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  • Arithmetic
  • Std/basic

Arith-equivs

Definitions for congruence reasoning about integers/naturals/bits.

Note: to use this book at full strength, do:

(include-book "std/basic/arith-equivs" :dir :system)
(local (in-theory (enable* arith-equiv-forwarding)))

You can also load just the definitions and bare-minimum theorems using

(include-book "std/basic/arith-equiv-defs" :dir :system)

Subtopics

Nat-equiv
Equivalence under nfix, i.e., natural number equivalence.
Bit->bool
Coerce a bit into a Boolean.
Bit-equiv
Equivalence under bfix, i.e., bit equivalence.
Int-equiv
Equivalence under ifix, i.e., integer equivalence.
Negp
Recognizer for negative integers.
Bool->bit
Coerce a Boolean into a bitp.