℝ
⊢ x ≠ 0 → 1 ≤ m → m < ↑(↑fmt).r → abs x = m * ↑(↑fmt).r ^ e → greatest_e fmt x = e ∧ greatest_m fmt x = m | fmt : flformat
x : ℝ
e : ℤ
m : ℝ
hx : x ≠ 0
hm : 1 ≤ m
hr : m < ↑(↑fmt).r
he : abs x = m * ↑(↑fmt).r ^ e
⊢ greatest_e fmt x = e ∧ greatest_m fmt x = m | Please generate a tactic in lean4 to solve the state.
STATE:
fmt : flformat
x : ℝ
e : ℤ
m : ℝ
⊢ x ≠ 0 → 1 ≤ m → m < ↑(↑fmt).r → abs x = m * ↑(↑fmt).r ^ e → greatest_e fmt x = e ∧ greatest_m fmt x = m
TACTIC:
|
https://github.com/opencompl/HOLFloat-Lean.git | 6207518be26dcfc9980a63727bd1440cdbc6bb7a | HOLFloat/Float_theorem.lean | float_eq_ipow | [201, 1] | [227, 10] | apply And.intro | fmt : flformat
x : ℝ
e : ℤ
m : ℝ
hx : x ≠ 0
hm : 1 ≤ m
hr : m < ↑(↑fmt).r
he : abs x = m * ↑(↑fmt).r ^ e
⊢ greatest_e fmt x = e ∧ greatest_m fmt x = m | case left
fmt : flformat
x : ℝ
e : ℤ
m : ℝ
hx : x ≠ 0
hm : 1 ≤ m
hr : m < ↑(↑fmt).r
he : abs x = m * ↑(↑fmt).r ^ e
⊢ greatest_e fmt x = e
case right
fmt : flformat
x : ℝ
e : ℤ
m : ℝ
hx : x ≠ 0
hm : 1 ≤ m
hr : m < ↑(↑fmt).r
he : abs x = m * ↑(↑fmt).r ^ e
⊢ greatest_m fmt x = m | Please generate a tactic in lean4 to solve the state.
STATE:
fmt : flformat
x : ℝ
e : ℤ
m : ℝ
hx : x ≠ 0
hm : 1 ≤ m
hr : m < ↑(↑fmt).r
he : abs x = m * ↑(↑fmt).r ^ e
⊢ greatest_e fmt x = e ∧ greatest_m fmt x = m
TACTIC:
|
https://github.com/opencompl/HOLFloat-Lean.git | 6207518be26dcfc9980a63727bd1440cdbc6bb7a | HOLFloat/Float_theorem.lean | float_eq_ipow | [201, 1] | [227, 10] | case left =>
rw [greatest_e]
norm_cast
simp only [he]
have H : e ∈ {z : ℤ | (fmt.val.r : ℝ) ^ z ≤ abs x} := by
rw [he]
simp [float_real_le_1_le]
norm_cast
have H₁: ∀k, k ∈ {z : ℤ | (fmt.val.r : ℝ) ^ z ≤ abs x} → k ≥ e := by
intro k hk
rw [he] at hk
simp_all [float_real_le_1_le]
norm_cast
have R_REAL_GT_1: 1 <(fmt.val.r :ℝ) := by
simp_all only [lt_self_iff_false, ne_eq, Int.one_lt_zero_le_iff, Int.cast_lt_zero, Int.cast_eq_zero, Set.mem_setOf_eq,
gt_iff_lt, float_radix_ipow_lt_0, le_mul_iff_one_le_left, ge_iff_le, flformat_radix_lt_1_real]
apply ipow_monotone_le_pow R_REAL_GT_1
sorry | fmt : flformat
x : ℝ
e : ℤ
m : ℝ
hx : x ≠ 0
hm : 1 ≤ m
hr : m < ↑(↑fmt).r
he : abs x = m * ↑(↑fmt).r ^ e
⊢ greatest_e fmt x = e | fmt : flformat
x : ℝ
e : ℤ
m : ℝ
hx : x ≠ 0
hm : 1 ≤ m
hr : m < ↑(↑fmt).r
he : abs x = m * ↑(↑fmt).r ^ e
H : e ∈ { z | ↑(↑fmt).r ^ z ≤ abs x }
H₁ : ∀ (k : ℤ), k ∈ { z | ↑(↑fmt).r ^ z ≤ abs x } → k ≥ e
⊢ supₛ { z | ↑(↑fmt).r ^ z ≤ m * ↑(↑fmt).r ^ e } = e | Please generate a tactic in lean4 to solve the state.
STATE:
fmt : flformat
x : ℝ
e : ℤ
m : ℝ
hx : x ≠ 0
hm : 1 ≤ m
hr : m < ↑(↑fmt).r
he : abs x = m * ↑(↑fmt).r ^ e
⊢ greatest_e fmt x = e
TACTIC:
|
https://github.com/opencompl/HOLFloat-Lean.git | 6207518be26dcfc9980a63727bd1440cdbc6bb7a | HOLFloat/Float_theorem.lean | float_eq_ipow | [201, 1] | [227, 10] | case right =>
rw [greatest_m]
sorry | fmt : flformat
x : ℝ
e : ℤ
m : ℝ
hx : x ≠ 0
hm : 1 ≤ m
hr : m < ↑(↑fmt).r
he : abs x = m * ↑(↑fmt).r ^ e
⊢ greatest_m fmt x = m | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
fmt : flformat
x : ℝ
e : ℤ
m : ℝ
hx : x ≠ 0
hm : 1 ≤ m
hr : m < ↑(↑fmt).r
he : abs x = m * ↑(↑fmt).r ^ e
⊢ greatest_m fmt x = m
TACTIC:
|
https://github.com/opencompl/HOLFloat-Lean.git | 6207518be26dcfc9980a63727bd1440cdbc6bb7a | HOLFloat/Float_theorem.lean | float_eq_ipow | [201, 1] | [227, 10] | rw [greatest_e] | fmt : flformat
x : ℝ
e : ℤ
m : ℝ
hx : x ≠ 0
hm : 1 ≤ m
hr : m < ↑(↑fmt).r
he : abs x = m * ↑(↑fmt).r ^ e
⊢ greatest_e fmt x = e | fmt : flformat
x : ℝ
e : ℤ
m : ℝ
hx : x ≠ 0
hm : 1 ≤ m
hr : m < ↑(↑fmt).r
he : abs x = m * ↑(↑fmt).r ^ e
⊢ supₛ { z | ↑(↑fmt).r ^ z ≤ abs x } = e | Please generate a tactic in lean4 to solve the state.
STATE:
fmt : flformat
x : ℝ
e : ℤ
m : ℝ
hx : x ≠ 0
hm : 1 ≤ m
hr : m < ↑(↑fmt).r
he : abs x = m * ↑(↑fmt).r ^ e
⊢ greatest_e fmt x = e
TACTIC:
|
https://github.com/opencompl/HOLFloat-Lean.git | 6207518be26dcfc9980a63727bd1440cdbc6bb7a | HOLFloat/Float_theorem.lean | float_eq_ipow | [201, 1] | [227, 10] | simp only [he] | fmt : flformat
x : ℝ
e : ℤ
m : ℝ
hx : x ≠ 0
hm : 1 ≤ m
hr : m < ↑(↑fmt).r
he : abs x = m * ↑(↑fmt).r ^ e
⊢ supₛ { z | ↑(↑fmt).r ^ z ≤ abs x } = e | fmt : flformat
x : ℝ
e : ℤ
m : ℝ
hx : x ≠ 0
hm : 1 ≤ m
hr : m < ↑(↑fmt).r
he : abs x = m * ↑(↑fmt).r ^ e
⊢ supₛ { z | ↑(↑fmt).r ^ z ≤ m * ↑(↑fmt).r ^ e } = e | Please generate a tactic in lean4 to solve the state.
