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Proof step 14 from proof cast-mod-ls-most (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 15:
⊦ n = # bits → lastn(n, bits) = bits
Proof step 16:
i→n(i) = #(true ' + mklist(false, i→n(i) - 1)), i→n(i) ≤ 1 + (i→n(i) - 1), 1 < i, 0 < i ⊦ 2 ^ (i - 1) + bits2int(true ' + mklist(false, i→n(i) - 1)) = 0

Rule argument

seq: ⊦ n = # bits → lastn(n, bits) = bits subst: [bits, n] → [true ' + mklist(false, i→n(i) - 1), 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;% ⊦ # boolvar ' = 0 +1;% ⊦ # mklist(boolvar, n) = n;% ⊦ (bits + bits0) + bits1 = bits + bits0 + bits1;% ⊦ i < j → (¬ ¬ j ≤ i ↔ false);% ⊦ ¬ i < j ↔ j ≤ i;% ⊦ 1 ≤ i ↔ 0 < i;%0 ≤ i ⊦ (* m) ≤ i→n(i) ↔ n→i(m) ≤ i;% ⊦ ¬ i ≤ j ↔ j < i;% ⊦ i < j → ¬ j < i;%n ≤ m ⊦ (m - n) + n0 = n1 ↔ m + n0 = n + n1;% ⊦ (m + n0) + n1 = m + n0 + n1; Used terms: true ' + mklist(false, i→n(i) - 1), i→n(i)