apply f to h

Game/Metadata.lean

@@ -10,6 +10,7 @@ import Mathlib.Tactic
 import Game.Tactic.Induction
 import Game.Tactic.Rfl
 import Game.Tactic.Rw
+import Game.Tactic.Apply
 -- import Std.Tactic.RCases
 -- import Game.Tactic.Have
 -- import Game.Tactic.LeftRight

Game/Tactic/Apply.lean

@@ -0,0 +1,21 @@
+import Mathlib.Tactic.Replace
+
+open Lean Elab Tactic
+
+/--
+If `(h : A)` is a proof of `A` and `f : A → B` an implication then
+`apply f to h` turns `h` into a proof of `B`.
+
+This is a game specific implementation. It is equivalent to the
+tactic `replace h := f h`.
+-/
+syntax (name := applyTo) "apply" ident " to " ident : tactic
+
+elab_rules : tactic | `(tactic| apply $thm to $hyp) => do
+  evalTactic (← `(tactic| replace $hyp := $thm $hyp))
+
+-- Test
+example (A B C : Prop) (ha : A) (f : A → B) (g : B → C) : C := by
+  apply g
+  apply f to ha
+  assumption