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Commit 2022-08-06 05:32 e3d2f74c

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feat(data/nat): Add new binary recursors; prove the relationship between nat.bits and other pieces of code (#14990) This is in connection to https://github.com/leanprover-community/mathlib/pull/13208, because I was asked to write to_bits in terms of nat.size and nat.bits, but nat.bits was hard to use (there were no lemmas about it). This PR proves some statements about nat.bits, so that it can finally be used.

Estimated changes

added def nat.binary_rec'
added theorem nat.binary_rec_eq'
added theorem nat.bit0_bits
added theorem nat.bit1_bits
added theorem nat.bit_eq_zero_iff
added theorem nat.bits_append_bit
added theorem nat.bodd_eq_bits_head
added theorem nat.div2_bits_eq_tail
added theorem nat.one_bits
added theorem nat.size_eq_bits_len
added theorem nat.zero_bits