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Proof step 45 from proof bytes2bytes-fix (previous step)

b2i(by0) < 0, b2i(by0) < 0, ∀ bytes0. # bytes0 < #(i2b(~1) + by0 + bytes) → true → bytes0 = [] ∨ fix(# bytes0, int2bytes(bytes2int(bytes0))) = bytes0 ⊦ fix(2 + # bytes, int2bytes(bytes2int(by0 ' + bytes))) = i2b(~1) ' + by0 ' + bytes

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 46:
⊦ b2i(bytes.first) < 0 ∧ # bytes < n ∧ bytes ≠ [] → fix(n, bytes) = i2b(~1) ' + fix(n -1, bytes)
Proof step 47:
¬ ( b2i(int2bytes(bytes2int(by0 ' + bytes)).first) < 0 ∧ # int2bytes(bytes2int(by0 ' + bytes)) < 2 + # bytes ∧ int2bytes(bytes2int(by0 ' + bytes)) ≠ []), b2i(by0) < 0, b2i(by0) < 0, ∀ bytes0. # bytes0 < #(i2b(~1) + by0 + bytes) → true → bytes0 = [] ∨ fix(# bytes0, int2bytes(bytes2int(bytes0))) = bytes0 ⊦ fix(2 + # bytes, int2bytes(bytes2int(by0 ' + bytes))) = i2b(~1) ' + by0 ' + bytes
Proof step 50:
b2i(int2bytes(bytes2int(by0 ' + bytes)).first) < 0 ∧ # int2bytes(bytes2int(by0 ' + bytes)) < 2 + # bytes ∧ int2bytes(bytes2int(by0 ' + bytes)) ≠ [], b2i(by0) < 0, b2i(by0) < 0, ∀ bytes0. # bytes0 < #(i2b(~1) + by0 + bytes) → true → bytes0 = [] ∨ fix(# bytes0, int2bytes(bytes2int(bytes0))) = bytes0 ⊦ i2b(~1) ' + fix((2 + # bytes)-1, int2bytes(bytes2int(by0 ' + bytes))) = i2b(~1) ' + by0 ' + bytes

Rule argument

name: fix-rec-neg rotate: F subst: [bytes, n] → [int2bytes(bytes2int(by0 ' + bytes)), 2 + # bytes]

Additional information

Used terms: int2bytes(bytes2int(by0 ' + bytes)), 2 + # bytes