114 lines
2.9 KiB
Text
114 lines
2.9 KiB
Text
/--
|
||
error: `grind` failed
|
||
case grind
|
||
a b c d e f : Nat
|
||
h : max a b = max c d
|
||
h_1 : max b e = max d (max e f)
|
||
h_2 : ¬max c (max d e) = max (max a d) f
|
||
⊢ False
|
||
[grind] Goal diagnostics
|
||
[facts] Asserted facts
|
||
[prop] max a b = max c d
|
||
[prop] max b e = max d (max e f)
|
||
[prop] ¬max c (max d e) = max (max a d) f
|
||
[eqc] False propositions
|
||
[prop] max c (max d e) = max (max a d) f
|
||
[eqc] Equivalence classes
|
||
[eqc] {max a b, max c d}
|
||
[eqc] {max b e, max d (max e f)}
|
||
[assoc] Operator `max`
|
||
[basis] Basis
|
||
[_] max c d = max a b
|
||
[_] max b (max c e) = max a (max b e)
|
||
[_] max b (max e f) = max b e
|
||
[_] max b (max d e) = max b e
|
||
[_] max d (max e f) = max b e
|
||
[_] max a (max b d) = max a b
|
||
[_] max a (max b c) = max a b
|
||
[diseqs] Disequalities
|
||
[_] max a (max b e) ≠ max a (max d f)
|
||
[properties] Properties
|
||
[_] commutative
|
||
[_] idempotent
|
||
[_] identity: `0`
|
||
-/
|
||
#guard_msgs in
|
||
example (a b c d e f : Nat) :
|
||
max a b = max c d →
|
||
max b e = max d (max e f) →
|
||
max c (max d e) = max (max a d) f := by
|
||
grind -lia only
|
||
|
||
/--
|
||
error: `grind` failed
|
||
case grind
|
||
α : Sort u
|
||
op : α → α → α
|
||
inst : Std.Associative op
|
||
a b c d : α
|
||
h : op a b = op c d
|
||
h_1 : ¬op (op a b) (op b c) = op (op c d) c
|
||
⊢ False
|
||
[grind] Goal diagnostics
|
||
[facts] Asserted facts
|
||
[prop] Std.Associative op
|
||
[prop] op a b = op c d
|
||
[prop] ¬op (op a b) (op b c) = op (op c d) c
|
||
[eqc] True propositions
|
||
[prop] Std.Associative op
|
||
[eqc] False propositions
|
||
[prop] op (op a b) (op b c) = op (op c d) c
|
||
[eqc] Equivalence classes
|
||
[eqc] {op a b, op c d}
|
||
[assoc] Operator `op`
|
||
[basis] Basis
|
||
[_] op c d = op a b
|
||
[diseqs] Disequalities
|
||
[_] op a (op b (op b c)) ≠ op a (op b c)
|
||
-/
|
||
#guard_msgs in
|
||
example {α : Sort u} (op : α → α → α) [Std.Associative op] (a b c d : α)
|
||
: op a b = op c d → op (op a b) (op b c) = op (op c d) c := by
|
||
grind only
|
||
|
||
set_option warn.sorry false
|
||
set_option grind.debug true
|
||
|
||
opaque op : Int → Int → Int
|
||
instance : Std.Associative op := sorry
|
||
instance : Std.Commutative op := sorry
|
||
local infixr:64 "∘" => op
|
||
|
||
/--
|
||
error: `grind` failed
|
||
case grind
|
||
a b c d e p q : Int
|
||
h : a∘b = c∘d
|
||
h_1 : a∘q = p
|
||
h_2 : ¬(c∘d)∘e = a∘p∘q
|
||
⊢ False
|
||
[grind] Goal diagnostics
|
||
[facts] Asserted facts
|
||
[prop] a∘b = c∘d
|
||
[prop] a∘q = p
|
||
[prop] ¬(c∘d)∘e = a∘p∘q
|
||
[eqc] False propositions
|
||
[prop] (c∘d)∘e = a∘p∘q
|
||
[eqc] Equivalence classes
|
||
[eqc] {p, a∘q}
|
||
[eqc] {a∘b, c∘d}
|
||
[assoc] Operator `op`
|
||
[basis] Basis
|
||
[_] a∘q = p
|
||
[_] c∘d = a∘b
|
||
[diseqs] Disequalities
|
||
[_] a∘b∘e ≠ p∘p
|
||
[properties] Properties
|
||
[_] commutative
|
||
-/
|
||
#guard_msgs in
|
||
example (a b c d e p q : Int) :
|
||
a ∘ b = c ∘ d →
|
||
a ∘ q = p →
|
||
(c ∘ d) ∘ e = a ∘ (p ∘ q) := by
|
||
grind only
|