fix(lean/library/standard): fix tests, more cleanup

library/standard/data/bool.lean

@@ -3,6 +3,7 @@
 -- Author: Leonardo de Moura
 
 import logic.connectives.basic logic.classes.decidable logic.classes.inhabited
+
 using eq_ops decidable
 
 inductive bool : Type :=
@@ -14,7 +15,7 @@ namespace bool
 theorem induction_on {p : bool → Prop} (b : bool) (H0 : p ff) (H1 : p tt) : p b :=
 bool_rec H0 H1 b
 
-theorem inhabited_bool [instance] : inhabited bool :=
+theorem bool_inhabited [instance] : inhabited bool :=
 inhabited_mk ff
 
 definition cond {A : Type} (b : bool) (t e : A) :=

library/standard/data/num.lean

@@ -23,7 +23,7 @@ inductive num : Type :=
 theorem inhabited_pos_num [instance] : inhabited pos_num :=
 inhabited_mk one
 
-theorem inhabited_num [instance] : inhabited num :=
+theorem num_inhabited [instance] : inhabited num :=
 inhabited_mk zero
 
 end num

library/standard/data/option.lean

@@ -1,20 +1,22 @@
-----------------------------------------------------------------------------------------------------
 -- Copyright (c) 2014 Microsoft Corporation. All rights reserved.
 -- Released under Apache 2.0 license as described in the file LICENSE.
 -- Author: Leonardo de Moura
-----------------------------------------------------------------------------------------------------
+
 import logic.connectives.basic logic.connectives.eq logic.classes.inhabited logic.classes.decidable
 using eq_ops decidable
 
 namespace option
+
 inductive option (A : Type) : Type :=
 | none {} : option A
 | some    : A → option A
 
-theorem induction_on {A : Type} {p : option A → Prop} (o : option A) (H1 : p none) (H2 : ∀a, p (some a)) : p o :=
+theorem induction_on {A : Type} {p : option A → Prop} (o : option A) 
+  (H1 : p none) (H2 : ∀a, p (some a)) : p o :=
 option_rec H1 H2 o
 
-definition rec_on {A : Type} {C : option A → Type} (o : option A) (H1 : C none) (H2 : ∀a, C (some a)) : C o :=
+definition rec_on {A : Type} {C : option A → Type} (o : option A) 
+  (H1 : C none) (H2 : ∀a, C (some a)) : C o :=
 option_rec H1 H2 o
 
 definition is_none {A : Type} (o : option A) : Prop :=
@@ -34,10 +36,11 @@ assume H : none = some a, absurd
 theorem some_inj {A : Type} {a₁ a₂ : A} (H : some a₁ = some a₂) : a₁ = a₂ :=
 congr_arg (option_rec a₁ (λ a, a)) H
 
-theorem inhabited_option [instance] (A : Type) : inhabited (option A) :=
+theorem option_inhabited [instance] (A : Type) : inhabited (option A) :=
 inhabited_mk none
 
-theorem decidable_eq [instance] {A : Type} {H : ∀a₁ a₂ : A, decidable (a₁ = a₂)} (o₁ o₂ : option A) : decidable (o₁ = o₂) :=
+theorem decidable_eq [instance] {A : Type} {H : ∀a₁ a₂ : A, decidable (a₁ = a₂)} 
+    (o₁ o₂ : option A) : decidable (o₁ = o₂) :=
 rec_on o₁
   (rec_on o₂ (inl (refl _)) (take a₂, (inr (none_ne_some a₂))))
   (take a₁ : A, rec_on o₂
@@ -45,4 +48,5 @@ rec_on o₁
     (take a₂ : A, decidable.rec_on (H a₁ a₂)
       (assume Heq : a₁ = a₂, inl (Heq ▸ refl _))
       (assume Hne : a₁ ≠ a₂, inr (assume Hn : some a₁ = some a₂, absurd (some_inj Hn) Hne))))
+
 end option

library/standard/data/quotient/basic.lean

@@ -7,13 +7,14 @@ import logic.connectives.instances
 import .aux
 
 using relation prod inhabited nonempty tactic eq_ops
+using subtype relation.iff_ops
+
 
