data.rbtree.min_max
⟷
Mathlib.Data.Rbtree.MinMax
The following section lists changes to this file in mathlib3 and mathlib4 that occured after the initial port. Most recent changes are shown first. Hovering over a commit will show all commits associated with the same mathlib3 commit.
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(last sync)
mathlib commit https://github.com/leanprover-community/mathlib/commit/65a1391a0106c9204fe45bc73a039f056558cb83
@@ -65,15 +65,15 @@ theorem Std.RBNode.min_is_minimal {a : α} {t : Std.RBNode α} :
· simp [StrictWeakOrder.Equiv]; intro _ _ hs hmin b; contradiction
all_goals
cases t_lchild <;> intro lo hi hs hmin b hmem
- · simp [Std.RBNode.min] at hmin ; subst t_val
- simp [mem] at hmem ; cases' hmem with heqv hmem
+ · simp [Std.RBNode.min] at hmin; subst t_val
+ simp [mem] at hmem; cases' hmem with heqv hmem
· left; exact heqv.swap
· have := lt_of_mem_right hs (by constructor) hmem
right; assumption
all_goals
have hs' := hs
- cases hs; simp [Std.RBNode.min] at hmin
- rw [mem] at hmem ; cases_type* or.1
+ cases hs; simp [Std.RBNode.min] at hmin
+ rw [mem] at hmem; cases_type* or.1
· exact t_ih_lchild hs_hs₁ hmin hmem
· have hmm := mem_of_min_eq lt hmin
have a_lt_val := lt_of_mem_left hs' (by constructor) hmm
@@ -94,15 +94,15 @@ theorem Std.RBNode.max_is_maximal {a : α} {t : Std.RBNode α} :
· simp [StrictWeakOrder.Equiv]; intro _ _ hs hmax b; contradiction
all_goals
cases t_rchild <;> intro lo hi hs hmax b hmem
- · simp [Std.RBNode.max] at hmax ; subst t_val
- simp [mem] at hmem ; cases' hmem with hmem heqv
+ · simp [Std.RBNode.max] at hmax; subst t_val
+ simp [mem] at hmem; cases' hmem with hmem heqv
· have := lt_of_mem_left hs (by constructor) hmem
right; assumption
· left; exact heqv.swap
all_goals
have hs' := hs
- cases hs; simp [Std.RBNode.max] at hmax
- rw [mem] at hmem ; cases_type* or.1
+ cases hs; simp [Std.RBNode.max] at hmax
+ rw [mem] at hmem; cases_type* or.1
· have hmm := mem_of_max_eq lt hmax
have a_lt_b := lt_of_mem_left_right hs' (by constructor) hmem hmm
right; assumption
mathlib commit https://github.com/leanprover-community/mathlib/commit/65a1391a0106c9204fe45bc73a039f056558cb83
@@ -59,14 +59,58 @@ theorem Std.RBNode.min_is_minimal {a : α} {t : Std.RBNode α} :
∀ {lo hi},
Std.RBNode.IsSearchable lt t lo hi →
t.min = some a → ∀ {b}, Std.RBNode.Mem lt b t → a ≈[lt]b ∨ lt a b :=
- by classical
+ by
+ classical
+ induction t
+ · simp [StrictWeakOrder.Equiv]; intro _ _ hs hmin b; contradiction
+ all_goals
+ cases t_lchild <;> intro lo hi hs hmin b hmem
+ · simp [Std.RBNode.min] at hmin ; subst t_val
+ simp [mem] at hmem ; cases' hmem with heqv hmem
+ · left; exact heqv.swap
+ · have := lt_of_mem_right hs (by constructor) hmem
+ right; assumption
+ all_goals
+ have hs' := hs
+ cases hs; simp [Std.RBNode.min] at hmin
+ rw [mem] at hmem ; cases_type* or.1
+ · exact t_ih_lchild hs_hs₁ hmin hmem
+ · have hmm := mem_of_min_eq lt hmin
+ have a_lt_val := lt_of_mem_left hs' (by constructor) hmm
+ have a_lt_b := lt_of_lt_of_incomp a_lt_val hmem.swap
+ right; assumption
