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Proof step 26 from proof bytes2bytes-first-neg (previous step)

0 ≤ b2i(int2bytes(bytes2int(i2b(~1) ' + bytes)).first), ∀ by, bytes0. # bytes0 < # bytes → true → (b2i(int2bytes(bytes2int(by ' + bytes0)).first) < 0 ↔ ¬ 0 ≤ b2i(by)) ⊦ bytes = []

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 27:
1 < # bytes, b2i(bytes.first) = ~1, 0 ≤ b2i(bytes.rest.first) ⊦ int2bytes(bytes2int(bytes)) = bytes
Proof step 28:
¬(1 < #(i2b(~1) ' + bytes) ∧ b2i((i2b(~1) ' + bytes).first) = ~1 ∧ 0 ≤ b2i((i2b(~1) ' + bytes).rest.first)), 0 ≤ b2i(int2bytes(bytes2int(i2b(~1) ' + bytes)).first), ∀ by, bytes0. # bytes0 < # bytes → true → (b2i(int2bytes(bytes2int(by ' + bytes0)).first) < 0 ↔ ¬ 0 ≤ b2i(by)) ⊦ bytes = []

Rule argument

name: bytes2bytes-mone rotate: F subst: [bytes] → [i2b(~1) ' + bytes]

Additional information

Used simplifier rules: ⊦ (by ' + bytes).first = by;% ⊦ (bytes + bytes0) + bytes1 = bytes + bytes0 + bytes1;%~128 ≤ i, i ≤ 127 ⊦ b2i(i2b((* i))) = i;% ⊦ #(bytes + bytes0) = # bytes + # bytes0;% ⊦ # by ' = 0 +1;% ⊦ 1 < m ↔ ¬(m = 0 ∨ m = 1);% ⊦ m + 1 ≠ 0;% ⊦ (m + n0) + n1 = m + n0 + n1;% ⊦ m + n = n + m;% ⊦ m + n = 1 ↔ m = 0 ∧ n = 1 ∨ n = 0 ∧ m = 1;% ⊦ # bytes = 0 ↔ bytes = [];% ⊦ (by ' + bytes).rest = bytes; Used terms: i2b(~1) ' + bytes