 -- Theory data.quotient
 -- ====================
 
 namespace quotient
 
-using subtype
 
 -- definition and basics
 -- ---------------------
@@ -29,34 +30,6 @@ theorem intro {A B : Type} {R : A → A → Prop} {abs : A → B} {rep : B → A
   (H3 : ∀r s, R r s ↔ (R r r ∧ R s s ∧ abs r = abs s)) : is_quotient R abs rep := 
 and_intro H1 (and_intro H2 H3)
 
--- theorem intro_refl {A B : Type} {R : A → A → Prop} {abs : A → B} {rep : B → A}
---   (H1 : reflexive R) (H2 : ∀b, abs (rep b) = b)
---   (H3 : ∀r s, R r s ↔ abs r = abs s) : is_quotient R abs rep :=
--- intro
---   H2
---   (take b, H1 (rep b))
---   (take r s,
---     have H4 : R r s ↔ R s s ∧ abs r = abs s,
---       from 
---         gensubst.subst (relation.operations.symm (and_absorb_left _ (H1 s))) (H3 r s),
---     gensubst.subst (relation.operations.symm (and_absorb_left _ (H1 r))) H4)
-
--- these work now, but the above still does not
--- theorem test (a b c : Prop) (P : Prop → Prop) (H1 : a ↔ b) (H2 : c ∧ a) : c ∧ b :=
--- gensubst.subst H1 H2
-
--- theorem test2 {A : Type} {R : A → A → Prop} (Q : Prop) (r s : A) 
---   (H3 : R r s ↔ Q) (H1 : R s s) : Q ↔ (R s s ∧ Q) :=
--- relation.operations.symm (and_absorb_left Q H1)
-
--- theorem test3 {A : Type} {R : A → A → Prop} (Q : Prop) (r s : A) 
---   (H3 : R r s ↔ Q) (H1 : R s s) : R r s ↔ (R s s ∧ Q) :=
--- gensubst.subst (test2 Q r s H3 H1) H3
-
--- theorem test4 {A : Type} {R : A → A → Prop} (Q : Prop) (r s : A) 
---   (H3 : R r s ↔ Q) (H1 : R s s) : R r s ↔ (R s s ∧ Q) :=
--- gensubst.subst (relation.operations.symm (and_absorb_left Q H1)) H3
-
 theorem and_absorb_left {a : Prop} (b : Prop) (Ha : a) : a ∧ b ↔ b :=
 iff_intro (assume Hab, and_elim_right Hab) (assume Hb, and_intro Ha Hb)
 
@@ -69,20 +42,8 @@ intro
   (take r s,
     have H4 : R r s ↔ R s s ∧ abs r = abs s,
       from 
-        subst_iff (iff_symm (and_absorb_left _ (H1 s))) (H3 r s),
-    subst_iff (iff_symm (and_absorb_left _ (H1 r))) H4)
-
--- theorem intro_refl {A B : Type} {R : A → A → Prop} {abs : A → B} {rep : B → A}
---   (H1 : reflexive R) (H2 : ∀b, abs (rep b) = b)
---   (H3 : ∀r s, R r s ↔ abs r = abs s) : is_quotient R abs rep :=
--- intro
---   H2
---   (take b, H1 (rep b))
---   (take r s,
---     have H4 : R r s ↔ R s s ∧ abs r = abs s,
---       from 
---         substi (iff_symm (and_absorb_left _ (H1 s))) (H3 r s),
---     substi (iff_symm (and_absorb_left _ (H1 r))) H4)
+        subst (symm (and_absorb_left _ (H1 s))) (H3 r s),
+    subst (symm (and_absorb_left _ (H1 r))) H4)
 
 theorem abs_rep {A B : Type} {R : A → A → Prop} {abs : A → B} {rep : B → A}
   (Q : is_quotient R abs rep) (b : B) :  abs (rep b) = b := 
@@ -147,6 +108,7 @@ have Hc : R c c, from refl_right Q Hbc,
 have Hac : abs a = abs c, from trans (eq_abs Q Hab) (eq_abs Q Hbc),
 R_intro Q Ha Hc Hac
 