+ · have hmm := mem_of_min_eq lt hmin
+ have a_lt_b := lt_of_mem_left_right hs' (by constructor) hmm hmem
+ right; assumption
#align rbnode.min_is_minimal Std.RBNode.min_is_minimal
theorem Std.RBNode.max_is_maximal {a : α} {t : Std.RBNode α} :
∀ {lo hi},
Std.RBNode.IsSearchable lt t lo hi →
t.max = some a → ∀ {b}, Std.RBNode.Mem lt b t → a ≈[lt]b ∨ lt b a :=
- by classical
+ by
+ classical
+ induction t
+ · simp [StrictWeakOrder.Equiv]; intro _ _ hs hmax b; contradiction
+ all_goals
+ cases t_rchild <;> intro lo hi hs hmax b hmem
+ · simp [Std.RBNode.max] at hmax ; subst t_val
+ simp [mem] at hmem ; cases' hmem with hmem heqv
+ · have := lt_of_mem_left hs (by constructor) hmem
+ right; assumption
+ · left; exact heqv.swap
+ all_goals
+ have hs' := hs
+ cases hs; simp [Std.RBNode.max] at hmax
+ rw [mem] at hmem ; cases_type* or.1
+ · have hmm := mem_of_max_eq lt hmax
+ have a_lt_b := lt_of_mem_left_right hs' (by constructor) hmem hmm
+ right; assumption
+ · have hmm := mem_of_max_eq lt hmax
+ have val_lt_a := lt_of_mem_right hs' (by constructor) hmm
+ have a_lt_b := lt_of_incomp_of_lt hmem val_lt_a
+ right; assumption
+ · exact t_ih_rchild hs_hs₂ hmax hmem
#align rbnode.max_is_maximal Std.RBNode.max_is_maximal
end Std.RBNode
mathlib commit https://github.com/leanprover-community/mathlib/commit/65a1391a0106c9204fe45bc73a039f056558cb83
@@ -59,58 +59,14 @@ theorem Std.RBNode.min_is_minimal {a : α} {t : Std.RBNode α} :
∀ {lo hi},
Std.RBNode.IsSearchable lt t lo hi →
t.min = some a → ∀ {b}, Std.RBNode.Mem lt b t → a ≈[lt]b ∨ lt a b :=
- by
- classical
- induction t
- · simp [StrictWeakOrder.Equiv]; intro _ _ hs hmin b; contradiction
- all_goals
- cases t_lchild <;> intro lo hi hs hmin b hmem
- · simp [Std.RBNode.min] at hmin ; subst t_val
- simp [mem] at hmem ; cases' hmem with heqv hmem
- · left; exact heqv.swap
- · have := lt_of_mem_right hs (by constructor) hmem
- right; assumption
- all_goals
- have hs' := hs
- cases hs; simp [Std.RBNode.min] at hmin
- rw [mem] at hmem ; cases_type* or.1
- · exact t_ih_lchild hs_hs₁ hmin hmem
- · have hmm := mem_of_min_eq lt hmin
- have a_lt_val := lt_of_mem_left hs' (by constructor) hmm
- have a_lt_b := lt_of_lt_of_incomp a_lt_val hmem.swap
- right; assumption
- · have hmm := mem_of_min_eq lt hmin
- have a_lt_b := lt_of_mem_left_right hs' (by constructor) hmm hmem
- right; assumption
+ by classical
#align rbnode.min_is_minimal Std.RBNode.min_is_minimal
theorem Std.RBNode.max_is_maximal {a : α} {t : Std.RBNode α} :
∀ {lo hi},
Std.RBNode.IsSearchable lt t lo hi →
t.max = some a → ∀ {b}, Std.RBNode.Mem lt b t → a ≈[lt]b ∨ lt b a :=
- by
- classical
- induction t
- · simp [StrictWeakOrder.Equiv]; intro _ _ hs hmax b; contradiction
- all_goals
- cases t_rchild <;> intro lo hi hs hmax b hmem
- · simp [Std.RBNode.max] at hmax ; subst t_val
- simp [mem] at hmem ; cases' hmem with hmem heqv
- · have := lt_of_mem_left hs (by constructor) hmem
- right; assumption
- · left; exact heqv.swap
- all_goals
- have hs' := hs
- cases hs; simp [Std.RBNode.max] at hmax
- rw [mem] at hmem ; cases_type* or.1
