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Proof step 7 from proof cast-size-fits (previous step)

n→i(# int2bits(j)) ≤ i0 + 1, 0 ≤ i0 ⊦ cast(i0 + 1, j) = j, ¬ 2 ^ i0 ≤ j ∧ ¬ 2 ^ i0 + j < 0

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 8:
0 ≤ i ⊦ n→i(n) ≤ i ↔ n ≤ i→n(i)
Proof step 9:
0 ≤ i0 + 1, # int2bits(j) ≤ i→n(i0 + 1), 0 ≤ i0 ⊦ cast(i0 + 1, j) = j, ¬ 2 ^ i0 ≤ j ∧ ¬ 2 ^ i0 + j < 0

Rule argument

seq: 0 ≤ i ⊦ n→i(n) ≤ (* i) ↔ n ≤ i→n(i) subst: [i, n] → [i0 + 1, # int2bits(j)] rotate: F spec: intnat inst: name: num-n2i-ls-04

Additional information

Used simplifier rules: ⊦ (* j) ≤ i0 + (* j0) ↔ j - j0 ≤ i0;%i0 ≠ 0, i0 ≤ i ⊦ (* i) ≤ j → (* i0) ≤ j;% ⊦ i + j + i0 = (i + j) + i0;% ⊦ i + j = j + i; Used terms: i0 + 1, # int2bits(j)