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