PD0016 · conservative definition

AllBits

Every decoded entry below l is zero or one.

Current library: Alpha v34, 4,223 checked-use theorems; Stable remains 432. Historical first admissions, original proof editions, and non-admitted aliases are preserved. Exact original first-admission records.

Readable signature

AllBits(b,c,l)

Exact expansion

forall ff_i_defined_all_bits. (exists ff_lt_defined_all_bits_bound. ff_lt_defined_all_bits_bound + S ff_i_defined_all_bits = l) -> exists ff_bit_defined_all_bits. ((((exists ff_h_defined_all_bits_decoded. ff_h_defined_all_bits_decoded + S (ff_bit_defined_all_bits) = S ((S (ff_i_defined_all_bits)) * c)) /\ exists ff_q_defined_all_bits_decoded. b = ff_q_defined_all_bits_decoded * S ((S (ff_i_defined_all_bits)) * c) + (ff_bit_defined_all_bits))) /\ (ff_bit_defined_all_bits = 0 \/ ff_bit_defined_all_bits = 1))

This node is notation, not a theorem, axiom, predicate constant, or kernel rule. The elaboration layer must expand it before proof checking.

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Used by theorem statements or local proof propositions