let A be set ; :: thesis: for a, b, c being Element of (NormForm A) holds a "/\" (b "/\" c) = (a "/\" b) "/\" c
set G = NormForm A;
let a, b, c be Element of (NormForm A); :: thesis: a "/\" (b "/\" c) = (a "/\" b) "/\" c
reconsider a' = a, b' = b, c' = c as Element of Normal_forms_on A by Def14;
a "/\" (b "/\" c) = the L_meet of (NormForm A) . a,(mi (b' ^ c')) by Def14
.= mi (a' ^ (mi (b' ^ c'))) by Def14
.= mi (a' ^ (b' ^ c')) by Th75
.= mi ((a' ^ b') ^ c') by Th76
.= mi ((mi (a' ^ b')) ^ c') by Th74
.= the L_meet of (NormForm A) . (mi (a' ^ b')),c' by Def14
.= (a "/\" b) "/\" c by Def14 ;
hence a "/\" (b "/\" c) = (a "/\" b) "/\" c ; :: thesis: verum