import Lean
structure A :=
  x : Nat
  a' : x = 1 := by trivial

#check A.a'

example (z : A) : z.x = 1 := by
  have := z.a'
  trace_state
  exact this

example (z : A) : z.x = 1 := by
  have := z.2
  trace_state
  exact this

#check A.rec

example (z : A) : z.x = 1 := by
  have ⟨x, a'⟩ := z
  trace_state
  subst a'
  rfl

example (z : A) : z.x = 1 := by
  induction z with
  | mk x a' =>
    trace_state
    subst a'
    rfl

structure B :=
  x : Nat
  y : Nat := 2

example (b : B) : b = { x := b.x, y := b.y } := by
  cases b with
  | mk x y => trace_state; rfl

open Lean
open Lean.Meta

def tst : MetaM Unit :=
  withLocalDeclD `a (mkConst ``A) fun a => do
    let e := mkProj ``A 1 a
    IO.println (← Meta.ppExpr (← inferType e))

#eval tst

example (z : A) : z.x = 1 := by
  match z with
  | { a' := h } => trace_state; exact h

example (z : A) : z.x = 1 := by
  match z with
  | A.mk x a' => trace_state; exact a'

example : A :=
  { x := 1, a' := _ }

example : A :=
  A.mk 1 _

def f (x : Nat) (h : x = 1) : A := A.mk x h

example : A :=
  f 2 _

example : A := by
  apply f
  done