- · have hmm := mem_of_max_eq lt hmax
- have a_lt_b := lt_of_mem_left_right hs' (by constructor) hmem hmm
- right; assumption
- · have hmm := mem_of_max_eq lt hmax
- have val_lt_a := lt_of_mem_right hs' (by constructor) hmm
- have a_lt_b := lt_of_incomp_of_lt hmem val_lt_a
- right; assumption
- · exact t_ih_rchild hs_hs₂ hmax hmem
+ by classical
#align rbnode.max_is_maximal Std.RBNode.max_is_maximal
end Std.RBNode
mathlib commit https://github.com/leanprover-community/mathlib/commit/ce64cd319bb6b3e82f31c2d38e79080d377be451
@@ -3,7 +3,7 @@ Copyright (c) 2017 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Leonardo de Moura
-/
-import Mathbin.Data.Rbtree.Basic
+import Data.Rbtree.Basic
#align_import data.rbtree.min_max from "leanprover-community/mathlib"@"8f6fd1b69096c6a587f745d354306c0d46396915"
mathlib commit https://github.com/leanprover-community/mathlib/commit/8ea5598db6caeddde6cb734aa179cc2408dbd345
@@ -2,14 +2,11 @@
Copyright (c) 2017 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Leonardo de Moura
-
-! This file was ported from Lean 3 source module data.rbtree.min_max
-! leanprover-community/mathlib commit 8f6fd1b69096c6a587f745d354306c0d46396915
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
-/
import Mathbin.Data.Rbtree.Basic
+#align_import data.rbtree.min_max from "leanprover-community/mathlib"@"8f6fd1b69096c6a587f745d354306c0d46396915"
+
universe u
namespace Std.RBNode
mathlib commit https://github.com/leanprover-community/mathlib/commit/8b981918a93bc45a8600de608cde7944a80d92b9
@@ -12,66 +12,70 @@ import Mathbin.Data.Rbtree.Basic
universe u
-namespace Rbnode
+namespace Std.RBNode
variable {α : Type u} {lt : α → α → Prop}
-theorem mem_of_min_eq (lt : α → α → Prop) [IsIrrefl α lt] {a : α} {t : Rbnode α} :
- t.min = some a → Mem lt a t := by
+theorem Std.RBNode.mem_of_min_eq (lt : α → α → Prop) [IsIrrefl α lt] {a : α} {t : Std.RBNode α} :
+ t.min = some a → Std.RBNode.Mem lt a t :=
+ by
induction t
· intros; contradiction
all_goals
- cases t_lchild <;> simp [Rbnode.min] <;> intro h
+ cases t_lchild <;> simp [Std.RBNode.min] <;> intro h
· subst t_val; simp [mem, irrefl_of lt a]
all_goals rw [mem]; simp [t_ih_lchild h]
-#align rbnode.mem_of_min_eq Rbnode.mem_of_min_eq
+#align rbnode.mem_of_min_eq Std.RBNode.mem_of_min_eq
-theorem mem_of_max_eq (lt : α → α → Prop) [IsIrrefl α lt] {a : α} {t : Rbnode α} :
- t.max = some a → Mem lt a t := by
+theorem Std.RBNode.mem_of_max_eq (lt : α → α → Prop) [IsIrrefl α lt] {a : α} {t : Std.RBNode α} :
+ t.max = some a → Std.RBNode.Mem lt a t :=
+ by
induction t
· intros; contradiction
all_goals
- cases t_rchild <;> simp [Rbnode.max] <;> intro h
+ cases t_rchild <;> simp [Std.RBNode.max] <;> intro h
· subst t_val; simp [mem, irrefl_of lt a]
all_goals rw [mem]; simp [t_ih_rchild h]
-#align rbnode.mem_of_max_eq Rbnode.mem_of_max_eq
+#align rbnode.mem_of_max_eq Std.RBNode.mem_of_max_eq
variable [IsStrictWeakOrder α lt]
-theorem eq_leaf_of_min_eq_none {t : Rbnode α} : t.min = none → t = leaf :=
+theorem Std.RBNode.eq_nil_of_min_eq_none {t : Std.RBNode α} : t.min = none → t = Std.RBNode.nil :=
