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https://github.com/KisaraBlue/ec-tate-lean.git | b9d36a5b70bb0958bf9741ae6216a43b35c87ed4 | ECTate/Algebra/ValuedRing.lean | SurjVal.val_of_minus_one | [164, 1] | [170, 16] | rw [val_of_one] at contradiction | R : Type u
inst✝¹ : CommRing R
inst✝ : IsDomain R
p : R
nav : SurjVal p
x✝ : ¬v nav (-1) = 0
contradiction : v nav 1 > 0
⊢ False | R : Type u
inst✝¹ : CommRing R
inst✝ : IsDomain R
p : R
nav : SurjVal p
x✝ : ¬v nav (-1) = 0
contradiction : 0 > 0
⊢ False |
https://github.com/KisaraBlue/ec-tate-lean.git | b9d36a5b70bb0958bf9741ae6216a43b35c87ed4 | ECTate/Algebra/ValuedRing.lean | SurjVal.val_of_minus_one | [164, 1] | [170, 16] | contradiction | R : Type u
inst✝¹ : CommRing R
inst✝ : IsDomain R
p : R
nav : SurjVal p
x✝ : ¬v nav (-1) = 0
contradiction : 0 > 0
⊢ False | no goals |
https://github.com/KisaraBlue/ec-tate-lean.git | b9d36a5b70bb0958bf9741ae6216a43b35c87ed4 | ECTate/Algebra/ValuedRing.lean | SurjVal.val_of_minus_one | [164, 1] | [170, 16] | rw [←neg_neg 1, ←one_mul 1, neg_mul_eq_neg_mul, neg_mul_eq_mul_neg, nav.v_mul_eq_add_v] | R : Type u
inst✝¹ : CommRing R
inst✝ : IsDomain R
p : R
nav : SurjVal p
x✝ : ¬v nav (-1) = 0
⊢ v nav 1 > 0 | R : Type u
inst✝¹ : CommRing R
inst✝ : IsDomain R
p : R
nav : SurjVal p
x✝ : ¬v nav (-1) = 0
⊢ v nav (-1) + v nav (-1) > 0 |
https://github.com/KisaraBlue/ec-tate-lean.git | b9d36a5b70bb0958bf9741ae6216a43b35c87ed4 | ECTate/Algebra/ValuedRing.lean | SurjVal.val_of_minus_one | [164, 1] | [170, 16] | simpa [pos_iff_ne_zero] | R : Type u
inst✝¹ : CommRing R
inst✝ : IsDomain R
p : R
nav : SurjVal p
x✝ : ¬v nav (-1) = 0
⊢ v nav (-1) + v nav (-1) > 0 | no goals |
https://github.com/KisaraBlue/ec-tate-lean.git | b9d36a5b70bb0958bf9741ae6216a43b35c87ed4 | ECTate/Algebra/ValuedRing.lean | SurjVal.val_neg | [172, 1] | [174, 95] | rw [←one_mul x, neg_mul_eq_neg_mul, nav.v_mul_eq_add_v, val_of_minus_one, one_mul, zero_add] | R : Type u
inst✝¹ : CommRing R
inst✝ : IsDomain R
x p : R
nav : SurjVal p
⊢ v nav (-x) = v nav x | no goals |
https://github.com/KisaraBlue/ec-tate-lean.git | b9d36a5b70bb0958bf9741ae6216a43b35c87ed4 | ECTate/Algebra/ValuedRing.lean | SurjVal.v_sub_ge_min_v | [176, 1] | [179, 7] | rw [sub_eq_add_neg] | R : Type u
inst✝¹ : CommRing R
inst✝ : IsDomain R
p : R
nav : SurjVal p
a b : R
⊢ min (v nav a) (v nav b) ≤ v nav (a - b) | R : Type u
inst✝¹ : CommRing R
inst✝ : IsDomain R
p : R
nav : SurjVal p
a b : R
⊢ min (v nav a) (v nav b) ≤ v nav (a + -b) |
https://github.com/KisaraBlue/ec-tate-lean.git | b9d36a5b70bb0958bf9741ae6216a43b35c87ed4 | ECTate/Algebra/ValuedRing.lean | SurjVal.v_sub_ge_min_v | [176, 1] | [179, 7] | convert nav.v_add_ge_min_v a (-b) using 2 | R : Type u
inst✝¹ : CommRing R
inst✝ : IsDomain R
p : R
nav : SurjVal p
a b : R
⊢ min (v nav a) (v nav b) ≤ v nav (a + -b) | case h.e'_3.h.e'_4
R : Type u
inst✝¹ : CommRing R
inst✝ : IsDomain R
p : R
nav : SurjVal p
a b : R
⊢ v nav b = v nav (-b) |
https://github.com/KisaraBlue/ec-tate-lean.git | b9d36a5b70bb0958bf9741ae6216a43b35c87ed4 | ECTate/Algebra/ValuedRing.lean | SurjVal.v_sub_ge_min_v | [176, 1] | [179, 7] | simp | case h.e'_3.h.e'_4
R : Type u
inst✝¹ : CommRing R
inst✝ : IsDomain R
p : R
nav : SurjVal p
a b : R
⊢ v nav b = v nav (-b) | no goals |
https://github.com/KisaraBlue/ec-tate-lean.git | b9d36a5b70bb0958bf9741ae6216a43b35c87ed4 | ECTate/Algebra/ValuedRing.lean | SurjVal.val_sub_ge_of_ge | [181, 1] | [186, 8] | rw [sub_eq_add_neg] | R : Type u
inst✝¹ : CommRing R
inst✝ : IsDomain R
n : ℕ∞
p : R
nav : SurjVal p
a b : R
ha : n ≤ v nav a
hb : n ≤ v nav b
⊢ n ≤ v nav (a - b) | R : Type u
inst✝¹ : CommRing R
inst✝ : IsDomain R
n : ℕ∞
p : R
nav : SurjVal p
a b : R
ha : n ≤ v nav a
hb : n ≤ v nav b
⊢ n ≤ v nav (a + -b) |
https://github.com/KisaraBlue/ec-tate-lean.git | b9d36a5b70bb0958bf9741ae6216a43b35c87ed4 | ECTate/Algebra/ValuedRing.lean | SurjVal.val_sub_ge_of_ge | [181, 1] | [186, 8] | apply val_add_ge_of_ge | R : Type u
inst✝¹ : CommRing R
inst✝ : IsDomain R
n : ℕ∞
p : R
nav : SurjVal p
a b : R
ha : n ≤ v nav a
hb : n ≤ v nav b
⊢ n ≤ v nav (a + -b) | case ha
R : Type u
inst✝¹ : CommRing R
inst✝ : IsDomain R
n : ℕ∞
p : R
nav : SurjVal p
a b : R
ha : n ≤ v nav a
hb : n ≤ v nav b
⊢ n ≤ v nav a
case hb
R : Type u
inst✝¹ : CommRing R
inst✝ : IsDomain R
n : ℕ∞
p : R
nav : SurjVal p
a b : R
ha : n ≤ v nav a
hb : n ≤ v nav b
⊢ n ≤ v nav (-b) |
https://github.com/KisaraBlue/ec-tate-lean.git | b9d36a5b70bb0958bf9741ae6216a43b35c87ed4 | ECTate/Algebra/ValuedRing.lean | SurjVal.val_sub_ge_of_ge | [181, 1] | [186, 8] | assumption | case ha
R : Type u
inst✝¹ : CommRing R
inst✝ : IsDomain R
n : ℕ∞
p : R
nav : SurjVal p
a b : R
ha : n ≤ v nav a
hb : n ≤ v nav b
⊢ n ≤ v nav a
case hb
R : Type u
inst✝¹ : CommRing R
inst✝ : IsDomain R
n : ℕ∞
p : R
nav : SurjVal p
a b : R
ha : n ≤ v nav a
hb : n ≤ v nav b
⊢ n ≤ v nav (-b) | case hb
R : Type u
inst✝¹ : CommRing R
inst✝ : IsDomain R
n : ℕ∞
p : R
nav : SurjVal p
a b : R
ha : n ≤ v nav a
hb : n ≤ v nav b
⊢ n ≤ v nav (-b) |
https://github.com/KisaraBlue/ec-tate-lean.git | b9d36a5b70bb0958bf9741ae6216a43b35c87ed4 | ECTate/Algebra/ValuedRing.lean | SurjVal.val_sub_ge_of_ge | [181, 1] | [186, 8] | simpa | case hb
R : Type u
inst✝¹ : CommRing R
inst✝ : IsDomain R
n : ℕ∞
p : R
nav : SurjVal p
a b : R
ha : n ≤ v nav a
hb : n ≤ v nav b
⊢ n ≤ v nav (-b) | no goals |
https://github.com/KisaraBlue/ec-tate-lean.git | b9d36a5b70bb0958bf9741ae6216a43b35c87ed4 | ECTate/Algebra/ValuedRing.lean | SurjVal.v_add_eq_min_v | [188, 1] | [198, 89] | apply le_antisymm | R : Type u
inst✝¹ : CommRing R
inst✝ : IsDomain R
p : R
nav : SurjVal p
a b : R
h : v nav a < v nav b
⊢ v nav (a + b) = v nav a | case a
R : Type u
inst✝¹ : CommRing R
inst✝ : IsDomain R
p : R
nav : SurjVal p
a b : R
h : v nav a < v nav b
⊢ v nav (a + b) ≤ v nav a
case a
R : Type u
inst✝¹ : CommRing R
inst✝ : IsDomain R
p : R
nav : SurjVal p
a b : R
h : v nav a < v nav b
⊢ v nav a ≤ v nav (a + b) |
https://github.com/KisaraBlue/ec-tate-lean.git | b9d36a5b70bb0958bf9741ae6216a43b35c87ed4 | ECTate/Algebra/ValuedRing.lean | SurjVal.v_add_eq_min_v | [188, 1] | [198, 89] | . apply le_of_not_lt
intro h'
have hm : nav a < nav (-b) := by rwa [val_neg]
apply lt_irrefl (nav a)
apply lt_of_lt_of_le (lt_min h' hm)