+
 -- recursion
 -- ---------
 
@@ -299,28 +261,28 @@ calc
 -- ------------------------------------------
 
 theorem representative_map_idempotent {A : Type} {R : A → A → Prop} {f : A → A}
-  (H1 : ∀a, R a (f a)) (H2 : ∀a b, R a b ↔ R a a ∧ R b b ∧ f a = f b) (a : A)
-  : f (f a) = f a :=
+    (H1 : ∀a, R a (f a)) (H2 : ∀a b, R a b ↔ R a a ∧ R b b ∧ f a = f b) (a : A) :
+  f (f a) = f a :=
 symm (and_elim_right (and_elim_right (iff_elim_left (H2 a (f a)) (H1 a))))
 
 theorem representative_map_idempotent_equiv {A : Type} {R : A → A → Prop} {f : A → A}
-  (H1 : ∀a, R a (f a)) (H2 : ∀a b, R a b → f a = f b) (a : A)
-  : f (f a) = f a :=
+    (H1 : ∀a, R a (f a)) (H2 : ∀a b, R a b → f a = f b) (a : A) :
+  f (f a) = f a :=
 symm (H2 a (f a) (H1 a))
 
 theorem representative_map_refl_rep {A : Type} {R : A → A → Prop} {f : A → A}
-  (H1 : ∀a, R a (f a)) (H2 : ∀a b, R a b ↔ R a a ∧ R b b ∧ f a = f b) (a : A)
-  : R (f a) (f a) :=
+    (H1 : ∀a, R a (f a)) (H2 : ∀a b, R a b ↔ R a a ∧ R b b ∧ f a = f b) (a : A) :
+  R (f a) (f a) :=
 subst (representative_map_idempotent H1 H2 a) (H1 (f a)) 
 
 theorem representative_map_image_fix {A : Type} {R : A → A → Prop} {f : A → A}
-  (H1 : ∀a, R a (f a)) (H2 : ∀a a', R a a' ↔ R a a ∧ R a' a' ∧ f a = f a') (b : image f)
-  : f (elt_of b) = elt_of b :=
+    (H1 : ∀a, R a (f a)) (H2 : ∀a a', R a a' ↔ R a a ∧ R a' a' ∧ f a = f a') (b : image f) :
+  f (elt_of b) = elt_of b :=
 idempotent_image_fix (representative_map_idempotent H1 H2) b
 
 theorem representative_map_to_quotient {A : Type} {R : A → A → Prop} {f : A → A}
-  (H1 : ∀a, R a (f a)) (H2 : ∀a a', R a a' ↔ R a a ∧ R a' a' ∧ f a = f a')
-  : is_quotient _ (fun_image f) elt_of :=
+    (H1 : ∀a, R a (f a)) (H2 : ∀a a', R a a' ↔ R a a ∧ R a' a' ∧ f a = f a') :
+  is_quotient _ (fun_image f) elt_of :=
 let abs [inline] := fun_image f in
 intro
   (take u : image f,
@@ -337,30 +299,31 @@ intro
       obtain (a : A) (Ha : f a = elt_of u), from image_elt_of u,
         subst Ha (@representative_map_refl_rep A R f H1 H2 a))
   (take a a', 
-    subst_iff (fun_image_eq f a a') (H2 a a'))
+    subst (fun_image_eq f a a') (H2 a a'))
 
 theorem representative_map_equiv_inj {A : Type} {R : A → A → Prop}
-  (equiv : is_equivalence R) {f : A → A} (H1 : ∀a, R a (f a)) (H2 : ∀a b, R a b → f a = f b)
-  {a b : A} (H3 : f a = f b) : R a b :=
-have symmR : symmetric R, from is_symmetric.infer R,
-have transR : transitive R, from is_transitive.infer R,
+    (equiv : is_equivalence R) {f : A → A} 
+    (H1 : ∀a, R a (f a)) (H2 : ∀a b, R a b → f a = f b) {a b : A} (H3 : f a = f b) : 
+  R a b :=
+have symmR : symmetric R, from rel_symm R,
+have transR : transitive R, from rel_trans R,
 show R a b, from
   have H2 : R a (f b), from subst H3 (H1 a),
   have H3 : R (f b) b, from symmR (H1 b),
   transR H2 H3
 
