diff -r a435932a9f12 -r 3324a0078636 src/HOL/Word/Bit_Bit.thy --- a/src/HOL/Word/Bit_Bit.thy Mon Dec 23 16:29:43 2013 +0100 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,73 +0,0 @@ -(* Title: HOL/Word/Bit_Bit.thy - Author: Author: Brian Huffman, PSU and Gerwin Klein, NICTA -*) - -header {* Bit operations in $\cal Z_2$ *} - -theory Bit_Bit -imports Bit_Operations "~~/src/HOL/Library/Bit" -begin - -instantiation bit :: bit -begin - -primrec bitNOT_bit where - "NOT 0 = (1::bit)" - | "NOT 1 = (0::bit)" - -primrec bitAND_bit where - "0 AND y = (0::bit)" - | "1 AND y = (y::bit)" - -primrec bitOR_bit where - "0 OR y = (y::bit)" - | "1 OR y = (1::bit)" - -primrec bitXOR_bit where - "0 XOR y = (y::bit)" - | "1 XOR y = (NOT y :: bit)" - -instance .. - -end - -lemmas bit_simps = - bitNOT_bit.simps bitAND_bit.simps bitOR_bit.simps bitXOR_bit.simps - -lemma bit_extra_simps [simp]: - "x AND 0 = (0::bit)" - "x AND 1 = (x::bit)" - "x OR 1 = (1::bit)" - "x OR 0 = (x::bit)" - "x XOR 1 = NOT (x::bit)" - "x XOR 0 = (x::bit)" - by (cases x, auto)+ - -lemma bit_ops_comm: - "(x::bit) AND y = y AND x" - "(x::bit) OR y = y OR x" - "(x::bit) XOR y = y XOR x" - by (cases y, auto)+ - -lemma bit_ops_same [simp]: - "(x::bit) AND x = x" - "(x::bit) OR x = x" - "(x::bit) XOR x = 0" - by (cases x, auto)+ - -lemma bit_not_not [simp]: "NOT (NOT (x::bit)) = x" - by (cases x) auto - -lemma bit_or_def: "(b::bit) OR c = NOT (NOT b AND NOT c)" - by (induct b, simp_all) - -lemma bit_xor_def: "(b::bit) XOR c = (b AND NOT c) OR (NOT b AND c)" - by (induct b, simp_all) - -lemma bit_NOT_eq_1_iff [simp]: "NOT (b::bit) = 1 \ b = 0" - by (induct b, simp_all) - -lemma bit_AND_eq_1_iff [simp]: "(a::bit) AND b = 1 \ a = 1 \ b = 1" - by (induct a, simp_all) - -end