convert nav.v_add_ge_min_v (a + b) (-b)
simp | case a
R : Type u
inst✝¹ : CommRing R
inst✝ : IsDomain R
p : R
nav : SurjVal p
a b : R
h : v nav a < v nav b
⊢ v nav (a + b) ≤ v nav a
case a
R : Type u
inst✝¹ : CommRing R
inst✝ : IsDomain R
p : R
nav : SurjVal p
a b : R
h : v nav a < v nav b
⊢ v nav a ≤ v nav (a + b) | case a
R : Type u
inst✝¹ : CommRing R
inst✝ : IsDomain R
p : R
nav : SurjVal p
a b : R
h : v nav a < v nav b
⊢ v nav a ≤ v nav (a + b) |
https://github.com/KisaraBlue/ec-tate-lean.git | b9d36a5b70bb0958bf9741ae6216a43b35c87ed4 | ECTate/Algebra/ValuedRing.lean | SurjVal.v_add_eq_min_v | [188, 1] | [198, 89] | . exact le_trans (le_min (le_of_eq rfl) (le_of_lt h)) (SurjVal.v_add_ge_min_v nav a b) | case a
R : Type u
inst✝¹ : CommRing R
inst✝ : IsDomain R
p : R
nav : SurjVal p
a b : R
h : v nav a < v nav b
⊢ v nav a ≤ v nav (a + b) | no goals |
https://github.com/KisaraBlue/ec-tate-lean.git | b9d36a5b70bb0958bf9741ae6216a43b35c87ed4 | ECTate/Algebra/ValuedRing.lean | SurjVal.v_add_eq_min_v | [188, 1] | [198, 89] | apply le_of_not_lt | case a
R : Type u
inst✝¹ : CommRing R
inst✝ : IsDomain R
p : R
nav : SurjVal p
a b : R
h : v nav a < v nav b
⊢ v nav (a + b) ≤ v nav a | case a.h
R : Type u
inst✝¹ : CommRing R
inst✝ : IsDomain R
p : R
nav : SurjVal p
a b : R
h : v nav a < v nav b
⊢ ¬v nav a < v nav (a + b) |
https://github.com/KisaraBlue/ec-tate-lean.git | b9d36a5b70bb0958bf9741ae6216a43b35c87ed4 | ECTate/Algebra/ValuedRing.lean | SurjVal.v_add_eq_min_v | [188, 1] | [198, 89] | intro h' | case a.h
R : Type u
inst✝¹ : CommRing R
inst✝ : IsDomain R
p : R
nav : SurjVal p
a b : R
h : v nav a < v nav b
⊢ ¬v nav a < v nav (a + b) | case a.h
R : Type u
inst✝¹ : CommRing R
inst✝ : IsDomain R
p : R
nav : SurjVal p
a b : R
h : v nav a < v nav b
h' : v nav a < v nav (a + b)
⊢ False |
https://github.com/KisaraBlue/ec-tate-lean.git | b9d36a5b70bb0958bf9741ae6216a43b35c87ed4 | ECTate/Algebra/ValuedRing.lean | SurjVal.v_add_eq_min_v | [188, 1] | [198, 89] | have hm : nav a < nav (-b) := by rwa [val_neg] | case a.h
R : Type u
inst✝¹ : CommRing R
inst✝ : IsDomain R
p : R
nav : SurjVal p
a b : R
h : v nav a < v nav b
h' : v nav a < v nav (a + b)
⊢ False | case a.h
R : Type u
inst✝¹ : CommRing R
inst✝ : IsDomain R
p : R
nav : SurjVal p
a b : R
h : v nav a < v nav b
h' : v nav a < v nav (a + b)
hm : v nav a < v nav (-b)
⊢ False |
https://github.com/KisaraBlue/ec-tate-lean.git | b9d36a5b70bb0958bf9741ae6216a43b35c87ed4 | ECTate/Algebra/ValuedRing.lean | SurjVal.v_add_eq_min_v | [188, 1] | [198, 89] | apply lt_irrefl (nav a) | case a.h
R : Type u
inst✝¹ : CommRing R
inst✝ : IsDomain R
p : R
nav : SurjVal p
a b : R
h : v nav a < v nav b
h' : v nav a < v nav (a + b)
hm : v nav a < v nav (-b)
⊢ False | case a.h
R : Type u
inst✝¹ : CommRing R
inst✝ : IsDomain R
p : R
nav : SurjVal p
a b : R
h : v nav a < v nav b
h' : v nav a < v nav (a + b)
hm : v nav a < v nav (-b)
⊢ v nav a < v nav a |
https://github.com/KisaraBlue/ec-tate-lean.git | b9d36a5b70bb0958bf9741ae6216a43b35c87ed4 | ECTate/Algebra/ValuedRing.lean | SurjVal.v_add_eq_min_v | [188, 1] | [198, 89] | apply lt_of_lt_of_le (lt_min h' hm) | case a.h
R : Type u
inst✝¹ : CommRing R
inst✝ : IsDomain R
p : R
nav : SurjVal p
a b : R
h : v nav a < v nav b
h' : v nav a < v nav (a + b)
hm : v nav a < v nav (-b)
⊢ v nav a < v nav a | case a.h
R : Type u
inst✝¹ : CommRing R
inst✝ : IsDomain R
p : R
nav : SurjVal p
a b : R
h : v nav a < v nav b
h' : v nav a < v nav (a + b)
hm : v nav a < v nav (-b)
⊢ min (v nav (a + b)) (v nav (-b)) ≤ v nav a |
https://github.com/KisaraBlue/ec-tate-lean.git | b9d36a5b70bb0958bf9741ae6216a43b35c87ed4 | ECTate/Algebra/ValuedRing.lean | SurjVal.v_add_eq_min_v | [188, 1] | [198, 89] | convert nav.v_add_ge_min_v (a + b) (-b) | case a.h
R : Type u
inst✝¹ : CommRing R
inst✝ : IsDomain R
p : R
nav : SurjVal p
a b : R
h : v nav a < v nav b
h' : v nav a < v nav (a + b)
hm : v nav a < v nav (-b)
⊢ min (v nav (a + b)) (v nav (-b)) ≤ v nav a | case h.e'_4.h.e'_6
R : Type u
inst✝¹ : CommRing R
inst✝ : IsDomain R
p : R
nav : SurjVal p
a b : R
h : v nav a < v nav b
h' : v nav a < v nav (a + b)
hm : v nav a < v nav (-b)
⊢ a = a + b + -b |
https://github.com/KisaraBlue/ec-tate-lean.git | b9d36a5b70bb0958bf9741ae6216a43b35c87ed4 | ECTate/Algebra/ValuedRing.lean | SurjVal.v_add_eq_min_v | [188, 1] | [198, 89] | simp | case h.e'_4.h.e'_6
R : Type u
inst✝¹ : CommRing R
inst✝ : IsDomain R
p : R
nav : SurjVal p
a b : R
h : v nav a < v nav b
h' : v nav a < v nav (a + b)
hm : v nav a < v nav (-b)
⊢ a = a + b + -b | no goals |
https://github.com/KisaraBlue/ec-tate-lean.git | b9d36a5b70bb0958bf9741ae6216a43b35c87ed4 | ECTate/Algebra/ValuedRing.lean | SurjVal.v_add_eq_min_v | [188, 1] | [198, 89] | rwa [val_neg] | R : Type u
inst✝¹ : CommRing R
inst✝ : IsDomain R
p : R
nav : SurjVal p
a b : R
h : v nav a < v nav b
h' : v nav a < v nav (a + b)
⊢ v nav a < v nav (-b) | no goals |
https://github.com/KisaraBlue/ec-tate-lean.git | b9d36a5b70bb0958bf9741ae6216a43b35c87ed4 | ECTate/Algebra/ValuedRing.lean | SurjVal.v_add_eq_min_v | [188, 1] | [198, 89] | exact le_trans (le_min (le_of_eq rfl) (le_of_lt h)) (SurjVal.v_add_ge_min_v nav a b) | case a
R : Type u
inst✝¹ : CommRing R
inst✝ : IsDomain R
p : R
nav : SurjVal p
a b : R
h : v nav a < v nav b
⊢ v nav a ≤ v nav (a + b) | no goals |
https://github.com/KisaraBlue/ec-tate-lean.git | b9d36a5b70bb0958bf9741ae6216a43b35c87ed4 | ECTate/Algebra/ValuedRing.lean | SurjVal.val_of_pow_uniformizer | [200, 1] | [207, 41] | induction n with
| zero =>
rw [pow_zero]
exact val_of_one nav
| succ n ih =>
rw [pow_succ, SurjVal.v_mul_eq_add_v nav, ih, SurjVal.v_uniformizer nav]
simp [Nat.succ_eq_add_one, add_comm] | R : Type u
inst✝¹ : CommRing R
inst✝ : IsDomain R
p : R
nav : SurjVal p
n : ℕ
⊢ v nav (p ^ n) = ↑n | no goals |
https://github.com/KisaraBlue/ec-tate-lean.git | b9d36a5b70bb0958bf9741ae6216a43b35c87ed4 | ECTate/Algebra/ValuedRing.lean | SurjVal.val_of_pow_uniformizer | [200, 1] | [207, 41] | rw [pow_zero] | case zero
R : Type u
inst✝¹ : CommRing R
inst✝ : IsDomain R
p : R
nav : SurjVal p
⊢ v nav (p ^ Nat.zero) = ↑Nat.zero | case zero
R : Type u
inst✝¹ : CommRing R
inst✝ : IsDomain R
p : R
nav : SurjVal p
⊢ v nav 1 = ↑Nat.zero |