 theorem representative_map_to_quotient_equiv {A : Type} {R : A → A → Prop}
-  (equiv : is_equivalence R) {f : A → A} (H1 : ∀a, R a (f a)) (H2 : ∀a b, R a b → f a = f b)
-  : @is_quotient A (image f) R (fun_image f) elt_of :=
+    (equiv : is_equivalence R) {f : A → A} (H1 : ∀a, R a (f a)) (H2 : ∀a b, R a b → f a = f b) :
+  @is_quotient A (image f) R (fun_image f) elt_of :=
 representative_map_to_quotient
   H1
   (take a b,
-    have reflR : reflexive R, from is_reflexive.infer R,
+    have reflR : reflexive R, from rel_refl R,
     have H3 : f a = f b → R a b, from representative_map_equiv_inj equiv H1 H2,
     have H4 : R a b ↔ f a = f b, from iff_intro (H2 a b) H3,
     have H5 : R a b ↔ R b b ∧ f a = f b,
-      from subst_iff (iff_symm (and_absorb_left _ (reflR b))) H4,
-    subst_iff (iff_symm (and_absorb_left _ (reflR a))) H5)
+      from subst (symm (and_absorb_left _ (reflR b))) H4,
+    subst (symm (and_absorb_left _ (reflR a))) H5)
 
 -- previously:
 -- opaque_hint (hiding fun_image rec is_quotient prelim_map)

library/standard/data/string.lean

@@ -15,10 +15,10 @@ inductive string : Type :=
 | empty : string
 | str   : char → string → string
 
-theorem inhabited_char [instance] : inhabited char :=
+theorem char_inhabited [instance] : inhabited char :=
 inhabited_mk (ascii ff ff ff ff ff ff ff ff)
 
-theorem inhabited_string [instance] : inhabited string :=
+theorem string_inhabited [instance] : inhabited string :=
 inhabited_mk empty
 
 end string

library/standard/data/unit.lean

@@ -1,13 +1,13 @@
-----------------------------------------------------------------------------------------------------
 -- Copyright (c) 2014 Microsoft Corporation. All rights reserved.
 -- Released under Apache 2.0 license as described in the file LICENSE.
 -- Author: Leonardo de Moura
-----------------------------------------------------------------------------------------------------
 
 import logic.classes.decidable logic.classes.inhabited
+
 using decidable
 
 namespace unit
+
 inductive unit : Type :=
 | star : unit
 
@@ -16,9 +16,10 @@ notation `⋆`:max := star
 theorem unit_eq (a b : unit) : a = b :=
 unit_rec (unit_rec (refl ⋆) b) a
 
-theorem inhabited_unit [instance] : inhabited unit :=
+theorem unit_inhabited [instance] : inhabited unit :=
 inhabited_mk ⋆
 
 theorem decidable_eq [instance] (a b : unit) : decidable (a = b) :=
 inl (unit_eq a b)
+
 end unit

library/standard/logic/axioms/hilbert.lean

@@ -27,7 +27,7 @@ theorem nonempty_imp_inhabited {A : Type} (H : nonempty A) : inhabited A :=
 let u : {x : A | (∃x : A, true) → true} := strong_indefinite_description (λa, true) H in
 inhabited_mk (elt_of u)
 
-theorem inhabited_exists {A : Type} {P : A → Prop} (H : ∃x, P x) : inhabited A :=
+theorem exists_imp_inhabited {A : Type} {P : A → Prop} (H : ∃x, P x) : inhabited A :=
 nonempty_imp_inhabited (obtain w Hw, from H, nonempty_intro w)
 
 

library/standard/logic/axioms/prop_decidable.lean

@@ -10,13 +10,13 @@ using decidable inhabited nonempty
 -- Excluded middle + Hilbert implies every proposition is decidable
 
 -- First, we show that (decidable a) is inhabited for any 'a' using the excluded middle
-theorem inhabited_decidable [instance] (a : Prop) : inhabited (decidable a) :=
+theorem decidable_inhabited [instance] (a : Prop) : inhabited (decidable a) :=
 nonempty_imp_inhabited
   (or_elim (em a)
     (assume Ha, nonempty_intro (inl Ha))
     (assume Hna, nonempty_intro (inr Hna)))
 
--- Note that inhabited_decidable is marked as an instance, and it is silently used
+-- Note that decidable_inhabited is marked as an instance, and it is silently used
 -- for synthesizing the implicit argument in the following 'epsilon'
 theorem prop_decidable [instance] (a : Prop) : decidable a :=
 epsilon (λd, true)

library/standard/logic/classes/inhabited.lean

@@ -12,10 +12,10 @@ namespace inhabited
 definition inhabited_destruct {A : Type} {B : Type} (H1 : inhabited A) (H2 : A → B) : B :=
 inhabited_rec H2 H1
 
