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Proof step 10 from proof cast-mod-ls-pos (previous step)

# int2bits(j) ≤ i→n(i), 0 ≤ j, j < 2 ^ (i - 1), 0 < i ⊦ bits2int(lastn(i→n(i), mklist(false, i→n(i) - # int2bits(j)) + int2bits(j))) = j

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 11:
⊦ n = # bits → lastn(n, bits) = bits
Proof step 12:
i→n(i) = #(mklist(false, i→n(i) - # int2bits(j)) + int2bits(j)), # int2bits(j) ≤ i→n(i), 0 ≤ j, j < 2 ^ (i - 1), 0 < i ⊦ bits2int(mklist(false, i→n(i) - # int2bits(j)) + int2bits(j)) = j

Rule argument

seq: ⊦ n = # bits → lastn(n, bits) = bits subst: [bits, n] → [mklist(false, i→n(i) - # int2bits(j)) + int2bits(j), i→n(i)] rotate: F spec: list-del inst: bitlista name: lastN-all

Additional information

Used simplifier rules: ⊦ m + n = n + m;% ⊦ #(bits + bits0) = # bits + # bits0;% ⊦ # mklist(boolvar, n) = n;% ⊦ (bits + bits0) + bits1 = bits + bits0 + bits1;% ⊦ m ≤ n → (n < m ↔ false);% ⊦ ¬ m ≤ n ↔ n < m;%n ≤ m ⊦ (m - n) + n0 = n1 ↔ m + n0 = n + n1;% ⊦ (m + n0) + n1 = m + n0 + n1; Used terms: mklist(false, i→n(i) - # int2bits(j)) + int2bits(j), i→n(i)