by
induction t
· intros; rfl
all_goals
- cases t_lchild <;> simp [Rbnode.min, false_imp_iff] <;> intro h
+ cases t_lchild <;> simp [Std.RBNode.min, false_imp_iff] <;> intro h
all_goals have := t_ih_lchild h; contradiction
-#align rbnode.eq_leaf_of_min_eq_none Rbnode.eq_leaf_of_min_eq_none
+#align rbnode.eq_leaf_of_min_eq_none Std.RBNode.eq_nil_of_min_eq_none
-theorem eq_leaf_of_max_eq_none {t : Rbnode α} : t.max = none → t = leaf :=
+theorem Std.RBNode.eq_nil_of_max_eq_none {t : Std.RBNode α} : t.max = none → t = Std.RBNode.nil :=
by
induction t
· intros; rfl
all_goals
- cases t_rchild <;> simp [Rbnode.max, false_imp_iff] <;> intro h
+ cases t_rchild <;> simp [Std.RBNode.max, false_imp_iff] <;> intro h
all_goals have := t_ih_rchild h; contradiction
-#align rbnode.eq_leaf_of_max_eq_none Rbnode.eq_leaf_of_max_eq_none
+#align rbnode.eq_leaf_of_max_eq_none Std.RBNode.eq_nil_of_max_eq_none
-theorem min_is_minimal {a : α} {t : Rbnode α} :
- ∀ {lo hi}, IsSearchable lt t lo hi → t.min = some a → ∀ {b}, Mem lt b t → a ≈[lt]b ∨ lt a b :=
+theorem Std.RBNode.min_is_minimal {a : α} {t : Std.RBNode α} :
+ ∀ {lo hi},
+ Std.RBNode.IsSearchable lt t lo hi →
+ t.min = some a → ∀ {b}, Std.RBNode.Mem lt b t → a ≈[lt]b ∨ lt a b :=
by
classical
induction t
· simp [StrictWeakOrder.Equiv]; intro _ _ hs hmin b; contradiction
all_goals
cases t_lchild <;> intro lo hi hs hmin b hmem
- · simp [Rbnode.min] at hmin ; subst t_val
+ · simp [Std.RBNode.min] at hmin ; subst t_val
simp [mem] at hmem ; cases' hmem with heqv hmem
· left; exact heqv.swap
· have := lt_of_mem_right hs (by constructor) hmem
right; assumption
all_goals
have hs' := hs
- cases hs; simp [Rbnode.min] at hmin
+ cases hs; simp [Std.RBNode.min] at hmin
rw [mem] at hmem ; cases_type* or.1
· exact t_ih_lchild hs_hs₁ hmin hmem
· have hmm := mem_of_min_eq lt hmin
@@ -81,24 +85,26 @@ theorem min_is_minimal {a : α} {t : Rbnode α} :
· have hmm := mem_of_min_eq lt hmin
have a_lt_b := lt_of_mem_left_right hs' (by constructor) hmm hmem
right; assumption
-#align rbnode.min_is_minimal Rbnode.min_is_minimal
+#align rbnode.min_is_minimal Std.RBNode.min_is_minimal
-theorem max_is_maximal {a : α} {t : Rbnode α} :
- ∀ {lo hi}, IsSearchable lt t lo hi → t.max = some a → ∀ {b}, Mem lt b t → a ≈[lt]b ∨ lt b a :=
+theorem Std.RBNode.max_is_maximal {a : α} {t : Std.RBNode α} :
+ ∀ {lo hi},
+ Std.RBNode.IsSearchable lt t lo hi →
+ t.max = some a → ∀ {b}, Std.RBNode.Mem lt b t → a ≈[lt]b ∨ lt b a :=
by
classical
induction t
· simp [StrictWeakOrder.Equiv]; intro _ _ hs hmax b; contradiction
all_goals
cases t_rchild <;> intro lo hi hs hmax b hmem
- · simp [Rbnode.max] at hmax ; subst t_val
+ · simp [Std.RBNode.max] at hmax ; subst t_val
simp [mem] at hmem ; cases' hmem with hmem heqv
· have := lt_of_mem_left hs (by constructor) hmem
right; assumption
· left; exact heqv.swap
all_goals
have hs' := hs
- cases hs; simp [Rbnode.max] at hmax
+ cases hs; simp [Std.RBNode.max] at hmax
rw [mem] at hmem ; cases_type* or.1
· have hmm := mem_of_max_eq lt hmax