STATE:
fmt : flformat
x : ℝ
e : ℤ
m : ℝ
hx : x ≠ 0
hm : 1 ≤ m
hr : m < ↑(↑fmt).r
he : abs x = m * ↑(↑fmt).r ^ e
⊢ supₛ { z | ↑(↑fmt).r ^ z ≤ abs x } = e
TACTIC:
|
https://github.com/opencompl/HOLFloat-Lean.git | 6207518be26dcfc9980a63727bd1440cdbc6bb7a | HOLFloat/Float_theorem.lean | float_eq_ipow | [201, 1] | [227, 10] | have H : e ∈ {z : ℤ | (fmt.val.r : ℝ) ^ z ≤ abs x} := by
rw [he]
simp [float_real_le_1_le]
norm_cast | fmt : flformat
x : ℝ
e : ℤ
m : ℝ
hx : x ≠ 0
hm : 1 ≤ m
hr : m < ↑(↑fmt).r
he : abs x = m * ↑(↑fmt).r ^ e
⊢ supₛ { z | ↑(↑fmt).r ^ z ≤ m * ↑(↑fmt).r ^ e } = e | fmt : flformat
x : ℝ
e : ℤ
m : ℝ
hx : x ≠ 0
hm : 1 ≤ m
hr : m < ↑(↑fmt).r
he : abs x = m * ↑(↑fmt).r ^ e
H : e ∈ { z | ↑(↑fmt).r ^ z ≤ abs x }
⊢ supₛ { z | ↑(↑fmt).r ^ z ≤ m * ↑(↑fmt).r ^ e } = e | Please generate a tactic in lean4 to solve the state.
STATE:
fmt : flformat
x : ℝ
e : ℤ
m : ℝ
hx : x ≠ 0
hm : 1 ≤ m
hr : m < ↑(↑fmt).r
he : abs x = m * ↑(↑fmt).r ^ e
⊢ supₛ { z | ↑(↑fmt).r ^ z ≤ m * ↑(↑fmt).r ^ e } = e
TACTIC:
|
https://github.com/opencompl/HOLFloat-Lean.git | 6207518be26dcfc9980a63727bd1440cdbc6bb7a | HOLFloat/Float_theorem.lean | float_eq_ipow | [201, 1] | [227, 10] | have H₁: ∀k, k ∈ {z : ℤ | (fmt.val.r : ℝ) ^ z ≤ abs x} → k ≥ e := by
intro k hk
rw [he] at hk
simp_all [float_real_le_1_le]
norm_cast
have R_REAL_GT_1: 1 <(fmt.val.r :ℝ) := by
simp_all only [lt_self_iff_false, ne_eq, Int.one_lt_zero_le_iff, Int.cast_lt_zero, Int.cast_eq_zero, Set.mem_setOf_eq,
gt_iff_lt, float_radix_ipow_lt_0, le_mul_iff_one_le_left, ge_iff_le, flformat_radix_lt_1_real]
apply ipow_monotone_le_pow R_REAL_GT_1
sorry | fmt : flformat
x : ℝ
e : ℤ
m : ℝ
hx : x ≠ 0
hm : 1 ≤ m
hr : m < ↑(↑fmt).r
he : abs x = m * ↑(↑fmt).r ^ e
H : e ∈ { z | ↑(↑fmt).r ^ z ≤ abs x }
⊢ supₛ { z | ↑(↑fmt).r ^ z ≤ m * ↑(↑fmt).r ^ e } = e | fmt : flformat
x : ℝ
e : ℤ
m : ℝ
hx : x ≠ 0
hm : 1 ≤ m
hr : m < ↑(↑fmt).r
he : abs x = m * ↑(↑fmt).r ^ e
H : e ∈ { z | ↑(↑fmt).r ^ z ≤ abs x }
H₁ : ∀ (k : ℤ), k ∈ { z | ↑(↑fmt).r ^ z ≤ abs x } → k ≥ e
⊢ supₛ { z | ↑(↑fmt).r ^ z ≤ m * ↑(↑fmt).r ^ e } = e | Please generate a tactic in lean4 to solve the state.
STATE:
fmt : flformat
x : ℝ
e : ℤ
m : ℝ
hx : x ≠ 0
hm : 1 ≤ m
hr : m < ↑(↑fmt).r
he : abs x = m * ↑(↑fmt).r ^ e
H : e ∈ { z | ↑(↑fmt).r ^ z ≤ abs x }
⊢ supₛ { z | ↑(↑fmt).r ^ z ≤ m * ↑(↑fmt).r ^ e } = e
TACTIC:
|
https://github.com/opencompl/HOLFloat-Lean.git | 6207518be26dcfc9980a63727bd1440cdbc6bb7a | HOLFloat/Float_theorem.lean | float_eq_ipow | [201, 1] | [227, 10] | rw [he] | fmt : flformat
x : ℝ
e : ℤ
m : ℝ
hx : x ≠ 0
hm : 1 ≤ m
hr : m < ↑(↑fmt).r
he : abs x = m * ↑(↑fmt).r ^ e
⊢ e ∈ { z | ↑(↑fmt).r ^ z ≤ abs x } | fmt : flformat
x : ℝ
e : ℤ
m : ℝ
hx : x ≠ 0
hm : 1 ≤ m
hr : m < ↑(↑fmt).r
he : abs x = m * ↑(↑fmt).r ^ e
⊢ e ∈ { z | ↑(↑fmt).r ^ z ≤ m * ↑(↑fmt).r ^ e } | Please generate a tactic in lean4 to solve the state.
STATE:
fmt : flformat
x : ℝ
e : ℤ
m : ℝ
hx : x ≠ 0
hm : 1 ≤ m
hr : m < ↑(↑fmt).r
he : abs x = m * ↑(↑fmt).r ^ e
⊢ e ∈ { z | ↑(↑fmt).r ^ z ≤ abs x }
TACTIC:
|
https://github.com/opencompl/HOLFloat-Lean.git | 6207518be26dcfc9980a63727bd1440cdbc6bb7a | HOLFloat/Float_theorem.lean | float_eq_ipow | [201, 1] | [227, 10] | simp [float_real_le_1_le] | fmt : flformat
x : ℝ
e : ℤ
m : ℝ
hx : x ≠ 0
hm : 1 ≤ m
hr : m < ↑(↑fmt).r
he : abs x = m * ↑(↑fmt).r ^ e
⊢ e ∈ { z | ↑(↑fmt).r ^ z ≤ m * ↑(↑fmt).r ^ e } | fmt : flformat
x : ℝ
e : ℤ
m : ℝ
hx : x ≠ 0
hm : 1 ≤ m
hr : m < ↑(↑fmt).r
he : abs x = m * ↑(↑fmt).r ^ e
⊢ 1 ≤ m | Please generate a tactic in lean4 to solve the state.
STATE:
fmt : flformat
x : ℝ
e : ℤ
m : ℝ
hx : x ≠ 0
hm : 1 ≤ m
hr : m < ↑(↑fmt).r
he : abs x = m * ↑(↑fmt).r ^ e
⊢ e ∈ { z | ↑(↑fmt).r ^ z ≤ m * ↑(↑fmt).r ^ e }
TACTIC:
|
https://github.com/opencompl/HOLFloat-Lean.git | 6207518be26dcfc9980a63727bd1440cdbc6bb7a | HOLFloat/Float_theorem.lean | float_eq_ipow | [201, 1] | [227, 10] | norm_cast | fmt : flformat
x : ℝ
e : ℤ
m : ℝ
hx : x ≠ 0
hm : 1 ≤ m
hr : m < ↑(↑fmt).r
he : abs x = m * ↑(↑fmt).r ^ e
⊢ 1 ≤ m | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
fmt : flformat
x : ℝ
e : ℤ
m : ℝ
hx : x ≠ 0
hm : 1 ≤ m
hr : m < ↑(↑fmt).r
he : abs x = m * ↑(↑fmt).r ^ e
⊢ 1 ≤ m
TACTIC:
|
https://github.com/opencompl/HOLFloat-Lean.git | 6207518be26dcfc9980a63727bd1440cdbc6bb7a | HOLFloat/Float_theorem.lean | float_eq_ipow | [201, 1] | [227, 10] | intro k hk | fmt : flformat
x : ℝ
e : ℤ
m : ℝ
hx : x ≠ 0
hm : 1 ≤ m
hr : m < ↑(↑fmt).r
he : abs x = m * ↑(↑fmt).r ^ e
H : e ∈ { z | ↑(↑fmt).r ^ z ≤ abs x }
⊢ ∀ (k : ℤ), k ∈ { z | ↑(↑fmt).r ^ z ≤ abs x } → k ≥ e | fmt : flformat
x : ℝ
e : ℤ
m : ℝ
hx : x ≠ 0
hm : 1 ≤ m
hr : m < ↑(↑fmt).r
he : abs x = m * ↑(↑fmt).r ^ e
H : e ∈ { z | ↑(↑fmt).r ^ z ≤ abs x }
k : ℤ
hk : k ∈ { z | ↑(↑fmt).r ^ z ≤ abs x }
⊢ k ≥ e | Please generate a tactic in lean4 to solve the state.