-definition inhabited_Prop [instance] : inhabited Prop :=
+definition Prop_inhabited [instance] : inhabited Prop :=
 inhabited_mk true
 
-definition inhabited_fun [instance] (A : Type) {B : Type} (H : inhabited B) : inhabited (A → B) :=
+definition fun_inhabited [instance] (A : Type) {B : Type} (H : inhabited B) : inhabited (A → B) :=
 inhabited_destruct H (take b, inhabited_mk (λa, b))
 
 definition default (A : Type) {H : inhabited A} : A := inhabited_destruct H (take a, a)

library/standard/logic/connectives/basic.lean

@@ -153,10 +153,12 @@ theorem iff_intro {a b : Prop} (H1 : a → b) (H2 : b → a) : a ↔ b := and_in
 
 theorem iff_elim {a b c : Prop} (H1 : (a → b) → (b → a) → c) (H2 : a ↔ b) : c := and_rec H1 H2
 
-theorem iff_elim_left {a b : Prop} (H : a ↔ b) : a → b :=
+theorem iff_elim_left ⦃a b : Prop⦄ (H : a ↔ b) : a → b :=
 iff_elim (assume H1 H2, H1) H
 
-theorem iff_elim_right {a b : Prop} (H : a ↔ b) : b → a :=
+abbreviation iff_mp := iff_elim_left
+
+theorem iff_elim_right ⦃a b : Prop⦄ (H : a ↔ b) : b → a :=
 iff_elim (assume H1 H2, H2) H
 
 theorem iff_flip_sign {a b : Prop} (H1 : a ↔ b) : ¬a ↔ ¬b :=
@@ -167,12 +169,12 @@ iff_intro
 theorem iff_refl (a : Prop) : a ↔ a :=
 iff_intro (assume H, H) (assume H, H)
 
-theorem iff_trans {a b c : Prop} (H1 : a ↔ b) (H2 : b ↔ c) : a ↔ c :=
+theorem iff_trans ⦃a b c : Prop⦄ (H1 : a ↔ b) (H2 : b ↔ c) : a ↔ c :=
 iff_intro
   (assume Ha, iff_elim_left H2 (iff_elim_left H1 Ha))
   (assume Hc, iff_elim_right H1 (iff_elim_right H2 Hc))
 
-theorem iff_symm {a b : Prop} (H : a ↔ b) : b ↔ a :=
+theorem iff_symm ⦃a b : Prop⦄ (H : a ↔ b) : b ↔ a :=
 iff_intro
   (assume Hb, iff_elim_right H Hb)
   (assume Ha, iff_elim_left H Ha)

library/standard/logic/connectives/examples/instances_test.lean

@@ -44,6 +44,6 @@ theorem test7 (T : Type) (a b c d : T) (H1 : a = b) (H2 : c = b) (H3 : c = d) :
 trans H1 (trans (symm H2) H3)
 
 theorem test8 (a b c d : Prop) (H1 : a ↔ b) (H2 : c ↔ b) (H3 : c ↔ d) : a ↔ d :=
-trans iff H1 (trans iff (symm iff H2) H3)
+trans H1 (trans (symm H2) H3)
 
 end

library/standard/logic/connectives/instances.lean

@@ -107,30 +107,34 @@ relation.is_transitive_mk (@iff_trans)
 theorem mp_like_iff [instance] (a b : Prop) (H : a ↔ b) : relation.mp_like H :=
 relation.mp_like_mk (iff_elim_left H)
 
+
 -- Substition for iff
 -- ------------------
 
-theorem subst_iff {P : Prop → Prop} {C : congr iff iff P} {a b : Prop} (H : a ↔ b) (H1 : P a) :
+theorem subst_iff ⦃P : Prop → Prop⦄ {C : congr iff iff P} {a b : Prop} (H : a ↔ b) (H1 : P a) :
   P b :=
 @general_operations.subst Prop iff P C a b H H1
 
--- Support for calc
+
+-- Support for calculations with iff
 -- ----------------
 
 calc_refl iff_refl
-calc_subst subst_iff
 calc_trans iff_trans
+calc_subst subst_iff
 
 namespace iff_ops
   postfix `⁻¹`:100 := iff_symm
   infixr `⬝`:75     := iff_trans
   infixr `▸`:75    := subst_iff
+  abbreviation refl := iff_refl
+  abbreviation symm := iff_symm
+  abbreviation trans := iff_trans
+  abbreviation subst := subst_iff
+  abbreviation mp := iff_mp
 end iff_ops
 
