feat: more UInt bitwise theorems#6188
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This PR upstreams `Nat.lt_pow_self` and `Nat.lt_two_pow` from Mathlib and uses them to prove the simp theorem `Nat.mod_two_pow`. This simplifies expressions like `System.Platform.numBits % 2 ^ System.Platform.numBits = System.Platform.numBits`, which is needed for #6188.
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This PR completes the `toNat` theorems for the bitwise operations (`and`, `or`, `xor`, `shiftLeft`, `shiftRight`) of the UInt types and adds `toBitVec` theorems as well. It also renames `and_toNat` to `toNat_and` to fit with the current naming convention.
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This PR upstreams `Nat.lt_pow_self` and `Nat.lt_two_pow` from Mathlib and uses them to prove the simp theorem `Nat.mod_two_pow`. This simplifies expressions like `System.Platform.numBits % 2 ^ System.Platform.numBits = System.Platform.numBits`, which is needed for leanprover#6188.
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This PR completes the `toNat` theorems for the bitwise operations (`and`, `or`, `xor`, `shiftLeft`, `shiftRight`) of the UInt types and adds `toBitVec` theorems as well. It also renames `and_toNat` to `toNat_and` to fit with the current naming convention.
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This PR completes the
toNattheorems for the bitwise operations (and,or,xor,shiftLeft,shiftRight) of the UInt types and addstoBitVectheorems as well. It also renamesand_toNattotoNat_andto fit with the current naming convention.