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Proof step 5 from proof cast-size-fits-01 (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 6:
0 ≤ i ⊦ i < n→i(n) ↔ i→n(i) < n
Proof step 7:
0 ≤ i, i→n(i) < # int2bits(j), 0 ≤ 2 ^ (i - 1) + j, 0 < i, j < 2 ^ (i - 1) ⊦ cast(i, j) = j, # int2bits(j) = 1

Rule argument

seq: 0 ≤ i ⊦ (* i) < n→i(n) ↔ i→n(i) < n subst: [n, i] → [# int2bits(j), i] rotate: F spec: intnat inst: name: num-n2i-ls-02

Additional information

Used simplifier rules: ⊦ ¬ i ≤ j ↔ j < i;% ⊦ i < j → ¬ j < i; Used terms: # int2bits(j), i