 
-
-
-
 -- Boolean calculations
 -- --------------------
 
@@ -144,4 +148,7 @@ calc
 
 -- TODO: add or_left_comm, and_right_comm, and_left_comm
 
+-- TODO: this is only temporary, until the calc bug is fixed
+calc_subst subst
+
 end relation

library/standard/struc/relation.lean

@@ -187,21 +187,10 @@ end mp_like
 -- Notation for operations on general symbols
 -- ------------------------------------------
 
-namespace general_operations
-
 -- e.g. if R is an instance of the class, then "refl R" is reflexivity for the class
-definition refl := is_reflexive.infer
-definition symm := is_symmetric.infer
-definition trans := is_transitive.infer
-definition mp := mp_like.infer
-
-end general_operations
-
--- namespace
---
--- postfix `⁻¹`:100 := operations.symm
--- infixr `⬝`:75     := operations.trans
-
--- end symbols
+definition rel_refl := is_reflexive.infer
+definition rel_symm := is_symmetric.infer
+definition rel_trans := is_transitive.infer
+definition rel_mp := mp_like.infer
 
 end relation

src/library/string.cpp

@@ -14,9 +14,9 @@ namespace lean {
 static name g_string_macro("string_macro");
 static std::string g_string_opcode("Str");
 
-static expr g_bool(Const(name("bool", "bool")));
-static expr g_ff(Const(name("bool", "ff")));
-static expr g_tt(Const(name("bool", "tt")));
+static expr g_bool(Const(name("bool")));
+static expr g_ff(Const(name("ff")));
+static expr g_tt(Const(name("tt")));
 static expr g_char(Const(name("string", "char")));
 static expr g_ascii(Const(name("string", "ascii")));
 static expr g_string(Const(name("string", "string")));

tests/lean/empty.lean

@@ -1,4 +1,5 @@
 import logic logic.axioms.hilbert
+using inhabited nonempty
 
 definition v1 : Prop := epsilon (λ x, true)
 inductive Empty : Type

tests/lean/have1.lean

@@ -1,5 +1,5 @@
 import standard
-using bool eq_proofs tactic
+using bool eq_ops tactic
 
 variables a b c : bool
 axiom H1 : a = b

tests/lean/run/class1.lean

@@ -1,5 +1,5 @@
 import standard
-using num prod
+using num prod inhabited
 
 definition H : inhabited (Prop × num × (num → num)) := _
 

tests/lean/run/class2.lean

@@ -1,5 +1,5 @@
 import standard
-using num prod
+using num prod nonempty inhabited
 
 theorem H {A B : Type} (H1 : inhabited A) : inhabited (Prop × A × (B → num))
 := _

tests/lean/run/class3.lean

@@ -1,5 +1,5 @@
 import standard
-using num prod
+using num prod inhabited
 
 section
   parameter {A : Type}

tests/lean/run/class6.lean

@@ -8,10 +8,10 @@ inductive t2 : Type :=
 | mk2 : t2
 
 theorem inhabited_t1 : inhabited t1
-:= inhabited_intro mk1
+:= inhabited_mk mk1
 
 theorem inhabited_t2 : inhabited t2
-:= inhabited_intro mk2
+:= inhabited_mk mk2
 
 instance inhabited_t1 inhabited_t2
 

tests/lean/run/list_elab1.lean

@@ -10,8 +10,7 @@
 -- Basic properties of lists.
 
 import data.nat
-using nat eq_proofs
-
+using nat eq_ops
 inductive list (T : Type) : Type :=
 | nil {} : list T
 | cons : T → list T → list T

tests/lean/run/nat_bug.lean

@@ -16,10 +16,10 @@ theorem zero_or_succ (n : nat) : n = zero ∨ n = succ (pred n)
 := induction_on n
     (or_intro_left _ (refl zero))
     (take m IH, or_intro_right _
-      (show succ m = succ (pred (succ m)), from congr2 succ (symm (pred_succ m))))
+      (show succ m = succ (pred (succ m)), from congr_arg succ (symm (pred_succ m))))
 