have a_lt_b := lt_of_mem_left_right hs' (by constructor) hmem hmm
@@ -108,7 +114,7 @@ theorem max_is_maximal {a : α} {t : Rbnode α} :
have a_lt_b := lt_of_incomp_of_lt hmem val_lt_a
right; assumption
· exact t_ih_rchild hs_hs₂ hmax hmem
-#align rbnode.max_is_maximal Rbnode.max_is_maximal
+#align rbnode.max_is_maximal Std.RBNode.max_is_maximal
-end Rbnode
+end Std.RBNode
mathlib commit https://github.com/leanprover-community/mathlib/commit/5f25c089cb34db4db112556f23c50d12da81b297
@@ -60,54 +60,54 @@ theorem min_is_minimal {a : α} {t : Rbnode α} :
∀ {lo hi}, IsSearchable lt t lo hi → t.min = some a → ∀ {b}, Mem lt b t → a ≈[lt]b ∨ lt a b :=
by
classical
- induction t
- · simp [StrictWeakOrder.Equiv]; intro _ _ hs hmin b; contradiction
+ induction t
+ · simp [StrictWeakOrder.Equiv]; intro _ _ hs hmin b; contradiction
+ all_goals
+ cases t_lchild <;> intro lo hi hs hmin b hmem
+ · simp [Rbnode.min] at hmin ; subst t_val
+ simp [mem] at hmem ; cases' hmem with heqv hmem
+ · left; exact heqv.swap
+ · have := lt_of_mem_right hs (by constructor) hmem
+ right; assumption
all_goals
- cases t_lchild <;> intro lo hi hs hmin b hmem
- · simp [Rbnode.min] at hmin ; subst t_val
- simp [mem] at hmem ; cases' hmem with heqv hmem
- · left; exact heqv.swap
- · have := lt_of_mem_right hs (by constructor) hmem
- right; assumption
- all_goals
- have hs' := hs
- cases hs; simp [Rbnode.min] at hmin
- rw [mem] at hmem ; cases_type*or.1
- · exact t_ih_lchild hs_hs₁ hmin hmem
- · have hmm := mem_of_min_eq lt hmin
- have a_lt_val := lt_of_mem_left hs' (by constructor) hmm
- have a_lt_b := lt_of_lt_of_incomp a_lt_val hmem.swap
- right; assumption
- · have hmm := mem_of_min_eq lt hmin
- have a_lt_b := lt_of_mem_left_right hs' (by constructor) hmm hmem
- right; assumption
+ have hs' := hs
+ cases hs; simp [Rbnode.min] at hmin
+ rw [mem] at hmem ; cases_type* or.1
+ · exact t_ih_lchild hs_hs₁ hmin hmem
+ · have hmm := mem_of_min_eq lt hmin
+ have a_lt_val := lt_of_mem_left hs' (by constructor) hmm
+ have a_lt_b := lt_of_lt_of_incomp a_lt_val hmem.swap
+ right; assumption
+ · have hmm := mem_of_min_eq lt hmin
+ have a_lt_b := lt_of_mem_left_right hs' (by constructor) hmm hmem
+ right; assumption
#align rbnode.min_is_minimal Rbnode.min_is_minimal
theorem max_is_maximal {a : α} {t : Rbnode α} :
∀ {lo hi}, IsSearchable lt t lo hi → t.max = some a → ∀ {b}, Mem lt b t → a ≈[lt]b ∨ lt b a :=
by
classical
- induction t
- · simp [StrictWeakOrder.Equiv]; intro _ _ hs hmax b; contradiction
+ induction t
+ · simp [StrictWeakOrder.Equiv]; intro _ _ hs hmax b; contradiction
+ all_goals
+ cases t_rchild <;> intro lo hi hs hmax b hmem
+ · simp [Rbnode.max] at hmax ; subst t_val
+ simp [mem] at hmem ; cases' hmem with hmem heqv
+ · have := lt_of_mem_left hs (by constructor) hmem
+ right; assumption
+ · left; exact heqv.swap
all_goals
- cases t_rchild <;> intro lo hi hs hmax b hmem
- · simp [Rbnode.max] at hmax ; subst t_val
- simp [mem] at hmem ; cases' hmem with hmem heqv
- · have := lt_of_mem_left hs (by constructor) hmem
- right; assumption
- · left; exact heqv.swap
