Changes between Version 1 and Version 2 of TypeNats/Rules


Ignore:
Timestamp:
Dec 15, 2010 6:01:18 PM (5 years ago)
Author:
diatchki
Comment:

--

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  • TypeNats/Rules

    v1 v2  
    55}}}
    66
    7 Top-level interaction for +.
     7Top-level interactions for {{{TypeNat}}}:
     8{{{
     9TypeNat m
     10}}}
     11
     12Top-level interactions for <=
     13{{{
     14m <= n   <=> {m <= n} = True
     150 <= a   <=> True
     16a <= 0   <=> a ~ 0
     17}}}
     18
     19Top-level interactions for +.
    820{{{
    921(m + n ~ k) <=> {m + n} = k
     
    1729(a + a ~ b) <=> (2 * a ~ b)
    1830}}}
     31
     32Top-level interactions for *.
     33{{{
     34(m * n ~ k) <=> {m * n} = k
     35(m * a ~ n) <=> a ~ {n / m}     -- m `divides` n
     36(a * m ~ n) <=> a ~ {n / m}     -- m `divides` n
     37(0 * a ~ b) <=> b ~ 0
     38(a * 0 ~ b) <=> b ~ 0
     39(1 * a ~ b) <=> a ~ b
     40(a * 1 ~ b) <=> a ~ b
     41(a * b ~ 1) <=> (a ~ 1, b ~ 1)
     42(a + a ~ b) <=> 2 ^ a ~ b
     43}}}
     44
     45Top-level interactions for ^
     46{{{
     47(m ^ n ~ k) <=> {m ^ n} = k
     48(m ^ a ~ n) <=> a ~ {log m n}   -- log (base m) of n exists
     49(a ^ m ~ n) <=> a ~ {root m n}  -- m-th root of n exists
     50(a ^ 0 ~ b) <=> b ~ 1
     51(1 ^ a ~ b) <=> b ~ 1
     52}}}