 theorem zero_or_succ2 (n : nat) : n = zero ∨ n = succ (pred n)
 := @induction_on _ n
     (or_intro_left _ (refl zero))
     (take m IH, or_intro_right _
-      (show succ m = succ (pred (succ m)), from congr2 succ (symm (pred_succ m))))
+      (show succ m = succ (pred (succ m)), from congr_arg succ (symm (pred_succ m))))

tests/lean/run/nat_bug2.lean

@@ -1,5 +1,5 @@
 import standard
-using num eq_proofs
+using num eq_ops
 
 inductive nat : Type :=
 | zero : nat

tests/lean/run/nat_bug3.lean

@@ -1,5 +1,5 @@
 import standard
-using num eq_proofs
+using num eq_ops
 
 inductive nat : Type :=
 | zero : nat

tests/lean/run/nat_bug4.lean

@@ -1,5 +1,5 @@
 import standard
-using num eq_proofs
+using num eq_ops
 
 inductive nat : Type :=
 | zero : nat

tests/lean/run/nat_bug5.lean

@@ -1,5 +1,5 @@
 import standard
-using num eq_proofs
+using num eq_ops
 
 inductive nat : Type :=
 | zero : nat

tests/lean/run/nat_bug6.lean

@@ -1,5 +1,5 @@
 import standard
-using eq_proofs
+using eq_ops
 
 inductive nat : Type :=
 | zero : nat

tests/lean/run/rel.lean

@@ -4,15 +4,15 @@ using relation
 namespace is_equivalence
 
   inductive class {T : Type} (R : T → T → Type) : Prop :=
-  | mk : is_reflexive.class R → is_symmetric.class R → is_transitive.class R → class R
+  | mk : is_reflexive R → is_symmetric R → is_transitive R → class R
 
-  theorem is_reflexive {T : Type} {R : T → T → Type} {C : class R} : is_reflexive.class R :=
+  theorem is_reflexive {T : Type} {R : T → T → Type} {C : class R} : is_reflexive R :=
   class_rec (λx y z, x) C
 
-  theorem is_symmetric {T : Type} {R : T → T → Type} {C : class R} : is_symmetric.class R :=
+  theorem is_symmetric {T : Type} {R : T → T → Type} {C : class R} : is_symmetric R :=
   class_rec (λx y z, y) C
 
-  theorem is_transitive {T : Type} {R : T → T → Type} {C : class R} : is_transitive.class R :=
+  theorem is_transitive {T : Type} {R : T → T → Type} {C : class R} : is_transitive R :=
   class_rec (λx y z, z) C
 
 end is_equivalence
@@ -25,14 +25,13 @@ theorem and_inhabited_left {a : Prop} (b : Prop) (Ha : a) : a ∧ b ↔ b :=
 iff_intro (take Hab, and_elim_right Hab) (take Hb, and_intro Ha Hb)
 
 theorem test (a b c : Prop) (P : Prop → Prop) (H1 : a ↔ b) (H2 : c ∧ a) : c ∧ b :=
-gensubst.subst H1 H2
+subst_iff H1 H2
 
 theorem test2 (Q R S : Prop) (H3 : R ↔ Q) (H1 : S) : Q ↔ (S ∧ Q) :=
-relation.operations.symm (and_inhabited_left Q H1)
+iff_symm (and_inhabited_left Q H1)
 
 theorem test3 (Q R S : Prop) (H3 : R ↔ Q) (H1 : S) : R ↔ (S ∧ Q) :=
-gensubst.subst (test2 Q R S H3 H1) H3
+subst_iff (test2 Q R S H3 H1) H3
 
--- the composition of test2' and test3' fails
 theorem test4 (Q R S : Prop) (H3 : R ↔ Q) (H1 : S) : R ↔ (S ∧ Q) :=
-gensubst.subst (relation.operations.symm (and_inhabited_left Q H1)) H3
+subst_iff (iff_symm (and_inhabited_left Q H1)) H3

tests/lean/run/tactic16.lean

@@ -1,4 +1,4 @@
-import standard
+import standard data.string
 using tactic
 
 variable A : Type.{1}

tests/lean/run/tactic17.lean

@@ -6,7 +6,7 @@ variable f : A → A → A
 
 theorem tst {a b c : A} (H1 : a = b) (H2 : b = c) : f a b = f b c
 := by apply (@congr A A (f a) (f b));
-      apply (congr2 f);
+      apply (congr_arg f);
       !assumption
 
