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Proof step 52 from proof bxor-flip-one-bit (previous step)

0 < i, 2 < i, 0 ≤ i ⊦ (int2bits(bits2int(bitsxor(int2bits(i), false ' + true ')))[# int2bits(i) - 1] ↔ ¬ int2bits(i).last) ∧ int2bits(bits2int(bitsxor(int2bits(i), false ' + true ')))[# int2bits(i) - 1, int2bits(i).last] = int2bits(i)

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

name: bitsxor-rec-01 rotate: F subst: [bits0, bits] → [false ' + true ', int2bits(i)]

Additional information

Used simplifier rules: bitsxor-zerol: ⊦ bitsxor(false ', bits + boolvar ') = bits + boolvar;% ⊦ 1 < m ↔ ¬(m = 0 ∨ m = 1);% ⊦ # bits = 0 ↔ bits = [];% ⊦ int2bits(j) ≠ [];% ⊦ 0 ≤ i → (# int2bits(i) = 1 ↔ i = 0);% ⊦ #(bits + bits0) = # bits + # bits0;% ⊦ # boolvar ' = 0 +1;% ⊦ (bits + bits0) + bits1 = bits + bits0 + bits1;% ⊦ boolvar ' + bits ≠ [];% ⊦ bits + boolvar = bits + boolvar ';% ⊦ int2bits(0) = false ';%bits ≠ [] ⊦ int2bits(bits2int(bits)) = sgn(bits);% ⊦ boolvar ' ≠ [];% ⊦ ¬ bits + bits0 ≠ [] ↔ bits = [] ∧ bits0 = []; Used terms: false ' + true ', int2bits(i)