https://github.com/KisaraBlue/ec-tate-lean.git | b9d36a5b70bb0958bf9741ae6216a43b35c87ed4 | ECTate/Algebra/ValuedRing.lean | SurjVal.val_of_pow_uniformizer | [200, 1] | [207, 41] | exact val_of_one nav | case zero
R : Type u
inst✝¹ : CommRing R
inst✝ : IsDomain R
p : R
nav : SurjVal p
⊢ v nav 1 = ↑Nat.zero | no goals |
https://github.com/KisaraBlue/ec-tate-lean.git | b9d36a5b70bb0958bf9741ae6216a43b35c87ed4 | ECTate/Algebra/ValuedRing.lean | SurjVal.val_of_pow_uniformizer | [200, 1] | [207, 41] | rw [pow_succ, SurjVal.v_mul_eq_add_v nav, ih, SurjVal.v_uniformizer nav] | case succ
R : Type u
inst✝¹ : CommRing R
inst✝ : IsDomain R
p : R
nav : SurjVal p
n : ℕ
ih : v nav (p ^ n) = ↑n
⊢ v nav (p ^ Nat.succ n) = ↑(Nat.succ n) | case succ
R : Type u
inst✝¹ : CommRing R
inst✝ : IsDomain R
p : R
nav : SurjVal p
n : ℕ
ih : v nav (p ^ n) = ↑n
⊢ 1 + ↑n = ↑(Nat.succ n) |
https://github.com/KisaraBlue/ec-tate-lean.git | b9d36a5b70bb0958bf9741ae6216a43b35c87ed4 | ECTate/Algebra/ValuedRing.lean | SurjVal.val_of_pow_uniformizer | [200, 1] | [207, 41] | simp [Nat.succ_eq_add_one, add_comm] | case succ
R : Type u
inst✝¹ : CommRing R
inst✝ : IsDomain R
p : R
nav : SurjVal p
n : ℕ
ih : v nav (p ^ n) = ↑n
⊢ 1 + ↑n = ↑(Nat.succ n) | no goals |
https://github.com/KisaraBlue/ec-tate-lean.git | b9d36a5b70bb0958bf9741ae6216a43b35c87ed4 | ECTate/Algebra/ValuedRing.lean | ENatValRing.decr_val_zero | [238, 1] | [246, 59] | have v_decr_zero : p * evr.decr_val 0 = 0 := by
symm
apply evr.pos_valtn_decr
rw [val_zero]
decide | R : Type u
inst✝¹ : CommRing R
inst✝ : IsDomain R
p : R
evr : ENatValRing p
⊢ decr_val evr 0 = 0 | R : Type u
inst✝¹ : CommRing R
inst✝ : IsDomain R
p : R
evr : ENatValRing p
v_decr_zero : p * decr_val evr 0 = 0
⊢ decr_val evr 0 = 0 |
https://github.com/KisaraBlue/ec-tate-lean.git | b9d36a5b70bb0958bf9741ae6216a43b35c87ed4 | ECTate/Algebra/ValuedRing.lean | ENatValRing.decr_val_zero | [238, 1] | [246, 59] | rw [mul_eq_zero] at v_decr_zero | R : Type u
inst✝¹ : CommRing R
inst✝ : IsDomain R
p : R
evr : ENatValRing p
v_decr_zero : p * decr_val evr 0 = 0
⊢ decr_val evr 0 = 0 | R : Type u
inst✝¹ : CommRing R
inst✝ : IsDomain R
p : R
evr : ENatValRing p
v_decr_zero : p = 0 ∨ decr_val evr 0 = 0
⊢ decr_val evr 0 = 0 |
https://github.com/KisaraBlue/ec-tate-lean.git | b9d36a5b70bb0958bf9741ae6216a43b35c87ed4 | ECTate/Algebra/ValuedRing.lean | ENatValRing.decr_val_zero | [238, 1] | [246, 59] | exact Or.resolve_left v_decr_zero (p_non_zero evr.valtn) | R : Type u
inst✝¹ : CommRing R
inst✝ : IsDomain R
p : R
evr : ENatValRing p
v_decr_zero : p = 0 ∨ decr_val evr 0 = 0
⊢ decr_val evr 0 = 0 | no goals |
https://github.com/KisaraBlue/ec-tate-lean.git | b9d36a5b70bb0958bf9741ae6216a43b35c87ed4 | ECTate/Algebra/ValuedRing.lean | ENatValRing.decr_val_zero | [238, 1] | [246, 59] | symm | R : Type u
inst✝¹ : CommRing R
inst✝ : IsDomain R
p : R
evr : ENatValRing p
⊢ p * decr_val evr 0 = 0 | R : Type u
inst✝¹ : CommRing R
inst✝ : IsDomain R
p : R
evr : ENatValRing p
⊢ 0 = p * decr_val evr 0 |
https://github.com/KisaraBlue/ec-tate-lean.git | b9d36a5b70bb0958bf9741ae6216a43b35c87ed4 | ECTate/Algebra/ValuedRing.lean | ENatValRing.decr_val_zero | [238, 1] | [246, 59] | apply evr.pos_valtn_decr | R : Type u
inst✝¹ : CommRing R
inst✝ : IsDomain R
p : R
evr : ENatValRing p
⊢ 0 = p * decr_val evr 0 | R : Type u
inst✝¹ : CommRing R
inst✝ : IsDomain R
p : R
evr : ENatValRing p
⊢ v evr.valtn 0 > 0 |
https://github.com/KisaraBlue/ec-tate-lean.git | b9d36a5b70bb0958bf9741ae6216a43b35c87ed4 | ECTate/Algebra/ValuedRing.lean | ENatValRing.decr_val_zero | [238, 1] | [246, 59] | rw [val_zero] | R : Type u
inst✝¹ : CommRing R
inst✝ : IsDomain R
p : R
evr : ENatValRing p
⊢ v evr.valtn 0 > 0 | R : Type u
inst✝¹ : CommRing R
inst✝ : IsDomain R
p : R
evr : ENatValRing p
⊢ ⊤ > 0 |
https://github.com/KisaraBlue/ec-tate-lean.git | b9d36a5b70bb0958bf9741ae6216a43b35c87ed4 | ECTate/Algebra/ValuedRing.lean | ENatValRing.decr_val_zero | [238, 1] | [246, 59] | decide | R : Type u
inst✝¹ : CommRing R
inst✝ : IsDomain R
p : R
evr : ENatValRing p
⊢ ⊤ > 0 | no goals |
https://github.com/KisaraBlue/ec-tate-lean.git | b9d36a5b70bb0958bf9741ae6216a43b35c87ed4 | ECTate/Algebra/ValuedRing.lean | ENatValRing.decr_val_neg | [248, 1] | [257, 76] | cases @eq_zero_or_pos _ _ (evr.valtn x) with
| inl h =>
have hm : evr.valtn (-x) = 0 := by simp [h]
rw [evr.zero_valtn_decr h, evr.zero_valtn_decr hm]
| inr h =>
have hm : evr.valtn (-x) > 0 := by simp [h]
apply nzero_mul_left_cancel p _ _ (p_non_zero evr.valtn)
rw [←neg_mul_eq_mul_neg, ←evr.pos_valtn_decr h, ←evr.pos_valtn_decr hm] | R : Type u
inst✝¹ : CommRing R
inst✝ : IsDomain R
p : R
evr : ENatValRing p
x : R
⊢ decr_val evr (-x) = -decr_val evr x | no goals |
https://github.com/KisaraBlue/ec-tate-lean.git | b9d36a5b70bb0958bf9741ae6216a43b35c87ed4 | ECTate/Algebra/ValuedRing.lean | ENatValRing.decr_val_neg | [248, 1] | [257, 76] | have hm : evr.valtn (-x) = 0 := by simp [h] | case inl
R : Type u
inst✝¹ : CommRing R
inst✝ : IsDomain R
p : R
evr : ENatValRing p
x : R
h : v evr.valtn x = 0
⊢ decr_val evr (-x) = -decr_val evr x | case inl
R : Type u
inst✝¹ : CommRing R
inst✝ : IsDomain R
p : R
evr : ENatValRing p
x : R
h : v evr.valtn x = 0
hm : v evr.valtn (-x) = 0
⊢ decr_val evr (-x) = -decr_val evr x |
https://github.com/KisaraBlue/ec-tate-lean.git | b9d36a5b70bb0958bf9741ae6216a43b35c87ed4 | ECTate/Algebra/ValuedRing.lean | ENatValRing.decr_val_neg | [248, 1] | [257, 76] | rw [evr.zero_valtn_decr h, evr.zero_valtn_decr hm] | case inl
R : Type u
inst✝¹ : CommRing R
inst✝ : IsDomain R
p : R
evr : ENatValRing p
x : R
h : v evr.valtn x = 0
hm : v evr.valtn (-x) = 0
⊢ decr_val evr (-x) = -decr_val evr x | no goals |
https://github.com/KisaraBlue/ec-tate-lean.git | b9d36a5b70bb0958bf9741ae6216a43b35c87ed4 | ECTate/Algebra/ValuedRing.lean | ENatValRing.decr_val_neg | [248, 1] | [257, 76] | simp [h] | R : Type u
inst✝¹ : CommRing R
inst✝ : IsDomain R
p : R
evr : ENatValRing p
x : R
h : v evr.valtn x = 0
⊢ v evr.valtn (-x) = 0 | no goals |
https://github.com/KisaraBlue/ec-tate-lean.git | b9d36a5b70bb0958bf9741ae6216a43b35c87ed4 | ECTate/Algebra/ValuedRing.lean | ENatValRing.decr_val_neg | [248, 1] | [257, 76] | have hm : evr.valtn (-x) > 0 := by simp [h] | case inr
R : Type u
inst✝¹ : CommRing R
inst✝ : IsDomain R
p : R
evr : ENatValRing p
