06d6dbff5d
This PR implements basic model-based theory combination in `grind`.
`grind` can now solve examples such as
```lean
example (f : Int → Int) (x : Int)
: 0 ≤ x → x ≠ 0 → x ≤ 1 → f x = 2 → f 1 = 2 := by
grind
```
37 lines
800 B
Text
37 lines
800 B
Text
set_option grind.warning false
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variable (d : Nat) in
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inductive X : Nat → Prop
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| f {s : Nat} : X s
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| g {s : Nat} : X d → X s
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/--
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error: `grind` failed
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case grind.1
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c : Nat
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q : X c 0
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s : Nat
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h : 0 = s
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h_1 : HEq ⋯ ⋯
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⊢ False
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[grind] Goal diagnostics
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[facts] Asserted facts
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[prop] X c 0
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[prop] 0 = s
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[prop] HEq ⋯ ⋯
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[eqc] True propositions
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[prop] X c 0
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[prop] X c s
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[eqc] Equivalence classes
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[eqc] {s, 0}
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[cases] Case analyses
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[cases] [1/2]: X c 0
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[grind] Issues
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[issue] #1 other goal(s) were not fully processed due to previous failures, threshold: `(failures := 1)`
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-/
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#guard_msgs (error) in
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example {c : Nat} (q : X c 0) : False := by
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grind -mbtc [cases X]
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example {c : Nat} (q : X c 0) : False := by
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fail_if_success grind [cases X]
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sorry
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