- all_goals
- have hs' := hs
- cases hs; simp [Rbnode.max] at hmax
- rw [mem] at hmem ; cases_type*or.1
- · have hmm := mem_of_max_eq lt hmax
- have a_lt_b := lt_of_mem_left_right hs' (by constructor) hmem hmm
- right; assumption
- · have hmm := mem_of_max_eq lt hmax
- have val_lt_a := lt_of_mem_right hs' (by constructor) hmm
- have a_lt_b := lt_of_incomp_of_lt hmem val_lt_a
- right; assumption
- · exact t_ih_rchild hs_hs₂ hmax hmem
+ have hs' := hs
+ cases hs; simp [Rbnode.max] at hmax
+ rw [mem] at hmem ; cases_type* or.1
+ · have hmm := mem_of_max_eq lt hmax
+ have a_lt_b := lt_of_mem_left_right hs' (by constructor) hmem hmm
+ right; assumption
+ · have hmm := mem_of_max_eq lt hmax
+ have val_lt_a := lt_of_mem_right hs' (by constructor) hmm
+ have a_lt_b := lt_of_incomp_of_lt hmem val_lt_a
+ right; assumption
+ · exact t_ih_rchild hs_hs₂ hmax hmem
#align rbnode.max_is_maximal Rbnode.max_is_maximal
end Rbnode
mathlib commit https://github.com/leanprover-community/mathlib/commit/cca40788df1b8755d5baf17ab2f27dacc2e17acb
@@ -19,7 +19,7 @@ variable {α : Type u} {lt : α → α → Prop}
theorem mem_of_min_eq (lt : α → α → Prop) [IsIrrefl α lt] {a : α} {t : Rbnode α} :
t.min = some a → Mem lt a t := by
induction t
- · intros ; contradiction
+ · intros; contradiction
all_goals
cases t_lchild <;> simp [Rbnode.min] <;> intro h
· subst t_val; simp [mem, irrefl_of lt a]
@@ -29,7 +29,7 @@ theorem mem_of_min_eq (lt : α → α → Prop) [IsIrrefl α lt] {a : α} {t : R
theorem mem_of_max_eq (lt : α → α → Prop) [IsIrrefl α lt] {a : α} {t : Rbnode α} :
t.max = some a → Mem lt a t := by
induction t
- · intros ; contradiction
+ · intros; contradiction
all_goals
cases t_rchild <;> simp [Rbnode.max] <;> intro h
· subst t_val; simp [mem, irrefl_of lt a]
@@ -41,7 +41,7 @@ variable [IsStrictWeakOrder α lt]
theorem eq_leaf_of_min_eq_none {t : Rbnode α} : t.min = none → t = leaf :=
by
induction t
- · intros ; rfl
+ · intros; rfl
all_goals
cases t_lchild <;> simp [Rbnode.min, false_imp_iff] <;> intro h
all_goals have := t_ih_lchild h; contradiction
@@ -50,7 +50,7 @@ theorem eq_leaf_of_min_eq_none {t : Rbnode α} : t.min = none → t = leaf :=
theorem eq_leaf_of_max_eq_none {t : Rbnode α} : t.max = none → t = leaf :=
by
induction t
- · intros ; rfl
+ · intros; rfl
all_goals
cases t_rchild <;> simp [Rbnode.max, false_imp_iff] <;> intro h
all_goals have := t_ih_rchild h; contradiction
@@ -64,15 +64,15 @@ theorem min_is_minimal {a : α} {t : Rbnode α} :
· simp [StrictWeakOrder.Equiv]; intro _ _ hs hmin b; contradiction
all_goals
cases t_lchild <;> intro lo hi hs hmin b hmem
- · simp [Rbnode.min] at hmin; subst t_val
- simp [mem] at hmem; cases' hmem with heqv hmem
+ · simp [Rbnode.min] at hmin ; subst t_val
+ simp [mem] at hmem ; cases' hmem with heqv hmem
· left; exact heqv.swap
· have := lt_of_mem_right hs (by constructor) hmem
right; assumption
all_goals
have hs' := hs
- cases hs; simp [Rbnode.min] at hmin
- rw [mem] at hmem; cases_type*or.1
+ cases hs; simp [Rbnode.min] at hmin
+ rw [mem] at hmem ; cases_type*or.1
· exact t_ih_lchild hs_hs₁ hmin hmem