STATE:
fmt : flformat
x : ℝ
e : ℤ
m : ℝ
hx : x ≠ 0
hm : 1 ≤ m
hr : m < ↑(↑fmt).r
he : abs x = m * ↑(↑fmt).r ^ e
H : e ∈ { z | ↑(↑fmt).r ^ z ≤ abs x }
⊢ ∀ (k : ℤ), k ∈ { z | ↑(↑fmt).r ^ z ≤ abs x } → k ≥ e
TACTIC:
|
https://github.com/opencompl/HOLFloat-Lean.git | 6207518be26dcfc9980a63727bd1440cdbc6bb7a | HOLFloat/Float_theorem.lean | float_eq_ipow | [201, 1] | [227, 10] | rw [he] at hk | fmt : flformat
x : ℝ
e : ℤ
m : ℝ
hx : x ≠ 0
hm : 1 ≤ m
hr : m < ↑(↑fmt).r
he : abs x = m * ↑(↑fmt).r ^ e
H : e ∈ { z | ↑(↑fmt).r ^ z ≤ abs x }
k : ℤ
hk : k ∈ { z | ↑(↑fmt).r ^ z ≤ abs x }
⊢ k ≥ e | fmt : flformat
x : ℝ
e : ℤ
m : ℝ
hx : x ≠ 0
hm : 1 ≤ m
hr : m < ↑(↑fmt).r
he : abs x = m * ↑(↑fmt).r ^ e
H : e ∈ { z | ↑(↑fmt).r ^ z ≤ abs x }
k : ℤ
hk : k ∈ { z | ↑(↑fmt).r ^ z ≤ m * ↑(↑fmt).r ^ e }
⊢ k ≥ e | Please generate a tactic in lean4 to solve the state.
STATE:
fmt : flformat
x : ℝ
e : ℤ
m : ℝ
hx : x ≠ 0
hm : 1 ≤ m
hr : m < ↑(↑fmt).r
he : abs x = m * ↑(↑fmt).r ^ e
H : e ∈ { z | ↑(↑fmt).r ^ z ≤ abs x }
k : ℤ
hk : k ∈ { z | ↑(↑fmt).r ^ z ≤ abs x }
⊢ k ≥ e
TACTIC:
|
https://github.com/opencompl/HOLFloat-Lean.git | 6207518be26dcfc9980a63727bd1440cdbc6bb7a | HOLFloat/Float_theorem.lean | float_eq_ipow | [201, 1] | [227, 10] | simp_all [float_real_le_1_le] | fmt : flformat
x : ℝ
e : ℤ
m : ℝ
hx : x ≠ 0
hm : 1 ≤ m
hr : m < ↑(↑fmt).r
he : abs x = m * ↑(↑fmt).r ^ e
H : e ∈ { z | ↑(↑fmt).r ^ z ≤ abs x }
k : ℤ
hk : k ∈ { z | ↑(↑fmt).r ^ z ≤ m * ↑(↑fmt).r ^ e }
⊢ k ≥ e | fmt : flformat
x : ℝ
e : ℤ
m : ℝ
k : ℤ
hx : ¬x = 0
hm : 1 ≤ m
hr : m < ↑(↑fmt).r
he : abs x = m * ↑(↑fmt).r ^ e
hk : ↑(↑fmt).r ^ k ≤ m * ↑(↑fmt).r ^ e
⊢ e ≤ k | Please generate a tactic in lean4 to solve the state.
STATE:
fmt : flformat
x : ℝ
e : ℤ
m : ℝ
hx : x ≠ 0
hm : 1 ≤ m
hr : m < ↑(↑fmt).r
he : abs x = m * ↑(↑fmt).r ^ e
H : e ∈ { z | ↑(↑fmt).r ^ z ≤ abs x }
k : ℤ
hk : k ∈ { z | ↑(↑fmt).r ^ z ≤ m * ↑(↑fmt).r ^ e }
⊢ k ≥ e
TACTIC:
|
https://github.com/opencompl/HOLFloat-Lean.git | 6207518be26dcfc9980a63727bd1440cdbc6bb7a | HOLFloat/Float_theorem.lean | float_eq_ipow | [201, 1] | [227, 10] | have R_REAL_GT_1: 1 <(fmt.val.r :ℝ) := by
simp_all only [lt_self_iff_false, ne_eq, Int.one_lt_zero_le_iff, Int.cast_lt_zero, Int.cast_eq_zero, Set.mem_setOf_eq,
gt_iff_lt, float_radix_ipow_lt_0, le_mul_iff_one_le_left, ge_iff_le, flformat_radix_lt_1_real] | fmt : flformat
x : ℝ
e : ℤ
m : ℝ
k : ℤ
hx : ¬x = 0
hm : 1 ≤ m
hr : m < ↑(↑fmt).r
he : abs x = m * ↑(↑fmt).r ^ e
hk : ↑(↑fmt).r ^ k ≤ m * ↑(↑fmt).r ^ e
⊢ e ≤ k | fmt : flformat
x : ℝ
e : ℤ
m : ℝ
k : ℤ
hx : ¬x = 0
hm : 1 ≤ m
hr : m < ↑(↑fmt).r
he : abs x = m * ↑(↑fmt).r ^ e
hk : ↑(↑fmt).r ^ k ≤ m * ↑(↑fmt).r ^ e
R_REAL_GT_1 : 1 < ↑(↑fmt).r
⊢ e ≤ k | Please generate a tactic in lean4 to solve the state.
STATE:
fmt : flformat
x : ℝ
e : ℤ
m : ℝ
k : ℤ
hx : ¬x = 0
hm : 1 ≤ m
hr : m < ↑(↑fmt).r
he : abs x = m * ↑(↑fmt).r ^ e
hk : ↑(↑fmt).r ^ k ≤ m * ↑(↑fmt).r ^ e
⊢ e ≤ k
TACTIC:
|
https://github.com/opencompl/HOLFloat-Lean.git | 6207518be26dcfc9980a63727bd1440cdbc6bb7a | HOLFloat/Float_theorem.lean | float_eq_ipow | [201, 1] | [227, 10] | apply ipow_monotone_le_pow R_REAL_GT_1 | fmt : flformat
x : ℝ
e : ℤ
m : ℝ
k : ℤ
hx : ¬x = 0
hm : 1 ≤ m
hr : m < ↑(↑fmt).r
he : abs x = m * ↑(↑fmt).r ^ e
hk : ↑(↑fmt).r ^ k ≤ m * ↑(↑fmt).r ^ e
R_REAL_GT_1 : 1 < ↑(↑fmt).r
⊢ e ≤ k | fmt : flformat
x : ℝ
e : ℤ
m : ℝ
k : ℤ
hx : ¬x = 0
hm : 1 ≤ m
hr : m < ↑(↑fmt).r
he : abs x = m * ↑(↑fmt).r ^ e
hk : ↑(↑fmt).r ^ k ≤ m * ↑(↑fmt).r ^ e
R_REAL_GT_1 : 1 < ↑(↑fmt).r
⊢ ↑(↑fmt).r ^ e ≤ ↑(↑fmt).r ^ k | Please generate a tactic in lean4 to solve the state.
