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Proof step 2 from proof int2int-rest-01 (previous step)

j < ~1, j < 0 ⊦ bits2int(int2bits(j).rest) = j + 2 ^ (n→i(# int2bits(j)) - 1)

User applied rule insert lemma

And obtained the following new goals

Proof step 3:
i < ~ 1 ⊦ ∃ bits. int2bits(i) = true ' + false ' + bits
Proof step 4:
∃ bits. int2bits(j) = true ' + false ' + bits, j < ~1, j < 0 ⊦ bits2int(int2bits(j).rest) = j + 2 ^ (n→i(# int2bits(j)) - 1)

Rule argument

name: int2bits-exneg subst: [i] → [j]

Additional information

Used simplifier rules: int2bits-neg-num: i < 0 ⊦ int2bits((* i)) = sgn(bitsinvert(uint2bits(abs(i))) +1);%uint2bits-one: ⊦ uint2bits(1) = false + true;% ⊦ ¬ i < j ↔ j ≤ i;% ⊦ i < 0 → (~1 ≤ i ↔ i = ~1);% ⊦ boolvar + boolvar0 = boolvar ' + boolvar0 ';% ⊦ bitsinvert(false ' + bits) = true + bitsinvert(bits);% ⊦ bitsinvert(true ') = false ';% ⊦ boolvar + bits = boolvar ' + bits;% ⊦ (bits + bits0) + bits1 = bits + bits0 + bits1;% ⊦ (bits + false ')+1 = bits + true;% ⊦ bits + boolvar = bits + boolvar ';% ⊦ sgn(true ' + true ') = true ';% ⊦ boolvar '.rest = [];% ⊦ # boolvar ' = 0 +1; Used terms: j