x : R
h : 0 < v evr.valtn x
⊢ decr_val evr (-x) = -decr_val evr x | case inr
R : Type u
inst✝¹ : CommRing R
inst✝ : IsDomain R
p : R
evr : ENatValRing p
x : R
h : 0 < v evr.valtn x
hm : v evr.valtn (-x) > 0
⊢ decr_val evr (-x) = -decr_val evr x |
https://github.com/KisaraBlue/ec-tate-lean.git | b9d36a5b70bb0958bf9741ae6216a43b35c87ed4 | ECTate/Algebra/ValuedRing.lean | ENatValRing.decr_val_neg | [248, 1] | [257, 76] | apply nzero_mul_left_cancel p _ _ (p_non_zero evr.valtn) | case inr
R : Type u
inst✝¹ : CommRing R
inst✝ : IsDomain R
p : R
evr : ENatValRing p
x : R
h : 0 < v evr.valtn x
hm : v evr.valtn (-x) > 0
⊢ decr_val evr (-x) = -decr_val evr x | case inr
R : Type u
inst✝¹ : CommRing R
inst✝ : IsDomain R
p : R
evr : ENatValRing p
x : R
h : 0 < v evr.valtn x
hm : v evr.valtn (-x) > 0
⊢ p * decr_val evr (-x) = p * -decr_val evr x |
https://github.com/KisaraBlue/ec-tate-lean.git | b9d36a5b70bb0958bf9741ae6216a43b35c87ed4 | ECTate/Algebra/ValuedRing.lean | ENatValRing.decr_val_neg | [248, 1] | [257, 76] | rw [←neg_mul_eq_mul_neg, ←evr.pos_valtn_decr h, ←evr.pos_valtn_decr hm] | case inr
R : Type u
inst✝¹ : CommRing R
inst✝ : IsDomain R
p : R
evr : ENatValRing p
x : R
h : 0 < v evr.valtn x
hm : v evr.valtn (-x) > 0
⊢ p * decr_val evr (-x) = p * -decr_val evr x | no goals |
https://github.com/KisaraBlue/ec-tate-lean.git | b9d36a5b70bb0958bf9741ae6216a43b35c87ed4 | ECTate/Algebra/ValuedRing.lean | ENatValRing.decr_val_neg | [248, 1] | [257, 76] | simp [h] | R : Type u
inst✝¹ : CommRing R
inst✝ : IsDomain R
p : R
evr : ENatValRing p
x : R
h : 0 < v evr.valtn x
⊢ v evr.valtn (-x) > 0 | no goals |
https://github.com/KisaraBlue/ec-tate-lean.git | b9d36a5b70bb0958bf9741ae6216a43b35c87ed4 | ECTate/Algebra/ValuedRing.lean | ENatValRing.decr_val_p_mul | [259, 1] | [267, 15] | have h : (p * x) = p * decr_val evr (p * x) := by
apply evr.pos_valtn_decr
rw [evr.valtn.v_mul_eq_add_v, evr.valtn.v_uniformizer]
rw [add_comm]
simp | R : Type u
inst✝¹ : CommRing R
inst✝ : IsDomain R
p : R
evr : ENatValRing p
x : R
⊢ decr_val evr (p * x) = x | R : Type u
inst✝¹ : CommRing R
inst✝ : IsDomain R
p : R
evr : ENatValRing p
x : R
h : p * x = p * decr_val evr (p * x)
⊢ decr_val evr (p * x) = x |
https://github.com/KisaraBlue/ec-tate-lean.git | b9d36a5b70bb0958bf9741ae6216a43b35c87ed4 | ECTate/Algebra/ValuedRing.lean | ENatValRing.decr_val_p_mul | [259, 1] | [267, 15] | apply nzero_mul_left_cancel p _ _ (p_non_zero evr.valtn) | R : Type u
inst✝¹ : CommRing R
inst✝ : IsDomain R
p : R
evr : ENatValRing p
x : R
h : p * x = p * decr_val evr (p * x)
⊢ decr_val evr (p * x) = x | R : Type u
inst✝¹ : CommRing R
inst✝ : IsDomain R
p : R
evr : ENatValRing p
x : R
h : p * x = p * decr_val evr (p * x)
⊢ p * decr_val evr (p * x) = p * x |
https://github.com/KisaraBlue/ec-tate-lean.git | b9d36a5b70bb0958bf9741ae6216a43b35c87ed4 | ECTate/Algebra/ValuedRing.lean | ENatValRing.decr_val_p_mul | [259, 1] | [267, 15] | exact h.symm | R : Type u
inst✝¹ : CommRing R
inst✝ : IsDomain R
p : R
evr : ENatValRing p
x : R
h : p * x = p * decr_val evr (p * x)
⊢ p * decr_val evr (p * x) = p * x | no goals |
https://github.com/KisaraBlue/ec-tate-lean.git | b9d36a5b70bb0958bf9741ae6216a43b35c87ed4 | ECTate/Algebra/ValuedRing.lean | ENatValRing.decr_val_p_mul | [259, 1] | [267, 15] | apply evr.pos_valtn_decr | R : Type u
inst✝¹ : CommRing R
inst✝ : IsDomain R
p : R
evr : ENatValRing p
x : R
⊢ p * x = p * decr_val evr (p * x) | R : Type u
inst✝¹ : CommRing R
inst✝ : IsDomain R
p : R
evr : ENatValRing p
x : R
⊢ v evr.valtn (p * x) > 0 |
https://github.com/KisaraBlue/ec-tate-lean.git | b9d36a5b70bb0958bf9741ae6216a43b35c87ed4 | ECTate/Algebra/ValuedRing.lean | ENatValRing.decr_val_p_mul | [259, 1] | [267, 15] | rw [evr.valtn.v_mul_eq_add_v, evr.valtn.v_uniformizer] | R : Type u
inst✝¹ : CommRing R
inst✝ : IsDomain R
p : R
evr : ENatValRing p
x : R
⊢ v evr.valtn (p * x) > 0 | R : Type u
inst✝¹ : CommRing R
inst✝ : IsDomain R
p : R
evr : ENatValRing p
x : R
⊢ 1 + v evr.valtn x > 0 |
https://github.com/KisaraBlue/ec-tate-lean.git | b9d36a5b70bb0958bf9741ae6216a43b35c87ed4 | ECTate/Algebra/ValuedRing.lean | ENatValRing.decr_val_p_mul | [259, 1] | [267, 15] | rw [add_comm] | R : Type u
inst✝¹ : CommRing R
inst✝ : IsDomain R
p : R
evr : ENatValRing p
x : R
⊢ 1 + v evr.valtn x > 0 | R : Type u
inst✝¹ : CommRing R
inst✝ : IsDomain R
p : R
evr : ENatValRing p
x : R
⊢ v evr.valtn x + 1 > 0 |
https://github.com/KisaraBlue/ec-tate-lean.git | b9d36a5b70bb0958bf9741ae6216a43b35c87ed4 | ECTate/Algebra/ValuedRing.lean | ENatValRing.decr_val_p_mul | [259, 1] | [267, 15] | simp | R : Type u
inst✝¹ : CommRing R
inst✝ : IsDomain R
p : R
evr : ENatValRing p
x : R
⊢ v evr.valtn x + 1 > 0 | no goals |
https://github.com/KisaraBlue/ec-tate-lean.git | b9d36a5b70bb0958bf9741ae6216a43b35c87ed4 | ECTate/Algebra/ValuedRing.lean | ENatValRing.sub_val_zero_n | [269, 1] | [273, 60] | induction n with
| zero => simp [sub_val_eq]
| succ n ih => simpa [sub_val_eq, decr_val_zero] using ih | R : Type u
inst✝¹ : CommRing R
inst✝ : IsDomain R
p : R
evr : ENatValRing p
n : ℕ
⊢ sub_val evr n 0 = 0 | no goals |
https://github.com/KisaraBlue/ec-tate-lean.git | b9d36a5b70bb0958bf9741ae6216a43b35c87ed4 | ECTate/Algebra/ValuedRing.lean | ENatValRing.sub_val_zero_n | [269, 1] | [273, 60] | simp [sub_val_eq] | case zero
R : Type u
inst✝¹ : CommRing R
inst✝ : IsDomain R
p : R
evr : ENatValRing p
⊢ sub_val evr Nat.zero 0 = 0 | no goals |
https://github.com/KisaraBlue/ec-tate-lean.git | b9d36a5b70bb0958bf9741ae6216a43b35c87ed4 | ECTate/Algebra/ValuedRing.lean | ENatValRing.sub_val_zero_n | [269, 1] | [273, 60] | simpa [sub_val_eq, decr_val_zero] using ih | case succ
R : Type u
inst✝¹ : CommRing R
inst✝ : IsDomain R
p : R
evr : ENatValRing p
n : ℕ
ih : sub_val evr n 0 = 0
⊢ sub_val evr (Nat.succ n) 0 = 0 | no goals |
https://github.com/KisaraBlue/ec-tate-lean.git | b9d36a5b70bb0958bf9741ae6216a43b35c87ed4 | ECTate/Algebra/ValuedRing.lean | ENatValRing.sub_val_x_zero | [275, 1] | [276, 105] | simp [sub_val_eq] | R : Type u
inst✝¹ : CommRing R
inst✝ : IsDomain R
p : R
evr : ENatValRing p
x : R
⊢ sub_val evr 0 x = x | no goals |
https://github.com/KisaraBlue/ec-tate-lean.git | b9d36a5b70bb0958bf9741ae6216a43b35c87ed4 | ECTate/Algebra/ValuedRing.lean | ENatValRing.sub_val_val_zero | [278, 1] | [282, 66] | induction m with