STATE:
fmt : flformat
x : ℝ
e : ℤ
m : ℝ
k : ℤ
hx : ¬x = 0
hm : 1 ≤ m
hr : m < ↑(↑fmt).r
he : abs x = m * ↑(↑fmt).r ^ e
hk : ↑(↑fmt).r ^ k ≤ m * ↑(↑fmt).r ^ e
R_REAL_GT_1 : 1 < ↑(↑fmt).r
⊢ e ≤ k
TACTIC:
|
https://github.com/opencompl/HOLFloat-Lean.git | 6207518be26dcfc9980a63727bd1440cdbc6bb7a | HOLFloat/Float_theorem.lean | float_eq_ipow | [201, 1] | [227, 10] | sorry | fmt : flformat
x : ℝ
e : ℤ
m : ℝ
k : ℤ
hx : ¬x = 0
hm : 1 ≤ m
hr : m < ↑(↑fmt).r
he : abs x = m * ↑(↑fmt).r ^ e
hk : ↑(↑fmt).r ^ k ≤ m * ↑(↑fmt).r ^ e
R_REAL_GT_1 : 1 < ↑(↑fmt).r
⊢ ↑(↑fmt).r ^ e ≤ ↑(↑fmt).r ^ k | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
fmt : flformat
x : ℝ
e : ℤ
m : ℝ
k : ℤ
hx : ¬x = 0
hm : 1 ≤ m
hr : m < ↑(↑fmt).r
he : abs x = m * ↑(↑fmt).r ^ e
hk : ↑(↑fmt).r ^ k ≤ m * ↑(↑fmt).r ^ e
R_REAL_GT_1 : 1 < ↑(↑fmt).r
⊢ ↑(↑fmt).r ^ e ≤ ↑(↑fmt).r ^ k
TACTIC:
|
https://github.com/opencompl/HOLFloat-Lean.git | 6207518be26dcfc9980a63727bd1440cdbc6bb7a | HOLFloat/Float_theorem.lean | float_eq_ipow | [201, 1] | [227, 10] | simp_all only [lt_self_iff_false, ne_eq, Int.one_lt_zero_le_iff, Int.cast_lt_zero, Int.cast_eq_zero, Set.mem_setOf_eq,
gt_iff_lt, float_radix_ipow_lt_0, le_mul_iff_one_le_left, ge_iff_le, flformat_radix_lt_1_real] | fmt : flformat
x : ℝ
e : ℤ
m : ℝ
k : ℤ
hx : ¬x = 0
hm : 1 ≤ m
hr : m < ↑(↑fmt).r
he : abs x = m * ↑(↑fmt).r ^ e
hk : ↑(↑fmt).r ^ k ≤ m * ↑(↑fmt).r ^ e
⊢ 1 < ↑(↑fmt).r | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
fmt : flformat
x : ℝ
e : ℤ
m : ℝ
k : ℤ
hx : ¬x = 0
hm : 1 ≤ m
hr : m < ↑(↑fmt).r
he : abs x = m * ↑(↑fmt).r ^ e
hk : ↑(↑fmt).r ^ k ≤ m * ↑(↑fmt).r ^ e
⊢ 1 < ↑(↑fmt).r
TACTIC:
|
https://github.com/opencompl/HOLFloat-Lean.git | 6207518be26dcfc9980a63727bd1440cdbc6bb7a | HOLFloat/Float_theorem.lean | float_eq_ipow | [201, 1] | [227, 10] | rw [greatest_m] | fmt : flformat
x : ℝ
e : ℤ
m : ℝ
hx : x ≠ 0
hm : 1 ≤ m
hr : m < ↑(↑fmt).r
he : abs x = m * ↑(↑fmt).r ^ e
⊢ greatest_m fmt x = m | fmt : flformat
x : ℝ
e : ℤ
m : ℝ
hx : x ≠ 0
hm : 1 ≤ m
hr : m < ↑(↑fmt).r
he : abs x = m * ↑(↑fmt).r ^ e
⊢ supₛ { m | m * ↑((↑fmt).r ^ greatest_e fmt x) ≤ abs x } = m | Please generate a tactic in lean4 to solve the state.
STATE:
fmt : flformat
x : ℝ
e : ℤ
m : ℝ
hx : x ≠ 0
hm : 1 ≤ m
hr : m < ↑(↑fmt).r
he : abs x = m * ↑(↑fmt).r ^ e
⊢ greatest_m fmt x = m
TACTIC:
|
https://github.com/opencompl/HOLFloat-Lean.git | 6207518be26dcfc9980a63727bd1440cdbc6bb7a | HOLFloat/Float_theorem.lean | float_eq_ipow | [201, 1] | [227, 10] | sorry | fmt : flformat
x : ℝ
e : ℤ
m : ℝ
hx : x ≠ 0
hm : 1 ≤ m
hr : m < ↑(↑fmt).r
he : abs x = m * ↑(↑fmt).r ^ e
⊢ supₛ { m | m * ↑((↑fmt).r ^ greatest_e fmt x) ≤ abs x } = m | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
fmt : flformat
x : ℝ
e : ℤ
m : ℝ
hx : x ≠ 0
hm : 1 ≤ m
hr : m < ↑(↑fmt).r
he : abs x = m * ↑(↑fmt).r ^ e
⊢ supₛ { m | m * ↑((↑fmt).r ^ greatest_e fmt x) ≤ abs x } = m
TACTIC:
|
https://github.com/opencompl/HOLFloat-Lean.git | 6207518be26dcfc9980a63727bd1440cdbc6bb7a | HOLFloat/Common.lean | Int.one_lt_zero_lt | [28, 1] | [31, 22] | intro h | i : ℤ
⊢ 1 < i → 0 < i | i : ℤ
h : 1 < i
⊢ 0 < i | Please generate a tactic in lean4 to solve the state.
STATE:
i : ℤ
⊢ 1 < i → 0 < i
TACTIC:
|
https://github.com/opencompl/HOLFloat-Lean.git | 6207518be26dcfc9980a63727bd1440cdbc6bb7a | HOLFloat/Common.lean | Int.one_lt_zero_lt | [28, 1] | [31, 22] | have hz : (0: ℤ) < 1 := by simp | i : ℤ
h : 1 < i
⊢ 0 < i | i : ℤ
h : 1 < i
hz : 0 < 1
⊢ 0 < i | Please generate a tactic in lean4 to solve the state.
STATE:
i : ℤ
h : 1 < i
⊢ 0 < i
TACTIC:
|
https://github.com/opencompl/HOLFloat-Lean.git | 6207518be26dcfc9980a63727bd1440cdbc6bb7a | HOLFloat/Common.lean | Int.one_lt_zero_lt | [28, 1] | [31, 22] | apply lt_trans hz h | i : ℤ
h : 1 < i
hz : 0 < 1
⊢ 0 < i | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
i : ℤ
h : 1 < i
hz : 0 < 1
⊢ 0 < i
TACTIC:
|
https://github.com/opencompl/HOLFloat-Lean.git | 6207518be26dcfc9980a63727bd1440cdbc6bb7a | HOLFloat/Common.lean | Int.one_lt_zero_lt | [28, 1] | [31, 22] | simp | i : ℤ
h : 1 < i
⊢ 0 < 1 | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
i : ℤ
h : 1 < i
⊢ 0 < 1
TACTIC:
|
https://github.com/opencompl/HOLFloat-Lean.git | 6207518be26dcfc9980a63727bd1440cdbc6bb7a | HOLFloat/Common.lean | Int.one_lt_zero_le_iff | [34, 1] | [39, 12] | apply Iff.intro | i j : ℤ
⊢ j < i ↔ j + 1 ≤ i | case mp
i j : ℤ
⊢ j < i → j + 1 ≤ i
case mpr
i j : ℤ
⊢ j + 1 ≤ i → j < i | Please generate a tactic in lean4 to solve the state.
STATE:
i j : ℤ
⊢ j < i ↔ j + 1 ≤ i
TACTIC:
|
https://github.com/opencompl/HOLFloat-Lean.git | 6207518be26dcfc9980a63727bd1440cdbc6bb7a | HOLFloat/Common.lean | Int.one_lt_ne_one | [42, 1] | [44, 44] | intro a_1 | a : ℤ
h : 1 < a
⊢ a ≠ 1 | a : ℤ
h : 1 < a
a_1 : a = 1
⊢ False | Please generate a tactic in lean4 to solve the state.
