feat(library/tactic/boolean_tactics): avoid unnecessary Let expression in proof terms

Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>

src/kernel/abstract.h

@@ -52,6 +52,10 @@ inline expr Let(name const & x, expr const & v, expr const & b) { return mk_let(
 inline expr Let(expr const & x, expr const & v, expr const & b) { return mk_let(const_name(x), expr(), v, abstract(b, x)); }
 inline expr Let(std::pair<expr const &, expr const &> const & p, expr const & b) { return Let(p.first, p.second, b); }
        expr Let(std::initializer_list<std::pair<expr const &, expr const &>> const & l, expr const & b);
+/**
+   \brief Similar to Let(x, v, b), but returns v if x == b
+*/
+inline expr Let_simp(expr const & x, expr const & v, expr const & b) { return x == b ? v : Let(x, v, b); }
 
 /**
    \brief Create a Let expression (Let x : t := v in b), the term b is abstracted using abstract(b, x).

src/library/tactic/boolean_tactics.cpp

@@ -141,9 +141,9 @@ tactic conj_hyp_tactic(bool all) {
                                 expr const & H_1      = mk_constant(name(H_name, 1));
                                 expr const & H_2      = mk_constant(name(H_name, 2));
                                 if (occurs(H_1, pr))
-                                    pr = Let(H_1, Conjunct1(arg(H_prop, 1), arg(H_prop, 2), mk_constant(H_name)), pr);
+                                    pr = Let_simp(H_1, Conjunct1(arg(H_prop, 1), arg(H_prop, 2), mk_constant(H_name)), pr);
                                 if (occurs(H_2, pr))
-                                    pr = Let(H_2, Conjunct2(arg(H_prop, 1), arg(H_prop, 2), mk_constant(H_name)), pr);
+                                    pr = Let_simp(H_2, Conjunct2(arg(H_prop, 1), arg(H_prop, 2), mk_constant(H_name)), pr);
                             }
                             new_m.insert(goal_name, pr);
                         }

tests/lean/interactive/t12.lean

@@ -1,6 +1,6 @@
 (**
 -- Define a simple tactic using Lua
-auto = REPEAT(ORELSE(conj_hyp_tac, conj_tac, assumption_tac))
+auto = REPEAT(ORELSE(assumption_tac, conj_tac, conj_hyp_tac))
 **)
 
 (*
@@ -17,6 +17,8 @@ Theorem T1 (A B : Bool) : A /\ B -> B /\ A :=
               lemma2     : B      := (by auto)
           in (show B /\ A by auto)
 
+Show Environment 1. (* Show proof for the previous theorem *)
+
 (*
 When hints are not provided, the user must fill the (remaining) holes using tactic command sequences.
 Each hole must be filled with a tactic command sequence that terminates with the command 'done' and

tests/lean/interactive/t12.lean.expected.out

@@ -2,7 +2,9 @@ Type Ctrl-D or 'Exit.' to exit or 'Help.' for help.
 #   Set: pp::colors
   Set: pp::unicode
   Proved: T1
-Proof state:
+Theorem T1 (A B : Bool) (assumption : A ∧ B) : B ∧ A :=
+    let lemma1 : A := Conjunct1 assumption, lemma2 : B := Conjunct2 assumption in Conj lemma2 lemma1
+# Proof state:
 A : Bool, B : Bool, assumption : A ∧ B ⊢ A
 ## Proof state:
 no goals