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Proof step 20 from proof bits2int-nls (previous step)

bitsinvert(bits) +1.first ∧ bitsinvert(bits) +1 ≠ [], bits.first, 0 < bits2uint(bitsinvert(bits) +1), 2 ^ n→i(# bits) < bits2uint(bitsinvert(bits) +1), 2 + # bits ≤ #(false ' + bitsinvert(bits) +1), 0 ≤ bits2uint(bitsinvert(bits) +1), bitsinvert(bits) +1.first ⊦ bits = []

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 21:
# bits < # bitsinvert(bits) +1, 2 ^ n→i(# bits) < bits2uint(bitsinvert(bits) +1), 0 < bits2uint(bitsinvert(bits) +1), bits.first, bitsinvert(bits) +1.first, 0 ≤ bits2uint(bitsinvert(bits) +1) ⊦ bitsinvert(bits) +1 = [], bits = []

Rule argument

Additional information

Used simplifier rules: ⊦ # bits = 0 ↔ bits = [];% ⊦ m < n → n ≠ 0; (forward)% ⊦ m + n = n + m;% ⊦ (m + n0) + n1 = m + n0 + n1;% ⊦ m + 1 ≤ n ↔ m < n;%n0 < n ⊦ m + (* n) ≤ m0 + (* n0) ↔ m + (n - n0) ≤ m0;% ⊦ (bits + bits0) + bits1 = bits + bits0 + bits1;% ⊦ # boolvar ' = 0 +1;% ⊦ #(bits + bits0) = # bits + # bits0;