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Proof step 21 from proof int2bytes-len-le-neg-01 (previous step)

int2bytes(i).first = i2b(~1), 2 ^ (8 * (1 + n→i(# int2bytes(i) - 1 - 1)) - 1) + i < 0, 0 ≤ 2 ^ (8 * (1 + n→i(# int2bytes(i) - 1 - 1))) + i, 0 ≤ b2i(int2bytes(i).rest.first) ⊦ n ≤ # int2bytes(i) ↔ ¬ 0 ≤ i + 2 ^ (8 * (n→i(n) - 1) - 1), int2bytes(i).rest = []

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 22:
⊦ n ≤ m → n→i(m - n) = n→i(m) - n→i(n)
Proof step 23:
¬ 1 ≤ # int2bytes(i) - 1, int2bytes(i).first = i2b(~1), 2 ^ (8 * (1 + n→i(# int2bytes(i) - 1 - 1)) - 1) + i < 0, 0 ≤ 2 ^ (8 * (1 + n→i(# int2bytes(i) - 1 - 1))) + i, 0 ≤ b2i(int2bytes(i).rest.first) ⊦ n ≤ # int2bytes(i) ↔ ¬ 0 ≤ i + 2 ^ (8 * (n→i(n) - 1) - 1), int2bytes(i).rest = []
Proof step 28:
1 ≤ # int2bytes(i) - 1, int2bytes(i).first = i2b(~1), 2 ^ (8 * (1 + (n→i(# int2bytes(i) - 1) - n→i(1))) - 1) + i < 0, 0 ≤ 2 ^ (8 * (1 + (n→i(# int2bytes(i) - 1) - n→i(1)))) + i, 0 ≤ b2i(int2bytes(i).rest.first) ⊦ n ≤ # int2bytes(i) ↔ ¬ 0 ≤ i + 2 ^ (8 * (n→i(n) - 1) - 1), int2bytes(i).rest = []

Rule argument

seq: ⊦ n ≤ m → n→i(m - n) = n→i(m) - n→i(n) subst: [n, m] → [1, # int2bytes(i) - 1] rotate: F spec: intnat inst: name: n2i-sub

Additional information

Used terms: 1, # int2bytes(i) - 1