equal
deleted
inserted
replaced
114 "x ^ 1 = x" |
114 "x ^ 1 = x" |
115 "x * (y + z) = (x * y) + (x * z)" |
115 "x * (y + z) = (x * y) + (x * z)" |
116 "x ^ (Suc q) = x * (x ^ q)" |
116 "x ^ (Suc q) = x * (x ^ q)" |
117 "x ^ (2*n) = (x ^ n) * (x ^ n)" |
117 "x ^ (2*n) = (x ^ n) * (x ^ n)" |
118 "x ^ (Suc (2*n)) = x * ((x ^ n) * (x ^ n))" |
118 "x ^ (Suc (2*n)) = x * ((x ^ n) * (x ^ n))" |
119 by (simp_all add: algebra_simps power_add power2_eq_square power_mult_distrib power_mult) |
119 by (simp_all add: algebra_simps power_add power2_eq_square |
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120 power_mult_distrib power_mult del: one_add_one) |
120 |
121 |
121 lemmas normalizing_comm_semiring_1_axioms = |
122 lemmas normalizing_comm_semiring_1_axioms = |
122 comm_semiring_1_axioms [normalizer |
123 comm_semiring_1_axioms [normalizer |
123 semiring ops: normalizing_semiring_ops |
124 semiring ops: normalizing_semiring_ops |
124 semiring rules: normalizing_semiring_rules] |
125 semiring rules: normalizing_semiring_rules] |
216 hide_fact (open) normalizing_comm_ring_1_axioms |
217 hide_fact (open) normalizing_comm_ring_1_axioms |
217 normalizing_idom_axioms normalizing_ring_ops normalizing_ring_rules |
218 normalizing_idom_axioms normalizing_ring_ops normalizing_ring_rules |
218 |
219 |
219 hide_fact (open) normalizing_field_axioms normalizing_field_ops normalizing_field_rules |
220 hide_fact (open) normalizing_field_axioms normalizing_field_ops normalizing_field_rules |
220 |
221 |
221 end |
222 code_modulename SML |
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223 Semiring_Normalization Arith |
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224 |
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225 code_modulename OCaml |
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226 Semiring_Normalization Arith |
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227 |
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228 code_modulename Haskell |
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229 Semiring_Normalization Arith |
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230 |
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231 end |