Added Support For Reals - #76
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Lean-Auto can now handle Reals the same way it handles Ints whenever Mathlib is imported. The primary changes along with explanations are found in Auto/MathlibReal.lean and Auto/Lib/RealType.lean. The
RealTytypeclass is used to representRealin the embedding, so it is necessary to thread avariable (R? : Option ((R : Type) × RealTy R))throughout (this accounts for the majority of the changes in Auto/Embedding). The functiongetRealOpt(in Translation/LamUtils.lean) is called to provide R? and it returnsnoneunless Auto.MathlibReal has been imported by the calling file.Please let me know if you would like more explanation about anything or would like to meet to discuss my changes.
Some tests showing what lean-auto can prove while trusting smt solvers can be found in https://github.com/Mathletesv/lean-auto/blob/real-tests/Test/RealTests.lean.
This addition also enables Lean-smt to use Lean-auto's monomorphization to solve goals such as the ones in https://github.com/Mathletesv/lean-smt/blob/main/Test/AutoReals.lean