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Proof step 12 from proof int2int-rest-01 (previous step)

j < 0, 2 ^ n→i(# int2bits(j)) + j = bits2uint(true ' + false ' + bits), int2bits(j) = true ' + false ' + bits, j < 0, j < ~1 ⊦ j = 0, bits2uint(bits) = 2 ^ (1 + n→i(# bits)) + j

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 13:
⊦ # bits0 ≠ 0 → bits2uint(bits + bits0) = bits2uint(bits) * 2 ^ n→i(# bits0) + bits2uint(bits0)
Proof step 14:
#(false ' + bits) ≠ 0, j < 0, 2 ^ n→i(# int2bits(j)) + j = bits2uint(true ') * 2 ^ n→i(#(false ' + bits)) + bits2uint(false ' + bits), int2bits(j) = true ' + false ' + bits, j < 0, j < ~1 ⊦ j = 0, bits2uint(bits) = 2 ^ (1 + n→i(# bits)) + j

Rule argument

name: bits2uint-split rotate: F subst: [bits0, bits] → [false ' + bits, true ']

Additional information

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