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Proof step 11 from proof and-011x-neg (previous step)

bitsand(false ' + bits0, true ') = false ' + bits1, ∀ bits, bits2, bits1. # bits < # bits0 → bitsand(false ' + bits, true ' + bits2) = false ' + bits1 → 2 ^ n→i(# bits) = 1 + bits2uint(bitsinvert(bits2)) % 2 ^ n→i(# bits) + bits2uint(bits1) ∨ false ∈ bits ⊦ 2 ^ n→i(# bits0) = 1 + bits2uint(bits1), false ∈ bits0

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 12:
⊦ bits ≠ [] → bitsand(bits, true ') = bits
Proof step 13:
false ' + bits0 ≠ [], false ' + bits0 = false ' + bits1, ∀ bits, bits2, bits1. # bits < # bits0 → bitsand(false ' + bits, true ' + bits2) = false ' + bits1 → 2 ^ n→i(# bits) = 1 + bits2uint(bitsinvert(bits2)) % 2 ^ n→i(# bits) + bits2uint(bits1) ∨ false ∈ bits ⊦ 2 ^ n→i(# bits0) = 1 + bits2uint(bits1), false ∈ bits0

Rule argument

name: and-oner-01 rotate: F subst: [bits] → [false ' + bits0]

Additional information

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