import Lean
open Lean
open Lean.Elab
open Lean.Meta
open Lean.Elab.Tactic

example (a b c : Nat) (h₁ : a = b) (h₂ : b = c) : a = c := by
  apply Eq.trans _ h₂  -- the metavars created during elaboration become new goals
  trace_state
  exact h₁

example (a : Nat) : ∃ x, x = a := by
  apply Exists.intro  -- the goal for the witness should occur "after" the goal for x = a
  trace_state
  rfl

elab "fapply " e:term : tactic =>
  evalApplyLikeTactic (Meta.apply (cfg := {newGoals := ApplyNewGoals.all})) e

elab "eapply " e:term : tactic =>
  evalApplyLikeTactic (Meta.apply (cfg := {newGoals := ApplyNewGoals.nonDependentOnly})) e

example (a : Nat) : ∃ x, x = a := by
  eapply Exists.intro  -- only metavars with out forward dependencies are added as goals.
  trace_state
  rfl

example (a : Nat) : ∃ x, x = a := by
  fapply Exists.intro  -- all unassigned metavars are added as new goals using the order they were created.
  trace_state
  exact a
  trace_state
  rfl