STATE:
a : ℤ
h : 1 < a
⊢ a ≠ 1
TACTIC:
|
https://github.com/opencompl/HOLFloat-Lean.git | 6207518be26dcfc9980a63727bd1440cdbc6bb7a | HOLFloat/Common.lean | Int.one_lt_ne_one | [42, 1] | [44, 44] | simp_all only [one_lt_zero_le_iff, ne_eq] | a : ℤ
h : 1 < a
a_1 : a = 1
⊢ False | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
a : ℤ
h : 1 < a
a_1 : a = 1
⊢ False
TACTIC:
|
https://github.com/opencompl/HOLFloat-Lean.git | 6207518be26dcfc9980a63727bd1440cdbc6bb7a | HOLFloat/Common.lean | ipow_lt_zero | [49, 1] | [57, 64] | intro h | r : ℝ
i : ℤ
⊢ 0 < r → 0 < r ^ i | r : ℝ
i : ℤ
h : 0 < r
⊢ 0 < r ^ i | Please generate a tactic in lean4 to solve the state.
STATE:
r : ℝ
i : ℤ
⊢ 0 < r → 0 < r ^ i
TACTIC:
|
https://github.com/opencompl/HOLFloat-Lean.git | 6207518be26dcfc9980a63727bd1440cdbc6bb7a | HOLFloat/Common.lean | ipow_lt_zero | [49, 1] | [57, 64] | cases i with
| ofNat n =>
simp_all only [Int.ofNat_eq_coe, zpow_coe_nat, gt_iff_lt, pow_pos]
| negSucc n =>
simp_all only [zpow_negSucc, inv_pos, gt_iff_lt, pow_pos] | r : ℝ
i : ℤ
h : 0 < r
⊢ 0 < r ^ i | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
r : ℝ
i : ℤ
h : 0 < r
⊢ 0 < r ^ i
TACTIC:
|
https://github.com/opencompl/HOLFloat-Lean.git | 6207518be26dcfc9980a63727bd1440cdbc6bb7a | HOLFloat/Common.lean | ipow_lt_zero | [49, 1] | [57, 64] | simp_all only [Int.ofNat_eq_coe, zpow_coe_nat, gt_iff_lt, pow_pos] | case ofNat
r : ℝ
h : 0 < r
n : ℕ
⊢ 0 < r ^ ofNat n | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case ofNat
r : ℝ
h : 0 < r
n : ℕ
⊢ 0 < r ^ ofNat n
TACTIC:
|
https://github.com/opencompl/HOLFloat-Lean.git | 6207518be26dcfc9980a63727bd1440cdbc6bb7a | HOLFloat/Common.lean | ipow_lt_zero | [49, 1] | [57, 64] | simp_all only [zpow_negSucc, inv_pos, gt_iff_lt, pow_pos] | case negSucc
r : ℝ
h : 0 < r
n : ℕ
⊢ 0 < r ^ -[n+1] | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case negSucc
r : ℝ
h : 0 < r
n : ℕ
⊢ 0 < r ^ -[n+1]
TACTIC:
|
https://github.com/opencompl/HOLFloat-Lean.git | 6207518be26dcfc9980a63727bd1440cdbc6bb7a | HOLFloat/Common.lean | ipow_inv | [59, 1] | [62, 27] | induction i | r : ℝ
i : ℕ
⊢ r ^ negOfNat i = (r ^ i)⁻¹ | case zero
r : ℝ
⊢ r ^ negOfNat Nat.zero = (r ^ Nat.zero)⁻¹
case succ
r : ℝ
n✝ : ℕ
n_ih✝ : r ^ negOfNat n✝ = (r ^ n✝)⁻¹
⊢ r ^ negOfNat (Nat.succ n✝) = (r ^ Nat.succ n✝)⁻¹ | Please generate a tactic in lean4 to solve the state.
STATE:
r : ℝ
i : ℕ
⊢ r ^ negOfNat i = (r ^ i)⁻¹
TACTIC:
|
https://github.com/opencompl/HOLFloat-Lean.git | 6207518be26dcfc9980a63727bd1440cdbc6bb7a | HOLFloat/Common.lean | ipow_inv | [59, 1] | [62, 27] | case zero => simp; trivial | r : ℝ
⊢ r ^ negOfNat Nat.zero = (r ^ Nat.zero)⁻¹ | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
r : ℝ
⊢ r ^ negOfNat Nat.zero = (r ^ Nat.zero)⁻¹
TACTIC:
|
https://github.com/opencompl/HOLFloat-Lean.git | 6207518be26dcfc9980a63727bd1440cdbc6bb7a | HOLFloat/Common.lean | ipow_inv | [59, 1] | [62, 27] | case succ => constructor | r : ℝ
n✝ : ℕ
n_ih✝ : r ^ negOfNat n✝ = (r ^ n✝)⁻¹
⊢ r ^ negOfNat (Nat.succ n✝) = (r ^ Nat.succ n✝)⁻¹ | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
r : ℝ
n✝ : ℕ
n_ih✝ : r ^ negOfNat n✝ = (r ^ n✝)⁻¹
⊢ r ^ negOfNat (Nat.succ n✝) = (r ^ Nat.succ n✝)⁻¹
TACTIC:
|
https://github.com/opencompl/HOLFloat-Lean.git | 6207518be26dcfc9980a63727bd1440cdbc6bb7a | HOLFloat/Common.lean | ipow_inv | [59, 1] | [62, 27] | simp | r : ℝ
⊢ r ^ negOfNat Nat.zero = (r ^ Nat.zero)⁻¹ | r : ℝ
⊢ r ^ negOfNat 0 = 1 | Please generate a tactic in lean4 to solve the state.
STATE:
r : ℝ
⊢ r ^ negOfNat Nat.zero = (r ^ Nat.zero)⁻¹
TACTIC:
|
https://github.com/opencompl/HOLFloat-Lean.git | 6207518be26dcfc9980a63727bd1440cdbc6bb7a | HOLFloat/Common.lean | ipow_inv | [59, 1] | [62, 27] | trivial | r : ℝ
⊢ r ^ negOfNat 0 = 1 | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
r : ℝ
⊢ r ^ negOfNat 0 = 1
TACTIC:
|
https://github.com/opencompl/HOLFloat-Lean.git | 6207518be26dcfc9980a63727bd1440cdbc6bb7a | HOLFloat/Common.lean | ipow_inv | [59, 1] | [62, 27] | constructor | r : ℝ
n✝ : ℕ
n_ih✝ : r ^ negOfNat n✝ = (r ^ n✝)⁻¹
⊢ r ^ negOfNat (Nat.succ n✝) = (r ^ Nat.succ n✝)⁻¹ | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
r : ℝ
n✝ : ℕ
n_ih✝ : r ^ negOfNat n✝ = (r ^ n✝)⁻¹
⊢ r ^ negOfNat (Nat.succ n✝) = (r ^ Nat.succ n✝)⁻¹
TACTIC:
|
https://github.com/opencompl/HOLFloat-Lean.git | 6207518be26dcfc9980a63727bd1440cdbc6bb7a | HOLFloat/Common.lean | ipow_neg_succ | [65, 1] | [66, 31] | simp_all only [zpow_negSucc] | r : ℝ
i : ℕ
⊢ r ^ -[i+1] = (r ^ Nat.succ i)⁻¹ | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
r : ℝ
i : ℕ
⊢ r ^ -[i+1] = (r ^ Nat.succ i)⁻¹
TACTIC:
|
https://github.com/opencompl/HOLFloat-Lean.git | 6207518be26dcfc9980a63727bd1440cdbc6bb7a | HOLFloat/Common.lean | ipow_inv_neg | [69, 1] | [78, 61] | cases i with
| ofNat n =>
intros
simp_all only [ne_eq, Int.ofNat_eq_coe, zpow_coe_nat, zpow_neg, inv_inv]
| negSucc n =>
intros
simp_all only [ne_eq, zpow_negSucc, zpow_neg, inv_inv] | r : ℝ
i : ℤ
⊢ r ≠ 0 → r ^ i = (r ^ (-i))⁻¹ | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
r : ℝ
i : ℤ
⊢ r ≠ 0 → r ^ i = (r ^ (-i))⁻¹
TACTIC:
|
https://github.com/opencompl/HOLFloat-Lean.git | 6207518be26dcfc9980a63727bd1440cdbc6bb7a | HOLFloat/Common.lean | ipow_inv_neg | [69, 1] | [78, 61] | intros | case ofNat
r : ℝ
n : ℕ
⊢ r ≠ 0 → r ^ ofNat n = (r ^ (-ofNat n))⁻¹ | case ofNat
r : ℝ
n : ℕ
a✝ : r ≠ 0
⊢ r ^ ofNat n = (r ^ (-ofNat n))⁻¹ | Please generate a tactic in lean4 to solve the state.
