equal
deleted
inserted
replaced
103 Goal "[| abs x<r; abs y<s |] ==> abs x * abs y < r * (s::hypreal)"; |
103 Goal "[| abs x<r; abs y<s |] ==> abs x * abs y < r * (s::hypreal)"; |
104 by (subgoal_tac "0 < r" 1); |
104 by (subgoal_tac "0 < r" 1); |
105 by (asm_full_simp_tac (simpset() addsimps [hrabs_def] |
105 by (asm_full_simp_tac (simpset() addsimps [hrabs_def] |
106 addsplits [split_if_asm]) 2); |
106 addsplits [split_if_asm]) 2); |
107 by (case_tac "y = 0" 1); |
107 by (case_tac "y = 0" 1); |
108 by (asm_full_simp_tac (simpset() addsimps [hypreal_0_less_mult_iff]) 1); |
108 by (asm_full_simp_tac (simpset() addsimps [zero_less_mult_iff]) 1); |
109 by (rtac hypreal_mult_less_mono 1); |
109 by (rtac hypreal_mult_less_mono 1); |
110 by (auto_tac (claset(), |
110 by (auto_tac (claset(), |
111 simpset() addsimps [hrabs_def, linorder_neq_iff] |
111 simpset() addsimps [hrabs_def, linorder_neq_iff] |
112 addsplits [split_if_asm])); |
112 addsplits [split_if_asm])); |
113 qed "hrabs_mult_less"; |
113 qed "hrabs_mult_less"; |