# HG changeset patch # User obua # Date 1187335193 -7200 # Node ID 6c7f226b24c3a710687ca82c8b008b4c9196e6fe # Parent e170cee91c66a036b167c7a094486f3b7d562ee7 changed floatarith lemmas diff -r e170cee91c66 -r 6c7f226b24c3 src/HOL/Real/Float.thy --- a/src/HOL/Real/Float.thy Fri Aug 17 00:03:50 2007 +0200 +++ b/src/HOL/Real/Float.thy Fri Aug 17 09:19:53 2007 +0200 @@ -320,6 +320,12 @@ lemma pow2_int: "pow2 (int n) = 2^n" by (simp add: pow2_def) +lemma float_add_l0: "float (0, e) + x = x" + by (simp add: float_def) + +lemma float_add_r0: "x + float (0, e) = x" + by (simp add: float_def) + lemma float_add: "float (a1, e1) + float (a2, e2) = (if e1<=e2 then float (a1+a2*2^(nat(e2-e1)), e1) @@ -328,6 +334,44 @@ apply (auto simp add: pow2_int[symmetric] pow2_add[symmetric]) done +lemma float_add_assoc1: + "(x + float (y1, e1)) + float (y2, e2) = (float (y1, e1) + float (y2, e2)) + x" + by simp + +lemma float_add_assoc2: + "(float (y1, e1) + x) + float (y2, e2) = (float (y1, e1) + float (y2, e2)) + x" + by simp + +lemma float_add_assoc3: + "float (y1, e1) + (x + float (y2, e2)) = (float (y1, e1) + float (y2, e2)) + x" + by simp + +lemma float_add_assoc4: + "float (y1, e1) + (float (y2, e2) + x) = (float (y1, e1) + float (y2, e2)) + x" + by simp + +lemma float_mult_l0: "float (0, e) * x = float (0, 0)" + by (simp add: float_def) + +lemma float_mult_r0: "x * float (0, e) = float (0, 0)" + by (simp add: float_def) + +definition + lbound :: "real \ real" +where + "lbound x = min 0 x" + +definition + ubound :: "real \ real" +where + "ubound x = max 0 x" + +lemma lbound: "lbound x \ x" + by (simp add: lbound_def) + +lemma ubound: "x \ ubound x" + by (simp add: ubound_def) + lemma float_mult: "float (a1, e1) * float (a2, e2) = (float (a1 * a2, e1 + e2))" @@ -384,6 +428,18 @@ "pprt (float (a, b)) = (if 0 <= a then (float (a,b)) else (float (0, b)))" by (auto simp add: zero_le_float float_le_zero float_zero) +lemma pprt_lbound: "pprt (lbound x) = float (0, 0)" + apply (simp add: float_def) + apply (rule pprt_eq_0) + apply (simp add: lbound_def) + done + +lemma nprt_ubound: "nprt (ubound x) = float (0, 0)" + apply (simp add: float_def) + apply (rule nprt_eq_0) + apply (simp add: ubound_def) + done + lemma float_nprt: "nprt (float (a, b)) = (if 0 <= a then (float (0,b)) else (float (a, b)))" by (auto simp add: zero_le_float float_le_zero float_zero) @@ -513,7 +569,8 @@ zpower_number_of_odd[simplified zero_eq_Numeral0_nring one_eq_Numeral1_nring] zpower_Pls zpower_Min -lemmas floatarith[simplified norm_0_1] = float_add float_mult float_minus float_abs zero_le_float float_pprt float_nprt +lemmas floatarith[simplified norm_0_1] = float_add float_add_l0 float_add_r0 float_mult float_mult_l0 float_mult_r0 + float_minus float_abs zero_le_float float_pprt float_nprt pprt_lbound nprt_ubound float_add_assoc1 float_add_assoc2 (* for use with the compute oracle *) lemmas arith = binarith intarith intarithrel natarith powerarith floatarith not_false_eq_true not_true_eq_false