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Proof step 35 from proof bits2int-pos (previous step)

bits2int(true ' + firstn(# bits0 % 8, bits0)) < ~128, 7 < # bits0, # bits0 % 8 ≤ 7, # bits0 % 8 < # bits0, 0 ≤ bits2int(fillsgn(8, int2bits(b2i(i2b(bits2int(true ' + firstn(# bits0 % 8, bits0)))))) + bytes2bits(bits2bytes(restn(# bits0 % 8, bits0)))), bits2int(true ' + firstn(# bits0 % 8, bits0)) < 0 ⊦ bits0 = [], (# bits0 + 1) % 8 = 0

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

seq: ⊦ # bits ≤ 8 ∧ bits ≠ [] → ¬ bits2int(bits) < ~128 subst: [bits] → [true ' + firstn(# bits0 % 8, bits0)] rotate: F spec: int2bits inst: name: bits2int-le8

Additional information

Used simplifier rules: ⊦ #(bits + bits0) = # bits + # bits0;% ⊦ # boolvar ' = 0 +1;% ⊦ # firstn(n, bits) = n;% ⊦ (bits + bits0) + bits1 = bits + bits0 + bits1;%n < n0 ⊦ m + (* n) ≤ (* n0) ↔ m ≤ n0 - n;% ⊦ ¬ m ≤ n ↔ n < m;% ⊦ m ≤ n → (n < m ↔ false);% ⊦ (m + n0) + n1 = m + n0 + n1;% ⊦ m + n = n + m;% ⊦ ¬ bits + bits0 ≠ [] ↔ bits = [] ∧ bits0 = [];% ⊦ boolvar ' ≠ []; Used terms: true ' + firstn(# bits0 % 8, bits0)