STATE:
case ofNat
r : ℝ
n : ℕ
⊢ r ≠ 0 → r ^ ofNat n = (r ^ (-ofNat n))⁻¹
TACTIC:
|
https://github.com/opencompl/HOLFloat-Lean.git | 6207518be26dcfc9980a63727bd1440cdbc6bb7a | HOLFloat/Common.lean | ipow_inv_neg | [69, 1] | [78, 61] | simp_all only [ne_eq, Int.ofNat_eq_coe, zpow_coe_nat, zpow_neg, inv_inv] | case ofNat
r : ℝ
n : ℕ
a✝ : r ≠ 0
⊢ r ^ ofNat n = (r ^ (-ofNat n))⁻¹ | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case ofNat
r : ℝ
n : ℕ
a✝ : r ≠ 0
⊢ r ^ ofNat n = (r ^ (-ofNat n))⁻¹
TACTIC:
|
https://github.com/opencompl/HOLFloat-Lean.git | 6207518be26dcfc9980a63727bd1440cdbc6bb7a | HOLFloat/Common.lean | ipow_inv_neg | [69, 1] | [78, 61] | intros | case negSucc
r : ℝ
n : ℕ
⊢ r ≠ 0 → r ^ -[n+1] = (r ^ (- -[n+1]))⁻¹ | case negSucc
r : ℝ
n : ℕ
a✝ : r ≠ 0
⊢ r ^ -[n+1] = (r ^ (- -[n+1]))⁻¹ | Please generate a tactic in lean4 to solve the state.
STATE:
case negSucc
r : ℝ
n : ℕ
⊢ r ≠ 0 → r ^ -[n+1] = (r ^ (- -[n+1]))⁻¹
TACTIC:
|
https://github.com/opencompl/HOLFloat-Lean.git | 6207518be26dcfc9980a63727bd1440cdbc6bb7a | HOLFloat/Common.lean | ipow_inv_neg | [69, 1] | [78, 61] | simp_all only [ne_eq, zpow_negSucc, zpow_neg, inv_inv] | case negSucc
r : ℝ
n : ℕ
a✝ : r ≠ 0
⊢ r ^ -[n+1] = (r ^ (- -[n+1]))⁻¹ | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case negSucc
r : ℝ
n : ℕ
a✝ : r ≠ 0
⊢ r ^ -[n+1] = (r ^ (- -[n+1]))⁻¹
TACTIC:
|
https://github.com/opencompl/HOLFloat-Lean.git | 6207518be26dcfc9980a63727bd1440cdbc6bb7a | HOLFloat/Common.lean | ipow_add_exp | [80, 1] | [81, 8] | sorry | r : ℝ
u v : ℤ
⊢ r ≠ 0 → r ^ u * r ^ v = r ^ (u + v) | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
r : ℝ
u v : ℤ
⊢ r ≠ 0 → r ^ u * r ^ v = r ^ (u + v)
TACTIC:
|
https://github.com/opencompl/HOLFloat-Lean.git | 6207518be26dcfc9980a63727bd1440cdbc6bb7a | HOLFloat/Common.lean | ipow_to_one | [96, 1] | [97, 7] | simp | r : ℝ
⊢ r ^ 1 = r | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
r : ℝ
⊢ r ^ 1 = r
TACTIC:
|
https://github.com/opencompl/HOLFloat-Lean.git | 6207518be26dcfc9980a63727bd1440cdbc6bb7a | HOLFloat/Common.lean | ipow_to_zero | [100, 1] | [101, 7] | simp | r : ℝ
⊢ r ^ 0 = 1 | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
r : ℝ
⊢ r ^ 0 = 1
TACTIC:
|
https://github.com/opencompl/HOLFloat-Lean.git | 6207518be26dcfc9980a63727bd1440cdbc6bb7a | HOLFloat/Common.lean | ipow_le_one | [104, 1] | [105, 8] | sorry | r : ℝ
i : ℤ
⊢ 1 ≤ r → 0 ≤ i → 1 ≤ r ^ i | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
r : ℝ
i : ℤ
⊢ 1 ≤ r → 0 ≤ i → 1 ≤ r ^ i
TACTIC:
|
https://github.com/opencompl/HOLFloat-Lean.git | 6207518be26dcfc9980a63727bd1440cdbc6bb7a | HOLFloat/Common.lean | ipow_lt_one | [109, 1] | [110, 8] | sorry | r : ℝ
i : ℤ
⊢ 1 < r → 0 < i → 1 < r ^ i | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
r : ℝ
i : ℤ
⊢ 1 < r → 0 < i → 1 < r ^ i
TACTIC:
|
https://github.com/opencompl/HOLFloat-Lean.git | 6207518be26dcfc9980a63727bd1440cdbc6bb7a | HOLFloat/Common.lean | ipow_le_sum | [113, 1] | [114, 8] | sorry | i : ℕ
r n : ℝ
⊢ 2 ≤ r → 0 ≤ i → ∃ e, n ≤ r ^ e | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
i : ℕ
r n : ℝ
⊢ 2 ≤ r → 0 ≤ i → ∃ e, n ≤ r ^ e
TACTIC:
|
https://github.com/opencompl/HOLFloat-Lean.git | 6207518be26dcfc9980a63727bd1440cdbc6bb7a | HOLFloat/Common.lean | ipow_le_real_two | [118, 1] | [119, 8] | sorry | r z : ℝ
⊢ 0 < z → 2 ≤ r → ∃ e, r ^ e ≤ z | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
r z : ℝ
⊢ 0 < z → 2 ≤ r → ∃ e, r ^ e ≤ z
TACTIC:
|
https://github.com/opencompl/HOLFloat-Lean.git | 6207518be26dcfc9980a63727bd1440cdbc6bb7a | HOLFloat/Common.lean | ipow_monotone | [122, 1] | [123, 8] | sorry | r : ℝ
u v : ℤ
⊢ 1 ≤ r → u ≤ v → r ^ u ≤ r ^ v | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
r : ℝ
u v : ℤ
⊢ 1 ≤ r → u ≤ v → r ^ u ≤ r ^ v
TACTIC:
|
https://github.com/opencompl/HOLFloat-Lean.git | 6207518be26dcfc9980a63727bd1440cdbc6bb7a | HOLFloat/Common.lean | ipow_monotone_pow | [125, 1] | [126, 8] | sorry | r : ℝ
u v : ℤ
⊢ 1 ≤ r → r ^ u ≤ r ^ v → u ≤ v | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
r : ℝ
u v : ℤ
⊢ 1 ≤ r → r ^ u ≤ r ^ v → u ≤ v
TACTIC:
|
https://github.com/opencompl/HOLFloat-Lean.git | 6207518be26dcfc9980a63727bd1440cdbc6bb7a | HOLFloat/Common.lean | ipow_monotone_lt | [129, 1] | [131, 51] | intro a a_1 | r : ℝ
u v : ℤ
⊢ 1 < r → u < v → r ^ u < r ^ v | r : ℝ
u v : ℤ
a : 1 < r
a_1 : u < v
⊢ r ^ u < r ^ v | Please generate a tactic in lean4 to solve the state.