| zero => exact sub_val_x_zero evr x
| succ m ih => simpa [sub_val_eq, zero_valtn_decr _ h] using ih | R : Type u
inst✝¹ : CommRing R
inst✝ : IsDomain R
p : R
evr : ENatValRing p
x : R
m : ℕ
h : v evr.valtn x = 0
⊢ sub_val evr m x = x | no goals |
https://github.com/KisaraBlue/ec-tate-lean.git | b9d36a5b70bb0958bf9741ae6216a43b35c87ed4 | ECTate/Algebra/ValuedRing.lean | ENatValRing.sub_val_val_zero | [278, 1] | [282, 66] | exact sub_val_x_zero evr x | case zero
R : Type u
inst✝¹ : CommRing R
inst✝ : IsDomain R
p : R
evr : ENatValRing p
x : R
h : v evr.valtn x = 0
⊢ sub_val evr Nat.zero x = x | no goals |
https://github.com/KisaraBlue/ec-tate-lean.git | b9d36a5b70bb0958bf9741ae6216a43b35c87ed4 | ECTate/Algebra/ValuedRing.lean | ENatValRing.sub_val_val_zero | [278, 1] | [282, 66] | simpa [sub_val_eq, zero_valtn_decr _ h] using ih | case succ
R : Type u
inst✝¹ : CommRing R
inst✝ : IsDomain R
p : R
evr : ENatValRing p
x : R
h : v evr.valtn x = 0
m : ℕ
ih : sub_val evr m x = x
⊢ sub_val evr (Nat.succ m) x = x | no goals |
https://github.com/KisaraBlue/ec-tate-lean.git | b9d36a5b70bb0958bf9741ae6216a43b35c87ed4 | ECTate/Algebra/ValuedRing.lean | ENatValRing.sub_val_val_pos_succ | [284, 1] | [286, 20] | simp [sub_val_eq] | R : Type u
inst✝¹ : CommRing R
inst✝ : IsDomain R
p : R
evr : ENatValRing p
x : R
m : ℕ
⊢ sub_val evr (Nat.succ m) x = sub_val evr m (decr_val evr x) | no goals |
https://github.com/KisaraBlue/ec-tate-lean.git | b9d36a5b70bb0958bf9741ae6216a43b35c87ed4 | ECTate/Algebra/ValuedRing.lean | ENatValRing.val_decr_val | [288, 1] | [298, 10] | cases m with
| zero => rwa [evr.zero_valtn_decr h]
| succ m =>
have x_pos_val : evr.valtn x > 0 := by
rw [h]
exact NeZero.pos _
simp at * sorry | R : Type u
inst✝¹ : CommRing R
inst✝ : IsDomain R
p : R
evr : ENatValRing p
m : ℕ
x : R
h : v evr.valtn x = ↑m
⊢ v evr.valtn (decr_val evr x) = ↑m - 1 | no goals |
https://github.com/KisaraBlue/ec-tate-lean.git | b9d36a5b70bb0958bf9741ae6216a43b35c87ed4 | ECTate/Algebra/ValuedRing.lean | ENatValRing.val_decr_val | [288, 1] | [298, 10] | rwa [evr.zero_valtn_decr h] | case zero
R : Type u
inst✝¹ : CommRing R
inst✝ : IsDomain R
p : R
evr : ENatValRing p
x : R
h : v evr.valtn x = ↑Nat.zero
⊢ v evr.valtn (decr_val evr x) = ↑Nat.zero - 1 | no goals |
https://github.com/KisaraBlue/ec-tate-lean.git | b9d36a5b70bb0958bf9741ae6216a43b35c87ed4 | ECTate/Algebra/ValuedRing.lean | ENatValRing.val_decr_val | [288, 1] | [298, 10] | have x_pos_val : evr.valtn x > 0 := by
rw [h]
exact NeZero.pos _ | case succ
R : Type u
inst✝¹ : CommRing R
inst✝ : IsDomain R
p : R
evr : ENatValRing p
x : R
m : ℕ
h : v evr.valtn x = ↑(Nat.succ m)
⊢ v evr.valtn (decr_val evr x) = ↑(Nat.succ m) - 1 | case succ
R : Type u
inst✝¹ : CommRing R
inst✝ : IsDomain R
p : R
evr : ENatValRing p
x : R
m : ℕ
h : v evr.valtn x = ↑(Nat.succ m)
x_pos_val : v evr.valtn x > 0
⊢ v evr.valtn (decr_val evr x) = ↑(Nat.succ m) - 1 |
https://github.com/KisaraBlue/ec-tate-lean.git | b9d36a5b70bb0958bf9741ae6216a43b35c87ed4 | ECTate/Algebra/ValuedRing.lean | ENatValRing.val_decr_val | [288, 1] | [298, 10] | simp at * | case succ
R : Type u
inst✝¹ : CommRing R
inst✝ : IsDomain R
p : R
evr : ENatValRing p
x : R
m : ℕ
h : v evr.valtn x = ↑(Nat.succ m)
x_pos_val : v evr.valtn x > 0
⊢ v evr.valtn (decr_val evr x) = ↑(Nat.succ m) - 1 | case succ
R : Type u
inst✝¹ : CommRing R
inst✝ : IsDomain R
p : R
evr : ENatValRing p
x : R
m : ℕ
h : v evr.valtn x = ↑m + 1
x_pos_val : 0 < v evr.valtn x
⊢ v evr.valtn (decr_val evr x) = ↑m + 1 - 1 |
https://github.com/KisaraBlue/ec-tate-lean.git | b9d36a5b70bb0958bf9741ae6216a43b35c87ed4 | ECTate/Algebra/ValuedRing.lean | ENatValRing.val_decr_val | [288, 1] | [298, 10] | sorry | case succ
R : Type u
inst✝¹ : CommRing R
inst✝ : IsDomain R
p : R
evr : ENatValRing p
x : R
m : ℕ
h : v evr.valtn x = ↑m + 1
x_pos_val : 0 < v evr.valtn x
⊢ v evr.valtn (decr_val evr x) = ↑m + 1 - 1 | no goals |
https://github.com/KisaraBlue/ec-tate-lean.git | b9d36a5b70bb0958bf9741ae6216a43b35c87ed4 | ECTate/Algebra/ValuedRing.lean | ENatValRing.val_decr_val | [288, 1] | [298, 10] | rw [h] | R : Type u
inst✝¹ : CommRing R
inst✝ : IsDomain R
p : R
evr : ENatValRing p
x : R
m : ℕ
h : v evr.valtn x = ↑(Nat.succ m)
⊢ v evr.valtn x > 0 | R : Type u
inst✝¹ : CommRing R
inst✝ : IsDomain R
p : R
evr : ENatValRing p
x : R
m : ℕ
h : v evr.valtn x = ↑(Nat.succ m)
⊢ ↑(Nat.succ m) > 0 |
https://github.com/KisaraBlue/ec-tate-lean.git | b9d36a5b70bb0958bf9741ae6216a43b35c87ed4 | ECTate/Algebra/ValuedRing.lean | ENatValRing.val_decr_val | [288, 1] | [298, 10] | exact NeZero.pos _ | R : Type u
inst✝¹ : CommRing R
inst✝ : IsDomain R
p : R
evr : ENatValRing p
x : R
m : ℕ
h : v evr.valtn x = ↑(Nat.succ m)
⊢ ↑(Nat.succ m) > 0 | no goals |
https://github.com/KisaraBlue/ec-tate-lean.git | b9d36a5b70bb0958bf9741ae6216a43b35c87ed4 | ECTate/Algebra/ValuedRing.lean | ENatValRing.sub_val_decr_val_comm | [304, 1] | [308, 50] | simp [sub_val_eq] | R : Type u
inst✝¹ : CommRing R
inst✝ : IsDomain R
p : R
evr : ENatValRing p
x : R
n : ℕ
⊢ sub_val evr n (decr_val evr x) = decr_val evr (sub_val evr n x) | R : Type u
inst✝¹ : CommRing R
inst✝ : IsDomain R
p : R
evr : ENatValRing p
x : R
n : ℕ
⊢ evr.decr_val^[n] (decr_val evr x) = decr_val evr (evr.decr_val^[n] x) |
https://github.com/KisaraBlue/ec-tate-lean.git | b9d36a5b70bb0958bf9741ae6216a43b35c87ed4 | ECTate/Algebra/ValuedRing.lean | ENatValRing.sub_val_decr_val_comm | [304, 1] | [308, 50] | rw [← Function.iterate_succ_apply' evr.decr_val] | R : Type u
inst✝¹ : CommRing R
inst✝ : IsDomain R
p : R
evr : ENatValRing p
x : R
n : ℕ
⊢ evr.decr_val^[n] (decr_val evr x) = decr_val evr (evr.decr_val^[n] x) | R : Type u
inst✝¹ : CommRing R
inst✝ : IsDomain R
p : R
evr : ENatValRing p
x : R
n : ℕ
⊢ evr.decr_val^[n] (decr_val evr x) = evr.decr_val^[Nat.succ n] x |
https://github.com/KisaraBlue/ec-tate-lean.git | b9d36a5b70bb0958bf9741ae6216a43b35c87ed4 | ECTate/Algebra/ValuedRing.lean | ENatValRing.sub_val_decr_val_comm | [304, 1] | [308, 50] | rw [← Function.iterate_succ_apply evr.decr_val] | R : Type u
inst✝¹ : CommRing R
inst✝ : IsDomain R
p : R
evr : ENatValRing p
x : R
n : ℕ
⊢ evr.decr_val^[n] (decr_val evr x) = evr.decr_val^[Nat.succ n] x | no goals |
