Commit 297e12b9 by Heiko Becker

### Minor changes to proofs

parent d6aa770d
 ... ... @@ -8,8 +8,6 @@ open AbbrevsTheory ExpressionsTheory ExpressionSemanticsTheory RealSimpsTheory FloverTactics MachineTypeTheory ExpressionAbbrevsTheory EnvironmentsTheory; open preambleFloVer; val _ = temp_delsimps ["NORMEQ_CONV"] val _ = new_theory "ErrorBounds"; val _ = Parse.hide "delta"; (* so that it can be used as a variable *) ... ... @@ -394,6 +392,12 @@ Proof \\ metis_tac [REAL_LE_LMUL_IMP, ABS_POS, REAL_MUL_COMM] QED Theorem nonzerop_EQ1_I'[simp]: 0 < r ==> (nonzerop r = 1) Proof rw[nonzerop_def] QED Theorem err_prop_inversion_pos: !(nF:real) (nR:real) (err:real) (elo:real) (ehi:real). 0 < elo - err /\ 0 < elo /\ ... ... @@ -402,7 +406,8 @@ Theorem err_prop_inversion_pos: nR <= ehi /\ elo - err <= nF /\ nF <= ehi + err /\ 0 <= err ==> 0 <= err ==> abs (inv nR - inv nF) <= err * inv ((elo - err) * (elo - err)) Proof rpt strip_tac ... ... @@ -426,10 +431,9 @@ Proof \\ simp[] \\ qspec_then `1 / -nR + 1 / (nR - err)` match_mp_tac real_le_trans2 \\ conj_tac >- (match_mp_tac REAL_LE_LADD_IMP \\ rewrite_tac [GSYM REAL_INV_1OVER] \\ ‘0 < nR - err ∧ nR - err ≤ nF’ suffices_by (fs [REAL_INV_LE_ANTIMONO]) \\ REAL_ASM_ARITH_TAC) >- (` - nR <> 0 /\ nR - err <> 0` by REAL_ASM_ARITH_TAC \\ ‘0 < nR - err ∧ nR - err ≤ nF’ by REAL_ASM_ARITH_TAC \\ simp[GSYM REAL_INV_1OVER]) >- (`- nR <> 0 /\ nR - err <> 0` by REAL_ASM_ARITH_TAC \\ fs [REAL_ADD_RAT] \\ `nR - err + - nR = - err` by REAL_ASM_ARITH_TAC \\ qspec_then `nR` (fn thm => fs [real_div, GSYM thm]) REAL_NEG_LMUL ... ...
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