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Proof step 19 from proof bits2int-split-01 (previous step)

⊦ bits0 = [], bits2uint((false ' + bitsinvert(bits1))+1) * 2 ^ n→i(# bits0) = (bits2uint(bitsinvert(bits1)) * 2 ^ n→i(# bits0) + bits2uint(bitsinvert(bits0))) + 1, true ∈ bits0

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 20:
⊦ bits ≠ [] → bits2uint(bits +1) = bits2uint(bits) + 1
Proof step 21:
false ' + bitsinvert(bits1) ≠ [] ⊦ bits0 = [], (bits2uint(false ' + bitsinvert(bits1)) + 1) * 2 ^ n→i(# bits0) = (bits2uint(bitsinvert(bits1)) * 2 ^ n→i(# bits0) + bits2uint(bitsinvert(bits0))) + 1, true ∈ bits0

Rule argument

name: bits2uint-succ rotate: F subst: [bits] → [false ' + bitsinvert(bits1)]

Additional information

Used simplifier rules: ⊦ ¬ bits + bits0 ≠ [] ↔ bits = [] ∧ bits0 = [];% ⊦ boolvar ' ≠ [];% ⊦ bitsinvert(bits) = [] ↔ bits = [];% ⊦ (bits + bits0) + bits1 = bits + bits0 + bits1; Used terms: false ' + bitsinvert(bits1)