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Proof step 38 from proof bits2int-pos (previous step)

0 < bits2int(true ' + firstn(# bits0 % 8, bits0)), 0 ≤ bits2int(fillsgn(8, int2bits(b2i(i2b(bits2int(true ' + firstn(# bits0 % 8, bits0)))))) + bytes2bits(bits2bytes(restn(# bits0 % 8, bits0)))), # bits0 % 8 < # bits0, # bits0 % 8 ≤ 7, 7 < # bits0, 127 < bits2int(true ' + firstn(# bits0 % 8, bits0)) ⊦ (# bits0 + 1) % 8 = 0, bits0 = []

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

seq: ⊦ bits2int(true ' + bits) = ~ bits2uint(bitsinvert(true + bits) +1) subst: [bits] → [firstn(# bits0 % 8, bits0)] rotate: F spec: int2bits inst: name: bits2int-neg

Additional information

Used simplifier rules: ⊦ boolvar + bits = boolvar ' + bits;% ⊦ bitsinvert(true ' + bits) = false + bitsinvert(bits);% ⊦ (bits + bits0) + bits1 = bits + bits0 + bits1;% ⊦ 0 < ~ i ↔ i < 0;% ⊦ ¬ bits2uint(bits) < 0; Used terms: firstn(# bits0 % 8, bits0)