Datasets:
Tasks:
Text Generation
Modalities:
Text
Sub-tasks:
language-modeling
Languages:
English
Size:
100K - 1M
License:
| prioritize_real();; | |
| let (TRY_RULE:(thm->thm) -> (thm->thm)) = | |
| fun rl t -> try (rl t) with _ -> t;; | |
| let REAL_MUL_RTIMES = | |
| prove ((`!x a b. | |
| (((~(x=(&0))==>(a*x = b*x)) /\ ~(x=(&0))) ==> (a = b))`), | |
| MESON_TAC[REAL_EQ_MUL_RCANCEL]);; | |
| let GEOMETRIC_SUM = prove( | |
| `!m n x.(~(x=(&1)) ==> | |
| (sum(m,n) (\k.(x pow k)) = ((x pow m) - (x pow (m+n)))/((&1)-x)))`, | |
| let tac1 = | |
| GEN_TAC | |
| THEN INDUCT_TAC | |
| THEN GEN_TAC | |
| THEN DISCH_TAC | |
| THEN (REWRITE_TAC | |
| [sum_DEF;real_pow;ADD_CLAUSES;real_div;REAL_SUB_RDISTRIB; | |
| REAL_SUB_REFL]) in | |
| let tac2 = | |
| (RULE_ASSUM_TAC (TRY_RULE (SPEC (`x:real`)))) | |
| THEN (UNDISCH_EL_TAC 1) | |
| THEN (UNDISCH_EL_TAC 0) | |
| THEN (TAUT_TAC (`(A==>(B==>C)) ==> (A ==> ((A==>B) ==>C))`)) | |
| THEN (REPEAT DISCH_TAC) | |
| THEN (ASM_REWRITE_TAC[real_div]) | |
| THEN (ABBREV_TAC (`a:real = x pow m`)) | |
| THEN (ABBREV_TAC (`b:real = x pow (m+n)`)) in | |
| let tac3 = | |
| (MATCH_MP_TAC (SPEC (`&1 - x`) REAL_MUL_RTIMES)) | |
| THEN CONJ_TAC | |
| THENL [ALL_TAC; (UNDISCH_TAC (`~(x = (&1))`)) | |
| THEN (ACCEPT_TAC (REAL_ARITH (`~(x=(&1)) ==> ~((&1 - x = (&0)))`)))] | |
| THEN (REWRITE_TAC | |
| [GSYM REAL_MUL_ASSOC;REAL_ADD_RDISTRIB;REAL_SUB_RDISTRIB]) | |
| THEN (SIMP_TAC[REAL_MUL_LINV]) | |
| THEN DISCH_TAC | |
| THEN (REWRITE_TAC | |
| [REAL_SUB_LDISTRIB;REAL_MUL_LID;REAL_MUL_RID;REAL_MUL_ASSOC]) | |
| THEN (ACCEPT_TAC (REAL_ARITH (`a - b + b - b*x = a - x*b`))) in | |
| (tac1 THEN tac2 THEN tac3));; | |
| pop_priority();; | |