[Imprint][Data Privacy Statement][E-Mail]

View long theorem info. View the proof. Back to main index. View the specification. View theorem base summary, View theorem base listing, the used properties by spec, the dependency list, the symbol table,

Proof step 39 from proof no-leading-zero-01 (previous step)

i - 256 < 256 * i + j, int2bytes(i) = i2b(0) ' + by ' + bytes0, i2b(0) ∈ int2bytes(i), i * 256 + j < 0, i ≤ 0, j ≤ 0, i < 256 * (i + 1) + j, 0 ≤ b2i(by), i * 256 + j < ~383, abs(j) < 256, ∀ bytes, by, i0. i→n(i0) < i→n((i * 256 + j) + 255) → int2bytes(i0) = i2b(0) ' + by ' + bytes ∧ 0 ≤ b2i(by) ∧ i2b(0) ∈ int2bytes(i0) → false ⊦

User applied rule cut formula

And obtained the following new goals

Proof step 40:
i - 256 < ~383, i - 256 < 256 * i + j, int2bytes(i) = i2b(0) ' + by ' + bytes0, i2b(0) ∈ int2bytes(i), i * 256 + j < 0, i ≤ 0, j ≤ 0, i < 256 * (i + 1) + j, 0 ≤ b2i(by), i * 256 + j < ~383, abs(j) < 256, ∀ bytes, by, i0. i→n(i0) < i→n((i * 256 + j) + 255) → int2bytes(i0) = i2b(0) ' + by ' + bytes ∧ 0 ≤ b2i(by) ∧ i2b(0) ∈ int2bytes(i0) → false ⊦
Proof step 46:
i - 256 < 256 * i + j, int2bytes(i) = i2b(0) ' + by ' + bytes0, i2b(0) ∈ int2bytes(i), i * 256 + j < 0, i ≤ 0, j ≤ 0, i < 256 * (i + 1) + j, 0 ≤ b2i(by), i * 256 + j < ~383, abs(j) < 256, ∀ bytes, by, i0. i→n(i0) < i→n((i * 256 + j) + 255) → int2bytes(i0) = i2b(0) ' + by ' + bytes ∧ 0 ≤ b2i(by) ∧ i2b(0) ∈ int2bytes(i0) → false ⊦ i - 256 < ~383

Rule argument

fma: i - 256 < ~383

Additional information

Used formulas: i - 256 < ~383