STATE:
r : ℝ
u v : ℤ
⊢ 1 < r → u < v → r ^ u < r ^ v
TACTIC:
|
https://github.com/opencompl/HOLFloat-Lean.git | 6207518be26dcfc9980a63727bd1440cdbc6bb7a | HOLFloat/Common.lean | ipow_monotone_lt | [129, 1] | [131, 51] | simp_all only [ne_eq, gt_iff_lt, zpow_lt_iff_lt] | r : ℝ
u v : ℤ
a : 1 < r
a_1 : u < v
⊢ r ^ u < r ^ v | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
r : ℝ
u v : ℤ
a : 1 < r
a_1 : u < v
⊢ r ^ u < r ^ v
TACTIC:
|
https://github.com/opencompl/HOLFloat-Lean.git | 6207518be26dcfc9980a63727bd1440cdbc6bb7a | HOLFloat/Common.lean | ipow_monotone_lt_pow | [134, 1] | [136, 71] | intro a a_1 | r : ℝ
u v : ℤ
⊢ 1 < r → r ^ u < r ^ v → u < v | r : ℝ
u v : ℤ
a : 1 < r
a_1 : r ^ u < r ^ v
⊢ u < v | Please generate a tactic in lean4 to solve the state.
STATE:
r : ℝ
u v : ℤ
⊢ 1 < r → r ^ u < r ^ v → u < v
TACTIC:
|
https://github.com/opencompl/HOLFloat-Lean.git | 6207518be26dcfc9980a63727bd1440cdbc6bb7a | HOLFloat/Common.lean | ipow_monotone_lt_pow | [134, 1] | [136, 71] | simp_all only [ne_eq, gt_iff_lt, zpow_lt_iff_lt, one_lt_zero_le_iff] | r : ℝ
u v : ℤ
a : 1 < r
a_1 : r ^ u < r ^ v
⊢ u < v | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
r : ℝ
u v : ℤ
a : 1 < r
a_1 : r ^ u < r ^ v
⊢ u < v
TACTIC:
|
https://github.com/opencompl/HOLFloat-Lean.git | 6207518be26dcfc9980a63727bd1440cdbc6bb7a | HOLFloat/Common.lean | ipow_monotone_le_pow | [138, 1] | [140, 51] | intro a a_1 | r : ℝ
u v : ℤ
⊢ 1 < r → r ^ u ≤ r ^ v → u ≤ v | r : ℝ
u v : ℤ
a : 1 < r
a_1 : r ^ u ≤ r ^ v
⊢ u ≤ v | Please generate a tactic in lean4 to solve the state.
STATE:
r : ℝ
u v : ℤ
⊢ 1 < r → r ^ u ≤ r ^ v → u ≤ v
TACTIC:
|
https://github.com/opencompl/HOLFloat-Lean.git | 6207518be26dcfc9980a63727bd1440cdbc6bb7a | HOLFloat/Common.lean | ipow_monotone_le_pow | [138, 1] | [140, 51] | simp_all only [ne_eq, gt_iff_lt, zpow_le_iff_le] | r : ℝ
u v : ℤ
a : 1 < r
a_1 : r ^ u ≤ r ^ v
⊢ u ≤ v | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
r : ℝ
u v : ℤ
a : 1 < r
a_1 : r ^ u ≤ r ^ v
⊢ u ≤ v
TACTIC:
|
https://github.com/opencompl/HOLFloat-Lean.git | 6207518be26dcfc9980a63727bd1440cdbc6bb7a | HOLFloat/Common.lean | ipow_monotone_le | [143, 1] | [145, 51] | intro a a_1 | r : ℝ
u v : ℤ
⊢ 1 < r → u ≤ v → r ^ u ≤ r ^ v | r : ℝ
u v : ℤ
a : 1 < r
a_1 : u ≤ v
⊢ r ^ u ≤ r ^ v | Please generate a tactic in lean4 to solve the state.
STATE:
r : ℝ
u v : ℤ
⊢ 1 < r → u ≤ v → r ^ u ≤ r ^ v
TACTIC:
|
https://github.com/opencompl/HOLFloat-Lean.git | 6207518be26dcfc9980a63727bd1440cdbc6bb7a | HOLFloat/Common.lean | ipow_monotone_le | [143, 1] | [145, 51] | simp_all only [ne_eq, gt_iff_lt, zpow_le_iff_le] | r : ℝ
u v : ℤ
a : 1 < r
a_1 : u ≤ v
⊢ r ^ u ≤ r ^ v | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
r : ℝ
u v : ℤ
a : 1 < r
a_1 : u ≤ v
⊢ r ^ u ≤ r ^ v
TACTIC:
|
https://github.com/opencompl/HOLFloat-Lean.git | 6207518be26dcfc9980a63727bd1440cdbc6bb7a | HOLFloat/Common.lean | ipow_monotone_two | [147, 1] | [148, 8] | sorry | r : ℝ
u v : ℤ
⊢ 2 ≤ r → u ≤ v → r ^ u ≤ r ^ v | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
r : ℝ
u v : ℤ
⊢ 2 ≤ r → u ≤ v → r ^ u ≤ r ^ v
TACTIC:
|
https://github.com/opencompl/HOLFloat-Lean.git | 6207518be26dcfc9980a63727bd1440cdbc6bb7a | HOLFloat/Common.lean | ipow_mul_inv_eq_one | [151, 1] | [152, 8] | sorry | r : ℝ
i : ℤ
⊢ 0 < r → r ^ i * r ^ (-i) = 1 | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
r : ℝ
i : ℤ
⊢ 0 < r → r ^ i * r ^ (-i) = 1
TACTIC:
|
https://github.com/opencompl/HOLFloat-Lean.git | 6207518be26dcfc9980a63727bd1440cdbc6bb7a | HOLFloat/Common.lean | ipow_le_real | [154, 1] | [157, 8] | intros h | r z : ℝ
⊢ 2 ≤ r → ∃ e, z ≤ r ^ e | r z : ℝ
h : 2 ≤ r
⊢ ∃ e, z ≤ r ^ e | Please generate a tactic in lean4 to solve the state.
STATE:
r z : ℝ
⊢ 2 ≤ r → ∃ e, z ≤ r ^ e
TACTIC:
|
https://github.com/opencompl/HOLFloat-Lean.git | 6207518be26dcfc9980a63727bd1440cdbc6bb7a | HOLFloat/Common.lean | ipow_le_real | [154, 1] | [157, 8] | sorry | r z : ℝ
h : 2 ≤ r
⊢ ∃ e, z ≤ r ^ e | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
r z : ℝ
h : 2 ≤ r
⊢ ∃ e, z ≤ r ^ e
TACTIC:
|
https://github.com/opencompl/HOLFloat-Lean.git | 6207518be26dcfc9980a63727bd1440cdbc6bb7a | HOLFloat/Float.lean | flformat_to_fformat | [37, 1] | [47, 35] | apply And.intro | float : flformat
⊢ is_valid_fformat ↑float | case left
float : flformat
⊢ 1 < (↑float).r
case right
float : flformat
⊢ (↑float).r % 2 = 0 ∧ 0 < (↑float).p | Please generate a tactic in lean4 to solve the state.