https://github.com/KisaraBlue/ec-tate-lean.git | b9d36a5b70bb0958bf9741ae6216a43b35c87ed4 | ECTate/Algebra/ValuedRing.lean | ENatValRing.val_sub_val_eq | [310, 1] | [325, 16] | induction n with
| zero =>
simpa [sub_val_x_zero]
| succ n ih =>
cases m with
| zero =>
simp only [Nat.zero_eq, CharP.cast_eq_zero, Nat.cast_succ,
ge_iff_le, zero_le, tsub_eq_zero_of_le] at ih ⊢
rw [sub_val_val_zero evr x n.succ h]
exact h
| succ m =>
rw [sub_val_val_pos_succ, sub_val_decr_val_comm, val_decr_val evr (sub_val evr n x) ih,
Nat.succ_eq_add_one n]
norm_cast | R : Type u
inst✝¹ : CommRing R
inst✝ : IsDomain R
p : R
evr : ENatValRing p
x : R
m n : ℕ
h : v evr.valtn x = ↑m
⊢ v evr.valtn (sub_val evr n x) = ↑m - ↑n | no goals |
https://github.com/KisaraBlue/ec-tate-lean.git | b9d36a5b70bb0958bf9741ae6216a43b35c87ed4 | ECTate/Algebra/ValuedRing.lean | ENatValRing.val_sub_val_eq | [310, 1] | [325, 16] | simpa [sub_val_x_zero] | case zero
R : Type u
inst✝¹ : CommRing R
inst✝ : IsDomain R
p : R
evr : ENatValRing p
x : R
m : ℕ
h : v evr.valtn x = ↑m
⊢ v evr.valtn (sub_val evr Nat.zero x) = ↑m - ↑Nat.zero | no goals |
https://github.com/KisaraBlue/ec-tate-lean.git | b9d36a5b70bb0958bf9741ae6216a43b35c87ed4 | ECTate/Algebra/ValuedRing.lean | ENatValRing.val_sub_val_eq | [310, 1] | [325, 16] | cases m with
| zero =>
simp only [Nat.zero_eq, CharP.cast_eq_zero, Nat.cast_succ,
ge_iff_le, zero_le, tsub_eq_zero_of_le] at ih ⊢
rw [sub_val_val_zero evr x n.succ h]
exact h
| succ m =>
rw [sub_val_val_pos_succ, sub_val_decr_val_comm, val_decr_val evr (sub_val evr n x) ih,
Nat.succ_eq_add_one n]
norm_cast | case succ
R : Type u
inst✝¹ : CommRing R
inst✝ : IsDomain R
p : R
evr : ENatValRing p
x : R
m : ℕ
h : v evr.valtn x = ↑m
n : ℕ
ih : v evr.valtn (sub_val evr n x) = ↑m - ↑n
⊢ v evr.valtn (sub_val evr (Nat.succ n) x) = ↑m - ↑(Nat.succ n) | no goals |
https://github.com/KisaraBlue/ec-tate-lean.git | b9d36a5b70bb0958bf9741ae6216a43b35c87ed4 | ECTate/Algebra/ValuedRing.lean | ENatValRing.val_sub_val_eq | [310, 1] | [325, 16] | simp only [Nat.zero_eq, CharP.cast_eq_zero, Nat.cast_succ,
ge_iff_le, zero_le, tsub_eq_zero_of_le] at ih ⊢ | case succ.zero
R : Type u
inst✝¹ : CommRing R
inst✝ : IsDomain R
p : R
evr : ENatValRing p
x : R
n : ℕ
h : v evr.valtn x = ↑Nat.zero
ih : v evr.valtn (sub_val evr n x) = ↑Nat.zero - ↑n
⊢ v evr.valtn (sub_val evr (Nat.succ n) x) = ↑Nat.zero - ↑(Nat.succ n) | case succ.zero
R : Type u
inst✝¹ : CommRing R
inst✝ : IsDomain R
p : R
evr : ENatValRing p
x : R
n : ℕ
h : v evr.valtn x = ↑Nat.zero
ih : v evr.valtn (sub_val evr n x) = 0
⊢ v evr.valtn (sub_val evr (Nat.succ n) x) = 0 |
https://github.com/KisaraBlue/ec-tate-lean.git | b9d36a5b70bb0958bf9741ae6216a43b35c87ed4 | ECTate/Algebra/ValuedRing.lean | ENatValRing.val_sub_val_eq | [310, 1] | [325, 16] | rw [sub_val_val_zero evr x n.succ h] | case succ.zero
R : Type u
inst✝¹ : CommRing R
inst✝ : IsDomain R
p : R
evr : ENatValRing p
x : R
n : ℕ
h : v evr.valtn x = ↑Nat.zero
ih : v evr.valtn (sub_val evr n x) = 0
⊢ v evr.valtn (sub_val evr (Nat.succ n) x) = 0 | case succ.zero
R : Type u
inst✝¹ : CommRing R
inst✝ : IsDomain R
p : R
evr : ENatValRing p
x : R
n : ℕ
h : v evr.valtn x = ↑Nat.zero
ih : v evr.valtn (sub_val evr n x) = 0
⊢ v evr.valtn x = 0 |
https://github.com/KisaraBlue/ec-tate-lean.git | b9d36a5b70bb0958bf9741ae6216a43b35c87ed4 | ECTate/Algebra/ValuedRing.lean | ENatValRing.val_sub_val_eq | [310, 1] | [325, 16] | exact h | case succ.zero
R : Type u
inst✝¹ : CommRing R
inst✝ : IsDomain R
p : R
evr : ENatValRing p
x : R
n : ℕ
h : v evr.valtn x = ↑Nat.zero
ih : v evr.valtn (sub_val evr n x) = 0
⊢ v evr.valtn x = 0 | no goals |
https://github.com/KisaraBlue/ec-tate-lean.git | b9d36a5b70bb0958bf9741ae6216a43b35c87ed4 | ECTate/Algebra/ValuedRing.lean | ENatValRing.val_sub_val_eq | [310, 1] | [325, 16] | rw [sub_val_val_pos_succ, sub_val_decr_val_comm, val_decr_val evr (sub_val evr n x) ih,
Nat.succ_eq_add_one n] | case succ.succ
R : Type u
inst✝¹ : CommRing R
inst✝ : IsDomain R
p : R
evr : ENatValRing p
x : R
n m : ℕ
h : v evr.valtn x = ↑(Nat.succ m)
ih : v evr.valtn (sub_val evr n x) = ↑(Nat.succ m) - ↑n
⊢ v evr.valtn (sub_val evr (Nat.succ n) x) = ↑(Nat.succ m) - ↑(Nat.succ n) | case succ.succ
R : Type u
inst✝¹ : CommRing R
inst✝ : IsDomain R
p : R
evr : ENatValRing p
x : R
n m : ℕ
h : v evr.valtn x = ↑(Nat.succ m)
ih : v evr.valtn (sub_val evr n x) = ↑(Nat.succ m) - ↑n
⊢ ↑(Sub.sub ↑(Nat.succ m) ↑n) - 1 = ↑(Nat.succ m) - ↑(n + 1) |
https://github.com/KisaraBlue/ec-tate-lean.git | b9d36a5b70bb0958bf9741ae6216a43b35c87ed4 | ECTate/Algebra/ValuedRing.lean | ENatValRing.val_sub_val_eq | [310, 1] | [325, 16] | norm_cast | case succ.succ
R : Type u
inst✝¹ : CommRing R
inst✝ : IsDomain R
p : R
evr : ENatValRing p
x : R
n m : ℕ
h : v evr.valtn x = ↑(Nat.succ m)
ih : v evr.valtn (sub_val evr n x) = ↑(Nat.succ m) - ↑n
⊢ ↑(Sub.sub ↑(Nat.succ m) ↑n) - 1 = ↑(Nat.succ m) - ↑(n + 1) | no goals |
https://github.com/KisaraBlue/ec-tate-lean.git | b9d36a5b70bb0958bf9741ae6216a43b35c87ed4 | ECTate/Algebra/ValuedRing.lean | ENatValRing.val_sub_val_le | [327, 1] | [330, 8] | sorry | R : Type u
inst✝¹ : CommRing R
inst✝ : IsDomain R
p : R
evr : ENatValRing p
x : R
m n : ℕ
h : ↑m ≤ v evr.valtn x
⊢ v evr.valtn (sub_val evr n x) ≥ ↑m - ↑n | no goals |
https://github.com/KisaraBlue/ec-tate-lean.git | b9d36a5b70bb0958bf9741ae6216a43b35c87ed4 | ECTate/Algebra/ValuedRing.lean | ENatValRing.factor_p_of_le_val | [347, 1] | [362, 30] | induction n with
| zero => simp [sub_val_eq]
| succ n ih =>
rw [sub_val_val_pos_succ, sub_val_decr_val_comm, pow_succ', mul_assoc]
have pos_val : evr.valtn (sub_val evr n x) > 0 := by
have h' := val_sub_val_le evr x n h
rw [Nat.succ_eq_add_one] at h'
norm_cast at h'
rw [Nat.add_sub_self_left] at h'
exact one_le_iff_pos.mp h'
rw [←evr.pos_valtn_decr pos_val]
apply ih
rw [Nat.cast_succ] at h
exact le_of_add_le_left h | R : Type u
inst✝¹ : CommRing R
inst✝ : IsDomain R
p : R
evr : ENatValRing p
x : R
n : ℕ
h : ↑n ≤ v evr.valtn x
⊢ x = p ^ n * sub_val evr n x | no goals |
https://github.com/KisaraBlue/ec-tate-lean.git | b9d36a5b70bb0958bf9741ae6216a43b35c87ed4 | ECTate/Algebra/ValuedRing.lean | ENatValRing.factor_p_of_le_val | [347, 1] | [362, 30] | simp [sub_val_eq] | case zero
R : Type u
inst✝¹ : CommRing R
