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Proof step 8 from proof int2bytes-index-rightshift (previous step)

0 ≤ j, j < n→i(# int2bytes(i)), # int2bytes(i) ≤ # int2bytes(i) - i→n(j) + 1 ⊦ int2bytes(i)[i→n(j)] = i2b(i >> 8 * (n→i(# int2bytes(i)) - j + 1))

User applied rule insert elim lemma

And obtained the following new goals

Proof step 9:
0 ≤ j, j < n→i(# int2bytes(i)), # int2bytes(i) ≤ # int2bytes(i) - i→n(j) + 1 ⊦ i→n(j) + 1 ≤ # int2bytes(i), int2bytes(i)[i→n(j)] = i2b(i >> 8 * (n→i(# int2bytes(i)) - j + 1))
Proof step 12:
# int2bytes(i) = n + i→n(j) + 1 ∧ i→n(j) + 1 ≤ # int2bytes(i), 0 ≤ j, j < n→i(# int2bytes(i)), # int2bytes(i) ≤ n ⊦ int2bytes(i)[i→n(j)] = i2b(i >> 8 * (n→i(# int2bytes(i)) - j + 1))

Rule argument

seq: n ≤ m ⊦ n0 = m - n ↔ m = n0 + n subst: [m, n, n0] → [# int2bytes(i), i→n(j) + 1, n] rotate: T spec: nat inst: name: elim-sub

Additional information

Used simplifier rules: n ≤ m ⊦ n0 = m - n ↔ m = n0 + n; (elim) Used terms: # int2bytes(i), i→n(j) + 1, n