STATE:
float : flformat
⊢ is_valid_fformat ↑float
TACTIC:
|
https://github.com/opencompl/HOLFloat-Lean.git | 6207518be26dcfc9980a63727bd1440cdbc6bb7a | HOLFloat/Float.lean | flformat_to_fformat | [37, 1] | [47, 35] | case left =>
exact float.prop.left | float : flformat
⊢ 1 < (↑float).r | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
float : flformat
⊢ 1 < (↑float).r
TACTIC:
|
https://github.com/opencompl/HOLFloat-Lean.git | 6207518be26dcfc9980a63727bd1440cdbc6bb7a | HOLFloat/Float.lean | flformat_to_fformat | [37, 1] | [47, 35] | case right =>
apply And.intro
case left =>
exact float.prop.right.left
case right =>
apply Int.one_lt_zero_lt
exact float.prop.right.right | float : flformat
⊢ (↑float).r % 2 = 0 ∧ 0 < (↑float).p | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
float : flformat
⊢ (↑float).r % 2 = 0 ∧ 0 < (↑float).p
TACTIC:
|
https://github.com/opencompl/HOLFloat-Lean.git | 6207518be26dcfc9980a63727bd1440cdbc6bb7a | HOLFloat/Float.lean | flformat_to_fformat | [37, 1] | [47, 35] | exact float.prop.left | float : flformat
⊢ 1 < (↑float).r | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
float : flformat
⊢ 1 < (↑float).r
TACTIC:
|
https://github.com/opencompl/HOLFloat-Lean.git | 6207518be26dcfc9980a63727bd1440cdbc6bb7a | HOLFloat/Float.lean | flformat_to_fformat | [37, 1] | [47, 35] | apply And.intro | float : flformat
⊢ (↑float).r % 2 = 0 ∧ 0 < (↑float).p | case left
float : flformat
⊢ (↑float).r % 2 = 0
case right
float : flformat
⊢ 0 < (↑float).p | Please generate a tactic in lean4 to solve the state.
STATE:
float : flformat
⊢ (↑float).r % 2 = 0 ∧ 0 < (↑float).p
TACTIC:
|
https://github.com/opencompl/HOLFloat-Lean.git | 6207518be26dcfc9980a63727bd1440cdbc6bb7a | HOLFloat/Float.lean | flformat_to_fformat | [37, 1] | [47, 35] | case left =>
exact float.prop.right.left | float : flformat
⊢ (↑float).r % 2 = 0 | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
float : flformat
⊢ (↑float).r % 2 = 0
TACTIC:
|
https://github.com/opencompl/HOLFloat-Lean.git | 6207518be26dcfc9980a63727bd1440cdbc6bb7a | HOLFloat/Float.lean | flformat_to_fformat | [37, 1] | [47, 35] | case right =>
apply Int.one_lt_zero_lt
exact float.prop.right.right | float : flformat
⊢ 0 < (↑float).p | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
float : flformat
⊢ 0 < (↑float).p
TACTIC:
|
https://github.com/opencompl/HOLFloat-Lean.git | 6207518be26dcfc9980a63727bd1440cdbc6bb7a | HOLFloat/Float.lean | flformat_to_fformat | [37, 1] | [47, 35] | exact float.prop.right.left | float : flformat
⊢ (↑float).r % 2 = 0 | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
float : flformat
⊢ (↑float).r % 2 = 0
TACTIC:
|
https://github.com/opencompl/HOLFloat-Lean.git | 6207518be26dcfc9980a63727bd1440cdbc6bb7a | HOLFloat/Float.lean | flformat_to_fformat | [37, 1] | [47, 35] | apply Int.one_lt_zero_lt | float : flformat
⊢ 0 < (↑float).p | case a
float : flformat
⊢ 1 < (↑float).p | Please generate a tactic in lean4 to solve the state.
STATE:
float : flformat
⊢ 0 < (↑float).p
TACTIC:
|
https://github.com/opencompl/HOLFloat-Lean.git | 6207518be26dcfc9980a63727bd1440cdbc6bb7a | HOLFloat/Float.lean | flformat_to_fformat | [37, 1] | [47, 35] | exact float.prop.right.right | case a
float : flformat
⊢ 1 < (↑float).p | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case a
float : flformat
⊢ 1 < (↑float).p
TACTIC:
|
https://github.com/opencompl/HOLFloat-Lean.git | 6207518be26dcfc9980a63727bd1440cdbc6bb7a | HOLFloat/Fixed_theroem.lean | fformat_valid_imp_radix_lt_one | [8, 1] | [9, 24] | intro h | fmt : format
⊢ is_valid_fformat fmt → 1 < fmt.r | fmt : format
h : is_valid_fformat fmt
⊢ 1 < fmt.r | Please generate a tactic in lean4 to solve the state.
STATE:
fmt : format
⊢ is_valid_fformat fmt → 1 < fmt.r
TACTIC:
|
https://github.com/opencompl/HOLFloat-Lean.git | 6207518be26dcfc9980a63727bd1440cdbc6bb7a | HOLFloat/Fixed_theroem.lean | fformat_valid_imp_radix_lt_one | [8, 1] | [9, 24] | exact h.left | fmt : format
h : is_valid_fformat fmt
⊢ 1 < fmt.r | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
fmt : format
h : is_valid_fformat fmt
⊢ 1 < fmt.r
TACTIC:
|
https://github.com/opencompl/HOLFloat-Lean.git | 6207518be26dcfc9980a63727bd1440cdbc6bb7a | HOLFloat/Fixed_theroem.lean | fformat_valid_imp_radix_even | [12, 1] | [13, 30] | intro h | fmt : format
⊢ is_valid_fformat fmt → fmt.r % 2 = 0 | fmt : format
h : is_valid_fformat fmt
⊢ fmt.r % 2 = 0 | Please generate a tactic in lean4 to solve the state.
STATE:
fmt : format
⊢ is_valid_fformat fmt → fmt.r % 2 = 0
TACTIC:
|
https://github.com/opencompl/HOLFloat-Lean.git | 6207518be26dcfc9980a63727bd1440cdbc6bb7a | HOLFloat/Fixed_theroem.lean | fformat_valid_imp_radix_even | [12, 1] | [13, 30] | exact h.right.left | fmt : format
h : is_valid_fformat fmt
⊢ fmt.r % 2 = 0 | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
fmt : format
h : is_valid_fformat fmt
⊢ fmt.r % 2 = 0
TACTIC:
|
https://github.com/opencompl/HOLFloat-Lean.git | 6207518be26dcfc9980a63727bd1440cdbc6bb7a | HOLFloat/Fixed_theroem.lean | fformat_valid_imp_prec_lt_0 | [16, 1] | [17, 31] | intro h | fmt : format
⊢ is_valid_fformat fmt → 0 < fmt.p | fmt : format
h : is_valid_fformat fmt
⊢ 0 < fmt.p | Please generate a tactic in lean4 to solve the state.
STATE:
fmt : format
⊢ is_valid_fformat fmt → 0 < fmt.p
TACTIC:
|
https://github.com/opencompl/HOLFloat-Lean.git | 6207518be26dcfc9980a63727bd1440cdbc6bb7a | HOLFloat/Fixed_theroem.lean | fformat_valid_imp_prec_lt_0 | [16, 1] | [17, 31] | exact h.right.right | fmt : format
h : is_valid_fformat fmt
⊢ 0 < fmt.p | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
fmt : format
h : is_valid_fformat fmt
⊢ 0 < fmt.p
TACTIC:
|
https://github.com/opencompl/HOLFloat-Lean.git | 6207518be26dcfc9980a63727bd1440cdbc6bb7a | HOLFloat/Fixed_theroem.lean | fformat_radix_lt_1 | [20, 1] | [22, 20] | intro h | ⊢ ∀ (fmt : fformat), 1 < (↑fmt).r | h : fformat
⊢ 1 < (↑h).r | Please generate a tactic in lean4 to solve the state.
STATE:
⊢ ∀ (fmt : fformat), 1 < (↑fmt).r
TACTIC:
|
https://github.com/opencompl/HOLFloat-Lean.git | 6207518be26dcfc9980a63727bd1440cdbc6bb7a | HOLFloat/Fixed_theroem.lean | fformat_radix_lt_1 | [20, 1] | [22, 20] | exact h.prop.left | h : fformat
⊢ 1 < (↑h).r | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
h : fformat
⊢ 1 < (↑h).r
TACTIC:
|
https://github.com/opencompl/HOLFloat-Lean.git | 6207518be26dcfc9980a63727bd1440cdbc6bb7a | HOLFloat/Fixed_theroem.lean | fformat_radix_lt_0 | [25, 1] | [29, 27] | intro h | ⊢ ∀ (fmt : fformat), 0 < (↑fmt).r | h : fformat
⊢ 0 < (↑h).r | Please generate a tactic in lean4 to solve the state.
STATE:
⊢ ∀ (fmt : fformat), 0 < (↑fmt).r
TACTIC:
|
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