16711fcdba
TODO for `dsimp`: - Add an option for reducing [reducible] definitions - Add (to_unfold : list name) similar to the one in the `simp` tactic
80 lines
1.7 KiB
Text
80 lines
1.7 KiB
Text
example (b c : nat) : c = @bool.cases_on (λ _, nat) tt b c :=
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begin
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fail_if_success {dsimp {iota := ff}},
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dsimp {iota := tt},
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guard_target c = c,
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reflexivity
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end
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example (b c : nat) : c = @bool.cases_on (λ _, nat) tt b c :=
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begin
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dsimp, -- iota is tt by default
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guard_target c = c,
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reflexivity
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end
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example (b c : nat) : c = (λ x : nat, x) c :=
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begin
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fail_if_success {dsimp {beta := ff}},
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dsimp {beta := tt},
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guard_target c = c,
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reflexivity
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end
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example (b c : nat) : c = (λ x : nat, x) c :=
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begin
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dsimp, -- beta is tt by default
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guard_target c = c,
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reflexivity
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end
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example (b c : nat) : c = (b, c).2 :=
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begin
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fail_if_success {dsimp {proj := ff}},
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dsimp {proj := tt},
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guard_target c = c,
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reflexivity
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end
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example (b c : nat) : c = (b, c).2 :=
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begin
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dsimp, -- projection reduction is true by default IF argument is a constructor
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guard_target c = c,
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reflexivity
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end
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example (f g : nat → nat) : f ∘ g = λ x, f (g x) :=
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begin
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fail_if_success {dsimp}, -- reducible definition (e.g., function.comp) are not unfolded by default
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dsimp [(∘)],
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guard_target (λ x, f (g x)) = λ x, f (g x),
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reflexivity
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end
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example (f g : nat → nat) : f ∘ g = λ x, f (g x) :=
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begin
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dsimp [function.comp],
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guard_target (λ x, f (g x)) = λ x, f (g x),
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reflexivity
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end
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example (a : nat) : (let x := a in x) = a :=
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begin
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fail_if_success{dsimp {zeta := ff}},
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dsimp {zeta := tt},
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guard_target a = a,
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reflexivity
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end
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example (a : nat) : (let x := a in x) = a :=
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begin
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dsimp, -- zeta is tt by default
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guard_target a = a,
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reflexivity
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end
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example (a b : nat) : a + b = b + a :=
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begin
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fail_if_success{dsimp}, -- will not unfold has_add.add applications
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apply add_comm
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end
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