inst✝ : IsDomain R
p : R
evr : ENatValRing p
x : R
h : ↑Nat.zero ≤ v evr.valtn x
⊢ x = p ^ Nat.zero * sub_val evr Nat.zero x | no goals |
https://github.com/KisaraBlue/ec-tate-lean.git | b9d36a5b70bb0958bf9741ae6216a43b35c87ed4 | ECTate/Algebra/ValuedRing.lean | ENatValRing.factor_p_of_le_val | [347, 1] | [362, 30] | rw [sub_val_val_pos_succ, sub_val_decr_val_comm, pow_succ', mul_assoc] | case succ
R : Type u
inst✝¹ : CommRing R
inst✝ : IsDomain R
p : R
evr : ENatValRing p
x : R
n : ℕ
ih : ↑n ≤ v evr.valtn x → x = p ^ n * sub_val evr n x
h : ↑(Nat.succ n) ≤ v evr.valtn x
⊢ x = p ^ Nat.succ n * sub_val evr (Nat.succ n) x | case succ
R : Type u
inst✝¹ : CommRing R
inst✝ : IsDomain R
p : R
evr : ENatValRing p
x : R
n : ℕ
ih : ↑n ≤ v evr.valtn x → x = p ^ n * sub_val evr n x
h : ↑(Nat.succ n) ≤ v evr.valtn x
⊢ x = p ^ n * (p * decr_val evr (sub_val evr n x)) |
https://github.com/KisaraBlue/ec-tate-lean.git | b9d36a5b70bb0958bf9741ae6216a43b35c87ed4 | ECTate/Algebra/ValuedRing.lean | ENatValRing.factor_p_of_le_val | [347, 1] | [362, 30] | have pos_val : evr.valtn (sub_val evr n x) > 0 := by
have h' := val_sub_val_le evr x n h
rw [Nat.succ_eq_add_one] at h'
norm_cast at h'
rw [Nat.add_sub_self_left] at h'
exact one_le_iff_pos.mp h' | case succ
R : Type u
inst✝¹ : CommRing R
inst✝ : IsDomain R
p : R
evr : ENatValRing p
x : R
n : ℕ
ih : ↑n ≤ v evr.valtn x → x = p ^ n * sub_val evr n x
h : ↑(Nat.succ n) ≤ v evr.valtn x
⊢ x = p ^ n * (p * decr_val evr (sub_val evr n x)) | case succ
R : Type u
inst✝¹ : CommRing R
inst✝ : IsDomain R
p : R
evr : ENatValRing p
x : R
n : ℕ
ih : ↑n ≤ v evr.valtn x → x = p ^ n * sub_val evr n x
h : ↑(Nat.succ n) ≤ v evr.valtn x
pos_val : v evr.valtn (sub_val evr n x) > 0
⊢ x = p ^ n * (p * decr_val evr (sub_val evr n x)) |
https://github.com/KisaraBlue/ec-tate-lean.git | b9d36a5b70bb0958bf9741ae6216a43b35c87ed4 | ECTate/Algebra/ValuedRing.lean | ENatValRing.factor_p_of_le_val | [347, 1] | [362, 30] | rw [←evr.pos_valtn_decr pos_val] | case succ
R : Type u
inst✝¹ : CommRing R
inst✝ : IsDomain R
p : R
evr : ENatValRing p
x : R
n : ℕ
ih : ↑n ≤ v evr.valtn x → x = p ^ n * sub_val evr n x
h : ↑(Nat.succ n) ≤ v evr.valtn x
pos_val : v evr.valtn (sub_val evr n x) > 0
⊢ x = p ^ n * (p * decr_val evr (sub_val evr n x)) | case succ
R : Type u
inst✝¹ : CommRing R
inst✝ : IsDomain R
p : R
evr : ENatValRing p
x : R
n : ℕ
ih : ↑n ≤ v evr.valtn x → x = p ^ n * sub_val evr n x
h : ↑(Nat.succ n) ≤ v evr.valtn x
pos_val : v evr.valtn (sub_val evr n x) > 0
⊢ x = p ^ n * sub_val evr n x |
https://github.com/KisaraBlue/ec-tate-lean.git | b9d36a5b70bb0958bf9741ae6216a43b35c87ed4 | ECTate/Algebra/ValuedRing.lean | ENatValRing.factor_p_of_le_val | [347, 1] | [362, 30] | apply ih | case succ
R : Type u
inst✝¹ : CommRing R
inst✝ : IsDomain R
p : R
evr : ENatValRing p
x : R
n : ℕ
ih : ↑n ≤ v evr.valtn x → x = p ^ n * sub_val evr n x
h : ↑(Nat.succ n) ≤ v evr.valtn x
pos_val : v evr.valtn (sub_val evr n x) > 0
⊢ x = p ^ n * sub_val evr n x | case succ
R : Type u
inst✝¹ : CommRing R
inst✝ : IsDomain R
p : R
evr : ENatValRing p
x : R
n : ℕ
ih : ↑n ≤ v evr.valtn x → x = p ^ n * sub_val evr n x
h : ↑(Nat.succ n) ≤ v evr.valtn x
pos_val : v evr.valtn (sub_val evr n x) > 0
⊢ ↑n ≤ v evr.valtn x |
https://github.com/KisaraBlue/ec-tate-lean.git | b9d36a5b70bb0958bf9741ae6216a43b35c87ed4 | ECTate/Algebra/ValuedRing.lean | ENatValRing.factor_p_of_le_val | [347, 1] | [362, 30] | rw [Nat.cast_succ] at h | case succ
R : Type u
inst✝¹ : CommRing R
inst✝ : IsDomain R
p : R
evr : ENatValRing p
x : R
n : ℕ
ih : ↑n ≤ v evr.valtn x → x = p ^ n * sub_val evr n x
h : ↑(Nat.succ n) ≤ v evr.valtn x
pos_val : v evr.valtn (sub_val evr n x) > 0
⊢ ↑n ≤ v evr.valtn x | case succ
R : Type u
inst✝¹ : CommRing R
inst✝ : IsDomain R
p : R
evr : ENatValRing p
x : R
n : ℕ
ih : ↑n ≤ v evr.valtn x → x = p ^ n * sub_val evr n x
h : ↑n + 1 ≤ v evr.valtn x
pos_val : v evr.valtn (sub_val evr n x) > 0
⊢ ↑n ≤ v evr.valtn x |
https://github.com/KisaraBlue/ec-tate-lean.git | b9d36a5b70bb0958bf9741ae6216a43b35c87ed4 | ECTate/Algebra/ValuedRing.lean | ENatValRing.factor_p_of_le_val | [347, 1] | [362, 30] | exact le_of_add_le_left h | case succ
R : Type u
inst✝¹ : CommRing R
inst✝ : IsDomain R
p : R
evr : ENatValRing p
x : R
n : ℕ
ih : ↑n ≤ v evr.valtn x → x = p ^ n * sub_val evr n x
h : ↑n + 1 ≤ v evr.valtn x
pos_val : v evr.valtn (sub_val evr n x) > 0
⊢ ↑n ≤ v evr.valtn x | no goals |
https://github.com/KisaraBlue/ec-tate-lean.git | b9d36a5b70bb0958bf9741ae6216a43b35c87ed4 | ECTate/Algebra/ValuedRing.lean | ENatValRing.factor_p_of_le_val | [347, 1] | [362, 30] | have h' := val_sub_val_le evr x n h | R : Type u
inst✝¹ : CommRing R
inst✝ : IsDomain R
p : R
evr : ENatValRing p
x : R
n : ℕ
ih : ↑n ≤ v evr.valtn x → x = p ^ n * sub_val evr n x
h : ↑(Nat.succ n) ≤ v evr.valtn x
⊢ v evr.valtn (sub_val evr n x) > 0 | R : Type u
inst✝¹ : CommRing R
inst✝ : IsDomain R
p : R
evr : ENatValRing p
x : R
n : ℕ
ih : ↑n ≤ v evr.valtn x → x = p ^ n * sub_val evr n x
h : ↑(Nat.succ n) ≤ v evr.valtn x
h' : v evr.valtn (sub_val evr n x) ≥ ↑(Nat.succ n) - ↑n
⊢ v evr.valtn (sub_val evr n x) > 0 |
https://github.com/KisaraBlue/ec-tate-lean.git | b9d36a5b70bb0958bf9741ae6216a43b35c87ed4 | ECTate/Algebra/ValuedRing.lean | ENatValRing.factor_p_of_le_val | [347, 1] | [362, 30] | rw [Nat.succ_eq_add_one] at h' | R : Type u
inst✝¹ : CommRing R
inst✝ : IsDomain R
p : R
evr : ENatValRing p
x : R
n : ℕ
ih : ↑n ≤ v evr.valtn x → x = p ^ n * sub_val evr n x
h : ↑(Nat.succ n) ≤ v evr.valtn x
h' : v evr.valtn (sub_val evr n x) ≥ ↑(Nat.succ n) - ↑n
⊢ v evr.valtn (sub_val evr n x) > 0 | R : Type u
inst✝¹ : CommRing R
inst✝ : IsDomain R
p : R
evr : ENatValRing p
x : R
n : ℕ
ih : ↑n ≤ v evr.valtn x → x = p ^ n * sub_val evr n x
h : ↑(Nat.succ n) ≤ v evr.valtn x
h' : v evr.valtn (sub_val evr n x) ≥ ↑(n + 1) - ↑n
⊢ v evr.valtn (sub_val evr n x) > 0 |
https://github.com/KisaraBlue/ec-tate-lean.git | b9d36a5b70bb0958bf9741ae6216a43b35c87ed4 | ECTate/Algebra/ValuedRing.lean | ENatValRing.factor_p_of_le_val | [347, 1] | [362, 30] | norm_cast at h' | R : Type u
inst✝¹ : CommRing R
inst✝ : IsDomain R
p : R
evr : ENatValRing p
x : R
n : ℕ
ih : ↑n ≤ v evr.valtn x → x = p ^ n * sub_val evr n x
h : ↑(Nat.succ n) ≤ v evr.valtn x
h' : v evr.valtn (sub_val evr n x) ≥ ↑(n + 1) - ↑n