· have hmm := mem_of_min_eq lt hmin
have a_lt_val := lt_of_mem_left hs' (by constructor) hmm
@@ -91,15 +91,15 @@ theorem max_is_maximal {a : α} {t : Rbnode α} :
· simp [StrictWeakOrder.Equiv]; intro _ _ hs hmax b; contradiction
all_goals
cases t_rchild <;> intro lo hi hs hmax b hmem
- · simp [Rbnode.max] at hmax; subst t_val
- simp [mem] at hmem; cases' hmem with hmem heqv
+ · simp [Rbnode.max] at hmax ; subst t_val
+ simp [mem] at hmem ; cases' hmem with hmem heqv
· have := lt_of_mem_left hs (by constructor) hmem
right; assumption
· left; exact heqv.swap
all_goals
have hs' := hs
- cases hs; simp [Rbnode.max] at hmax
- rw [mem] at hmem; cases_type*or.1
+ cases hs; simp [Rbnode.max] at hmax
+ rw [mem] at hmem ; cases_type*or.1
· have hmm := mem_of_max_eq lt hmax
have a_lt_b := lt_of_mem_left_right hs' (by constructor) hmem hmm
right; assumption
mathlib commit https://github.com/leanprover-community/mathlib/commit/917c3c072e487b3cccdbfeff17e75b40e45f66cb
@@ -19,24 +19,20 @@ variable {α : Type u} {lt : α → α → Prop}
theorem mem_of_min_eq (lt : α → α → Prop) [IsIrrefl α lt] {a : α} {t : Rbnode α} :
t.min = some a → Mem lt a t := by
induction t
- · intros
- contradiction
+ · intros ; contradiction
all_goals
cases t_lchild <;> simp [Rbnode.min] <;> intro h
- · subst t_val
- simp [mem, irrefl_of lt a]
+ · subst t_val; simp [mem, irrefl_of lt a]
all_goals rw [mem]; simp [t_ih_lchild h]
#align rbnode.mem_of_min_eq Rbnode.mem_of_min_eq
theorem mem_of_max_eq (lt : α → α → Prop) [IsIrrefl α lt] {a : α} {t : Rbnode α} :
t.max = some a → Mem lt a t := by
induction t
- · intros
- contradiction
+ · intros ; contradiction
all_goals
cases t_rchild <;> simp [Rbnode.max] <;> intro h
- · subst t_val
- simp [mem, irrefl_of lt a]
+ · subst t_val; simp [mem, irrefl_of lt a]
all_goals rw [mem]; simp [t_ih_rchild h]
#align rbnode.mem_of_max_eq Rbnode.mem_of_max_eq
@@ -45,8 +41,7 @@ variable [IsStrictWeakOrder α lt]
theorem eq_leaf_of_min_eq_none {t : Rbnode α} : t.min = none → t = leaf :=
by
induction t
- · intros
- rfl
+ · intros ; rfl
all_goals
cases t_lchild <;> simp [Rbnode.min, false_imp_iff] <;> intro h
all_goals have := t_ih_lchild h; contradiction
@@ -55,8 +50,7 @@ theorem eq_leaf_of_min_eq_none {t : Rbnode α} : t.min = none → t = leaf :=
theorem eq_leaf_of_max_eq_none {t : Rbnode α} : t.max = none → t = leaf :=
by
induction t
- · intros
- rfl
+ · intros ; rfl
all_goals
cases t_rchild <;> simp [Rbnode.max, false_imp_iff] <;> intro h
all_goals have := t_ih_rchild h; contradiction
@@ -67,20 +61,14 @@ theorem min_is_minimal {a : α} {t : Rbnode α} :
by
classical
induction t
- · simp [StrictWeakOrder.Equiv]
- intro _ _ hs hmin b
- contradiction
+ · simp [StrictWeakOrder.Equiv]; intro _ _ hs hmin b; contradiction
all_goals
cases t_lchild <;> intro lo hi hs hmin b hmem
- · simp [Rbnode.min] at hmin
- subst t_val
- simp [mem] at hmem
- cases' hmem with heqv hmem
- · left
- exact heqv.swap
+ · simp [Rbnode.min] at hmin; subst t_val
+ simp [mem] at hmem; cases' hmem with heqv hmem
+ · left; exact heqv.swap