 

tests/lean/run/tactic26.lean

@@ -1,19 +1,19 @@
 import standard
-using tactic
+using tactic inhabited
 
 inductive sum (A : Type) (B : Type) : Type :=
 | inl  : A → sum A B
 | inr  : B → sum A B
 
 theorem inl_inhabited {A : Type} (B : Type) (H : inhabited A) : inhabited (sum A B)
-:= inhabited_elim H (λ a, inhabited_intro (inl B a))
+:= inhabited_destruct H (λ a, inhabited_mk (inl B a))
 
 theorem inr_inhabited (A : Type) {B : Type} (H : inhabited B) : inhabited (sum A B)
-:= inhabited_elim H (λ b, inhabited_intro (inr A b))
+:= inhabited_destruct H (λ b, inhabited_mk (inr A b))
 
 definition my_tac := fixpoint (λ t, [ apply @inl_inhabited; t
                                     | apply @inr_inhabited; t
-                                    | apply @num.inhabited_num
+                                    | apply @num.num_inhabited
                                     ])
 
 tactic_hint [inhabited] my_tac

tests/lean/run/tactic28.lean

@@ -1,22 +1,22 @@
 import standard
-using tactic
+using tactic inhabited
 
 inductive sum (A : Type) (B : Type) : Type :=
 | inl  : A → sum A B
 | inr  : B → sum A B
 
 theorem inl_inhabited {A : Type} (B : Type) (H : inhabited A) : inhabited (sum A B)
-:= inhabited_elim H (λ a, inhabited_intro (inl B a))
+:= inhabited_destruct H (λ a, inhabited_mk (inl B a))
 
 theorem inr_inhabited (A : Type) {B : Type} (H : inhabited B) : inhabited (sum A B)
-:= inhabited_elim H (λ b, inhabited_intro (inr A b))
+:= inhabited_destruct H (λ b, inhabited_mk (inr A b))
 
 infixl `..`:100 := append
 
 definition my_tac := repeat (trace "iteration"; state;
                               (  apply @inl_inhabited; trace "used inl"
                               .. apply @inr_inhabited; trace "used inr"
-                              .. apply @num.inhabited_num; trace "used num")) ; now
+                              .. apply @num.num_inhabited; trace "used num")) ; now
 
 
 tactic_hint [inhabited] my_tac

tests/lean/show1.lean

@@ -1,5 +1,5 @@
 import standard
-using bool eq_proofs tactic
+using bool eq_ops tactic
 
 variables a b c : bool
 axiom H1 : a = b

tests/lean/slow/list_elab2.lean

@@ -14,7 +14,7 @@ import logic data.nat
 
 using nat
 -- using congr
-using eq_proofs
+using eq_ops
 
 namespace list
 

tests/lean/slow/nat_wo_hints.lean

@@ -4,7 +4,7 @@
 -- Author: Floris van Doorn
 ----------------------------------------------------------------------------------------------------
 import standard struc.binary
-using tactic num binary eq_proofs
+using tactic num binary eq_ops
 using decidable
 
 namespace nat
@@ -57,7 +57,7 @@ theorem zero_or_succ (n : ℕ) : n = 0 ∨ n = succ (pred n)
 := induction_on n
     (or_intro_left _ (refl 0))
     (take m IH, or_intro_right _
-      (show succ m = succ (pred (succ m)), from congr2 succ (pred_succ m⁻¹)))
+      (show succ m = succ (pred (succ m)), from congr_arg succ (pred_succ m⁻¹)))
 
 theorem zero_or_succ2 (n : ℕ) : n = 0 ∨ ∃k, n = succ k
 := or_imp_or (zero_or_succ n) (assume H, H) (assume H : n = succ (pred n), exists_intro (pred n) H)
@@ -96,7 +96,7 @@ theorem decidable_eq [instance] (n m : ℕ) : decidable (n = m)
            (λ (n' : ℕ) (iH2 : decidable (n' = succ m')),
              have d1 : decidable (n' = m'), from iH1 n',
              decidable.rec_on d1
-               (assume Heq : n' = m', inl (congr2 succ Heq))
+               (assume Heq : n' = m', inl (congr_arg succ Heq))
                (assume Hne : n' ≠ m',
                  have H1 : succ n' ≠ succ m', from
                    assume Heq, absurd (succ_inj Heq) Hne,