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Proof step 18 from proof uint2int-rest (previous step)

uint2bits(i) = false ' + true ' + bits, 2 ^ n→i(#(false ' + true ' + bits)) = bits2uint(bitsinvert(false ' + true ' + bits)) + i + 1, 0 < i ⊦ 2 ^ (1 + n→i(# bits)) = 1 + bits2uint(bitsinvert(bits)) + i

User applied rule simplifier

And obtained the following new goals

Proof step 19:
uint2bits(i) = false ' + true ' + bits, 2 ^ (2 + n→i(# bits)) = 1 + bits2uint(true ' + false ' + bitsinvert(bits)) + i, 0 < i ⊦ 2 ^ (1 + n→i(# bits)) = 1 + bits2uint(bitsinvert(bits)) + i

Rule argument

Additional information

Used simplifier rules: ⊦ boolvar + bits = boolvar ' + bits;% ⊦ bitsinvert(true ' + bits) = false + bitsinvert(bits);% ⊦ bitsinvert(false ' + bits) = true + bitsinvert(bits);% ⊦ m + n = n + m;% ⊦ (m + n0) + n1 = m + n0 + n1;% ⊦ n→i(m + n) = n→i(m) + n→i(n);% ⊦ (bits + bits0) + bits1 = bits + bits0 + bits1;% ⊦ # boolvar ' = 0 +1;% ⊦ #(bits + bits0) = # bits + # bits0;