· have := lt_of_mem_right hs (by constructor) hmem
- right
- assumption
+ right; assumption
all_goals
have hs' := hs
cases hs; simp [Rbnode.min] at hmin
@@ -89,12 +77,10 @@ theorem min_is_minimal {a : α} {t : Rbnode α} :
· have hmm := mem_of_min_eq lt hmin
have a_lt_val := lt_of_mem_left hs' (by constructor) hmm
have a_lt_b := lt_of_lt_of_incomp a_lt_val hmem.swap
- right
- assumption
+ right; assumption
· have hmm := mem_of_min_eq lt hmin
have a_lt_b := lt_of_mem_left_right hs' (by constructor) hmm hmem
- right
- assumption
+ right; assumption
#align rbnode.min_is_minimal Rbnode.min_is_minimal
theorem max_is_maximal {a : α} {t : Rbnode α} :
@@ -102,33 +88,25 @@ theorem max_is_maximal {a : α} {t : Rbnode α} :
by
classical
induction t
- · simp [StrictWeakOrder.Equiv]
- intro _ _ hs hmax b
- contradiction
+ · simp [StrictWeakOrder.Equiv]; intro _ _ hs hmax b; contradiction
all_goals
cases t_rchild <;> intro lo hi hs hmax b hmem
- · simp [Rbnode.max] at hmax
- subst t_val
- simp [mem] at hmem
- cases' hmem with hmem heqv
+ · simp [Rbnode.max] at hmax; subst t_val
+ simp [mem] at hmem; cases' hmem with hmem heqv
· have := lt_of_mem_left hs (by constructor) hmem
- right
- assumption
- · left
- exact heqv.swap
+ right; assumption
+ · left; exact heqv.swap
all_goals
have hs' := hs
cases hs; simp [Rbnode.max] at hmax
rw [mem] at hmem; cases_type*or.1
· have hmm := mem_of_max_eq lt hmax
have a_lt_b := lt_of_mem_left_right hs' (by constructor) hmem hmm
- right
- assumption
+ right; assumption
· have hmm := mem_of_max_eq lt hmax
have val_lt_a := lt_of_mem_right hs' (by constructor) hmm
have a_lt_b := lt_of_incomp_of_lt hmem val_lt_a
- right
- assumption
+ right; assumption
· exact t_ih_rchild hs_hs₂ hmax hmem
#align rbnode.max_is_maximal Rbnode.max_is_maximal
mathlib commit https://github.com/leanprover-community/mathlib/commit/bd9851ca476957ea4549eb19b40e7b5ade9428cc
@@ -3,12 +3,13 @@ Copyright (c) 2017 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Leonardo de Moura
-/
+import Mathlib.Mathport.Rename
+
+#align_import data.rbtree.min_max from "leanprover-community/mathlib"@"8f6fd1b69096c6a587f745d354306c0d46396915"
/-!
# Porting note: essentially already ported to std4
-#align_import data.rbtree.min_max from "leanprover-community/mathlib"@"8f6fd1b69096c6a587f745d354306c0d46396915"
-
https://leanprover.zulipchat.com/#narrow/stream/287929-mathlib4/topic/Mathlib4.20porting.20meeting.20series/near/369848971
-/
@@ -2,16 +2,13 @@
Copyright (c) 2017 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Leonardo de Moura
-
-! This file was ported from Lean 3 source module data.rbtree.min_max
-! leanprover-community/mathlib commit 8f6fd1b69096c6a587f745d354306c0d46396915
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
-/
/-!
# Porting note: essentially already ported to std4
+#align_import data.rbtree.min_max from "leanprover-community/mathlib"@"8f6fd1b69096c6a587f745d354306c0d46396915"
+
https://leanprover.zulipchat.com/#narrow/stream/287929-mathlib4/topic/Mathlib4.20porting.20meeting.20series/near/369848971
-/
All dependencies are ported!