Datasets:
Tasks:
Text Generation
Modalities:
Text
Sub-tasks:
language-modeling
Languages:
English
Size:
100K - 1M
License:
File size: 577 Bytes
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let NSQRT_2 = prove
(`!p q. p * p = 2 * q * q ==> q = 0`,
MATCH_MP_TAC num_WF THEN REWRITE_TAC[RIGHT_IMP_FORALL_THM] THEN
REPEAT STRIP_TAC THEN FIRST_ASSUM(MP_TAC o AP_TERM `EVEN`) THEN
REWRITE_TAC[EVEN_MULT; ARITH] THEN REWRITE_TAC[EVEN_EXISTS] THEN
DISCH_THEN(X_CHOOSE_THEN `m:num` SUBST_ALL_TAC) THEN
FIRST_X_ASSUM(MP_TAC o SPECL [`q:num`; `m:num`]) THEN
ASM_REWRITE_TAC[ARITH_RULE
`q < 2 * m ==> q * q = 2 * m * m ==> m = 0 <=>
(2 * m) * 2 * m = 2 * q * q ==> 2 * m <= q`] THEN
ASM_MESON_TAC[LE_MULT2; MULT_EQ_0; ARITH_RULE `2 * x <= x <=> x = 0`]);;
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