feat: Congruence tactics

Pantograph/Tactic.lean

@@ -1,3 +1,4 @@
 
+import Pantograph.Tactic.Congruence
 import Pantograph.Tactic.MotivatedApply
 import Pantograph.Tactic.NoConfuse

Pantograph/Tactic/Congruence.lean

@@ -0,0 +1,78 @@
+import Lean
+
+open Lean
+
+namespace Pantograph.Tactic
+
+def congruenceArg: Elab.Tactic.TacticM Unit := do
+  let goal ← Elab.Tactic.getMainGoal
+  let .some (beta, _, _) := (← goal.getType).eq? | throwError "Goal is not an Eq"
+  -- Create the descendant goals
+
+  let nextGoals ← goal.withContext do
+    let u ← Meta.mkFreshLevelMVar
+    let alpha ← Meta.mkFreshExprMVar (.some $ mkSort u) .natural .anonymous
+    let f ← Meta.mkFreshExprMVar (.some <| .forallE .anonymous alpha beta .default)
+      .synthetic (userName := goal.name ++ `f)
+    let a₁ ← Meta.mkFreshExprMVar (.some alpha)
+      .synthetic (userName := goal.name ++ `a₁)
+    let a₂ ← Meta.mkFreshExprMVar (.some alpha)
+      .synthetic (userName := goal.name ++ `a₂)
+    let h ← Meta.mkEq a₁ a₂
+    let conduitType ← Meta.mkEq (← Meta.mkEq (.app f a₁) (.app f a₂)) (← goal.getType)
+    let conduit ← Meta.mkFreshExprMVar conduitType
+      .synthetic (userName := goal.name ++ `conduit)
+    goal.assign $ ← Meta.mkEqMP conduit (← Meta.mkCongrArg f h)
+    return [alpha, a₁, a₂, f,  h, conduit]
+  Elab.Tactic.setGoals <| nextGoals.map (·.mvarId!)
+
+def congruenceFun: Elab.Tactic.TacticM Unit := do
+  let goal ← Elab.Tactic.getMainGoal
+  let .some (beta, _, _) := (← goal.getType).eq? | throwError "Goal is not an Eq"
+  -- Create the descendant goals
+
+  let nextGoals ← goal.withContext do
+    let u ← Meta.mkFreshLevelMVar
+    let alpha ← Meta.mkFreshExprMVar (.some $ mkSort u) .natural .anonymous
+    let fType := .forallE .anonymous alpha beta .default
+    let f₁ ← Meta.mkFreshExprMVar (.some fType)
+      .synthetic (userName := goal.name ++ `f₁)
+    let f₂ ← Meta.mkFreshExprMVar (.some fType)
+      .synthetic (userName := goal.name ++ `f₂)
+    let a ← Meta.mkFreshExprMVar (.some alpha)
+      .synthetic (userName := goal.name ++ `a)
+    let h ← Meta.mkEq f₁ f₂
+    let conduitType ← Meta.mkEq (← Meta.mkEq (.app f₁ a) (.app f₂ a)) (← goal.getType)
+    let conduit ← Meta.mkFreshExprMVar conduitType
+      .synthetic (userName := goal.name ++ `conduit)
+    goal.assign $ ← Meta.mkEqMP conduit (← Meta.mkCongrFun h a)
+    return [alpha, f₁, f₂, h, a, conduit]
+  Elab.Tactic.setGoals <| nextGoals.map (·.mvarId!)
+
+def congruence: Elab.Tactic.TacticM Unit := do
+  let goal ← Elab.Tactic.getMainGoal
+  let .some (beta, _, _) := (← goal.getType).eq? | throwError "Goal is not an Eq"
+  -- Create the descendant goals
+
+  let nextGoals ← goal.withContext do
+    let u ← Meta.mkFreshLevelMVar
+    let alpha ← Meta.mkFreshExprMVar (.some $ mkSort u) .natural .anonymous
+    let fType := .forallE .anonymous alpha beta .default
+    let f₁ ← Meta.mkFreshExprMVar (.some fType)
+      .synthetic (userName := goal.name ++ `f₁)
+    let f₂ ← Meta.mkFreshExprMVar (.some fType)
+      .synthetic (userName := goal.name ++ `f₂)
+    let a₁ ← Meta.mkFreshExprMVar (.some alpha)
+      .synthetic (userName := goal.name ++ `a₁)
+    let a₂ ← Meta.mkFreshExprMVar (.some alpha)
+      .synthetic (userName := goal.name ++ `a₂)
+    let h₁ ← Meta.mkEq f₁ f₂
+    let h₂ ← Meta.mkEq a₁ a₂
+    let conduitType ← Meta.mkEq (← Meta.mkEq (.app f₁ a₁) (.app f₂ a₂)) (← goal.getType)
+    let conduit ← Meta.mkFreshExprMVar conduitType
+      .synthetic (userName := goal.name ++ `conduit)
+    goal.assign $ ← Meta.mkEqMP conduit (← Meta.mkCongr h₁ h₂)
+    return [alpha, f₁, f₂, a₁, a₂, h₁, h₂, conduit]
+  Elab.Tactic.setGoals <| nextGoals.map (·.mvarId!)
+
+end Pantograph.Tactic