⊢ v evr.valtn (sub_val evr n x) > 0 | R : Type u
inst✝¹ : CommRing R
inst✝ : IsDomain R
p : R
evr : ENatValRing p
x : R
n : ℕ
ih : ↑n ≤ v evr.valtn x → x = p ^ n * sub_val evr n x
h : ↑(Nat.succ n) ≤ v evr.valtn x
h' : v evr.valtn (sub_val evr n x) ≥ ↑(n + 1 - n)
⊢ v evr.valtn (sub_val evr n x) > 0 |
https://github.com/KisaraBlue/ec-tate-lean.git | b9d36a5b70bb0958bf9741ae6216a43b35c87ed4 | ECTate/Algebra/ValuedRing.lean | ENatValRing.factor_p_of_le_val | [347, 1] | [362, 30] | rw [Nat.add_sub_self_left] at h' | R : Type u
inst✝¹ : CommRing R
inst✝ : IsDomain R
p : R
evr : ENatValRing p
x : R
n : ℕ
ih : ↑n ≤ v evr.valtn x → x = p ^ n * sub_val evr n x
h : ↑(Nat.succ n) ≤ v evr.valtn x
h' : v evr.valtn (sub_val evr n x) ≥ ↑(n + 1 - n)
⊢ v evr.valtn (sub_val evr n x) > 0 | R : Type u
inst✝¹ : CommRing R
inst✝ : IsDomain R
p : R
evr : ENatValRing p
x : R
n : ℕ
ih : ↑n ≤ v evr.valtn x → x = p ^ n * sub_val evr n x
h : ↑(Nat.succ n) ≤ v evr.valtn x
h' : v evr.valtn (sub_val evr n x) ≥ ↑1
⊢ v evr.valtn (sub_val evr n x) > 0 |
https://github.com/KisaraBlue/ec-tate-lean.git | b9d36a5b70bb0958bf9741ae6216a43b35c87ed4 | ECTate/Algebra/ValuedRing.lean | ENatValRing.factor_p_of_le_val | [347, 1] | [362, 30] | exact one_le_iff_pos.mp h' | R : Type u
inst✝¹ : CommRing R
inst✝ : IsDomain R
p : R
evr : ENatValRing p
x : R
n : ℕ
ih : ↑n ≤ v evr.valtn x → x = p ^ n * sub_val evr n x
h : ↑(Nat.succ n) ≤ v evr.valtn x
h' : v evr.valtn (sub_val evr n x) ≥ ↑1
⊢ v evr.valtn (sub_val evr n x) > 0 | no goals |
https://github.com/KisaraBlue/ec-tate-lean.git | b9d36a5b70bb0958bf9741ae6216a43b35c87ed4 | ECTate/Algebra/ValuedRing.lean | ENatValRing.sub_val_p_mul | [367, 1] | [374, 72] | induction n with
| zero =>
rw [pow_zero, one_mul]
exact sub_val_x_zero evr x
| succ n ih =>
rwa [sub_val_val_pos_succ evr, pow_succ, mul_assoc, decr_val_p_mul] | R : Type u
inst✝¹ : CommRing R
inst✝ : IsDomain R
p : R
evr : ENatValRing p
x : R
n : ℕ
⊢ sub_val evr n (p ^ n * x) = x | no goals |
https://github.com/KisaraBlue/ec-tate-lean.git | b9d36a5b70bb0958bf9741ae6216a43b35c87ed4 | ECTate/Algebra/ValuedRing.lean | ENatValRing.sub_val_p_mul | [367, 1] | [374, 72] | rw [pow_zero, one_mul] | case zero
R : Type u
inst✝¹ : CommRing R
inst✝ : IsDomain R
p : R
evr : ENatValRing p
x : R
⊢ sub_val evr Nat.zero (p ^ Nat.zero * x) = x | case zero
R : Type u
inst✝¹ : CommRing R
inst✝ : IsDomain R
p : R
evr : ENatValRing p
x : R
⊢ sub_val evr Nat.zero x = x |
https://github.com/KisaraBlue/ec-tate-lean.git | b9d36a5b70bb0958bf9741ae6216a43b35c87ed4 | ECTate/Algebra/ValuedRing.lean | ENatValRing.sub_val_p_mul | [367, 1] | [374, 72] | exact sub_val_x_zero evr x | case zero
R : Type u
inst✝¹ : CommRing R
inst✝ : IsDomain R
p : R
evr : ENatValRing p
x : R
⊢ sub_val evr Nat.zero x = x | no goals |
https://github.com/KisaraBlue/ec-tate-lean.git | b9d36a5b70bb0958bf9741ae6216a43b35c87ed4 | ECTate/Algebra/ValuedRing.lean | ENatValRing.sub_val_p_mul | [367, 1] | [374, 72] | rwa [sub_val_val_pos_succ evr, pow_succ, mul_assoc, decr_val_p_mul] | case succ
R : Type u
inst✝¹ : CommRing R
inst✝ : IsDomain R
p : R
evr : ENatValRing p
x : R
n : ℕ
ih : sub_val evr n (p ^ n * x) = x
⊢ sub_val evr (Nat.succ n) (p ^ Nat.succ n * x) = x | no goals |
https://github.com/KisaraBlue/ec-tate-lean.git | b9d36a5b70bb0958bf9741ae6216a43b35c87ed4 | ECTate/Algebra/ValuedRing.lean | ENatValRing.sub_val_neg | [376, 1] | [387, 43] | induction n with
| zero => simp [sub_val_x_zero]
| succ n ih =>
cases @eq_zero_or_pos _ _ (evr.valtn x) with
| inl h' =>
have h'm : evr.valtn (-x) = 0 := by simp [h']
rw [sub_val_val_zero evr _ _ h', sub_val_val_zero evr _ _ h'm]
| inr h' =>
rw [sub_val_val_pos_succ evr _ _, sub_val_val_pos_succ evr _ _, sub_val_decr_val_comm, ih,
decr_val_neg, sub_val_decr_val_comm] | R : Type u
inst✝¹ : CommRing R
inst✝ : IsDomain R
p : R
evr : ENatValRing p
x : R
n : ℕ
⊢ sub_val evr n (-x) = -sub_val evr n x | no goals |
https://github.com/KisaraBlue/ec-tate-lean.git | b9d36a5b70bb0958bf9741ae6216a43b35c87ed4 | ECTate/Algebra/ValuedRing.lean | ENatValRing.sub_val_neg | [376, 1] | [387, 43] | simp [sub_val_x_zero] | case zero
R : Type u
inst✝¹ : CommRing R
inst✝ : IsDomain R
p : R
evr : ENatValRing p
x : R
⊢ sub_val evr Nat.zero (-x) = -sub_val evr Nat.zero x | no goals |
https://github.com/KisaraBlue/ec-tate-lean.git | b9d36a5b70bb0958bf9741ae6216a43b35c87ed4 | ECTate/Algebra/ValuedRing.lean | ENatValRing.sub_val_neg | [376, 1] | [387, 43] | cases @eq_zero_or_pos _ _ (evr.valtn x) with
| inl h' =>
have h'm : evr.valtn (-x) = 0 := by simp [h']
rw [sub_val_val_zero evr _ _ h', sub_val_val_zero evr _ _ h'm]
| inr h' =>
rw [sub_val_val_pos_succ evr _ _, sub_val_val_pos_succ evr _ _, sub_val_decr_val_comm, ih,
decr_val_neg, sub_val_decr_val_comm] | case succ
R : Type u
inst✝¹ : CommRing R
inst✝ : IsDomain R
p : R
evr : ENatValRing p
x : R
n : ℕ
ih : sub_val evr n (-x) = -sub_val evr n x
⊢ sub_val evr (Nat.succ n) (-x) = -sub_val evr (Nat.succ n) x | no goals |
https://github.com/KisaraBlue/ec-tate-lean.git | b9d36a5b70bb0958bf9741ae6216a43b35c87ed4 | ECTate/Algebra/ValuedRing.lean | ENatValRing.sub_val_neg | [376, 1] | [387, 43] | have h'm : evr.valtn (-x) = 0 := by simp [h'] | case succ.inl
R : Type u
inst✝¹ : CommRing R
inst✝ : IsDomain R
p : R
evr : ENatValRing p
x : R
n : ℕ
ih : sub_val evr n (-x) = -sub_val evr n x
h' : v evr.valtn x = 0
⊢ sub_val evr (Nat.succ n) (-x) = -sub_val evr (Nat.succ n) x | case succ.inl
R : Type u
inst✝¹ : CommRing R
inst✝ : IsDomain R
p : R
evr : ENatValRing p
x : R
n : ℕ
ih : sub_val evr n (-x) = -sub_val evr n x
h' : v evr.valtn x = 0
h'm : v evr.valtn (-x) = 0
⊢ sub_val evr (Nat.succ n) (-x) = -sub_val evr (Nat.succ n) x |
https://github.com/KisaraBlue/ec-tate-lean.git | b9d36a5b70bb0958bf9741ae6216a43b35c87ed4 | ECTate/Algebra/ValuedRing.lean | ENatValRing.sub_val_neg | [376, 1] | [387, 43] | rw [sub_val_val_zero evr _ _ h', sub_val_val_zero evr _ _ h'm] | case succ.inl
R : Type u
inst✝¹ : CommRing R
inst✝ : IsDomain R
p : R
evr : ENatValRing p
x : R
n : ℕ
ih : sub_val evr n (-x) = -sub_val evr n x
h' : v evr.valtn x = 0
h'm : v evr.valtn (-x) = 0
⊢ sub_val evr (Nat.succ n) (-x) = -sub_val evr (Nat.succ n) x | no goals |
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