1819dc88ff
This PR adds support for internalizing terms relevant to the cutsat module. This is required to implement equality propagation.
119 lines
2.5 KiB
Text
119 lines
2.5 KiB
Text
def g (i : Nat) (j : Nat) := i + j
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set_option grind.debug true
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set_option grind.debug.proofs true
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/--
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error: `grind` failed
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case grind
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i j : Nat
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h : j + 1 ≤ i
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h_1 : ¬g (i + 1) j = i + 1
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⊢ False
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[grind] Goal diagnostics
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[facts] Asserted facts
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[prop] j + 1 ≤ i
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[prop] ¬g (i + 1) j = i + 1
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[eqc] True propositions
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[prop] j + 1 ≤ i
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[eqc] False propositions
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[prop] g (i + 1) j = i + 1
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[offset] Assignment satisfying offset contraints
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[assign] j := 0
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[assign] i := 1
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[assign] 「i + 1」 := 2
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[assign] 「0」 := 0
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-/
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#guard_msgs (error) in
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example (i j : Nat) (h : i + 1 > j + 1) : g (i+1) j = i + 1 := by
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grind
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/--
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error: `grind` failed
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case grind
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i : Nat
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h : 101 ≤ i
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⊢ False
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[grind] Goal diagnostics
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[facts] Asserted facts
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[prop] 101 ≤ i
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[eqc] True propositions
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[prop] 101 ≤ i
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[offset] Assignment satisfying offset contraints
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[assign] 「0」 := 0
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[assign] i := 101
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-/
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#guard_msgs (error) in
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example (i : Nat) : i ≤ 100 := by
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grind
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/--
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error: `grind` failed
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case grind
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i : Nat
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h : i ≤ 99
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⊢ False
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[grind] Goal diagnostics
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[facts] Asserted facts
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[prop] i ≤ 99
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[eqc] True propositions
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[prop] i ≤ 99
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[offset] Assignment satisfying offset contraints
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[assign] i := 99
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[assign] 「0」 := 0
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-/
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#guard_msgs (error) in
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example (i : Nat) : 100 ≤ i := by
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grind
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/--
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error: `grind` failed
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case grind
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n m a j i : Nat
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h : g (n + 1) m = a
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h_1 : i ≤ j + 99
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⊢ False
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[grind] Goal diagnostics
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[facts] Asserted facts
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[prop] g (n + 1) m = a
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[prop] i ≤ j + 99
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[eqc] True propositions
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[prop] i ≤ j + 99
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[eqc] Equivalence classes
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[eqc] {g (n + 1) m, a}
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[offset] Assignment satisfying offset contraints
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[assign] 「n + 1」 := 1
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[assign] n := 0
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[assign] 「0」 := 0
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[assign] i := 99
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[assign] j := 0
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-/
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#guard_msgs (error) in
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example (i : Nat) : g (n + 1) m = a → 100 + j ≤ i := by
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grind
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/--
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error: `grind` failed
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case grind
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n m a j i : Nat
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h : g (n + 1) m = a
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h_1 : i + 101 ≤ j
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⊢ False
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[grind] Goal diagnostics
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[facts] Asserted facts
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[prop] g (n + 1) m = a
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[prop] i + 101 ≤ j
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[eqc] True propositions
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[prop] i + 101 ≤ j
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[eqc] Equivalence classes
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[eqc] {g (n + 1) m, a}
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[offset] Assignment satisfying offset contraints
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[assign] 「n + 1」 := 1
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[assign] n := 0
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[assign] 「0」 := 0
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[assign] i := 0
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[assign] j := 101
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-/
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#guard_msgs (error) in
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example (i : Nat) : g (n + 1) m = a → j ≤ i + 100 := by
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grind
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