[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 57 from proof no-leading-zero-01 (previous step)

int2bytes(i / 256) = i2b(0) ' + (by ' + bytes).butlast, int2bytes(i % 256).last = (by ' + bytes).last, 0 < i, 0 ≤ b2i(by), 255 < i, i2b(0) ∈ int2bytes(i / 256), ∀ bytes, by, i0. i→n(i0) < i→n(i) → int2bytes(i0) = i2b(0) ' + by ' + bytes ∧ 0 ≤ b2i(by) ∧ i2b(0) ∈ int2bytes(i0) → false ⊦ (by ' + bytes).last ≠ i2b(0) ∧ (by ' + bytes).last ≠ by ∧ ¬ (by ' + bytes).last ∈ bytes

Heuristic weak cut applied rule cut formula

And obtained the following new goals

Proof step 58:
bytes = [], int2bytes(i / 256) = i2b(0) ' + (by ' + bytes).butlast, int2bytes(i % 256).last = (by ' + bytes).last, 0 < i, 0 ≤ b2i(by), 255 < i, i2b(0) ∈ int2bytes(i / 256), ∀ bytes, by, i0. i→n(i0) < i→n(i) → int2bytes(i0) = i2b(0) ' + by ' + bytes ∧ 0 ≤ b2i(by) ∧ i2b(0) ∈ int2bytes(i0) → false ⊦ (by ' + bytes).last ≠ i2b(0) ∧ (by ' + bytes).last ≠ by ∧ ¬ (by ' + bytes).last ∈ bytes
Proof step 59:
int2bytes(i / 256) = i2b(0) ' + (by ' + bytes).butlast, int2bytes(i % 256).last = (by ' + bytes).last, 0 < i, 0 ≤ b2i(by), 255 < i, i2b(0) ∈ int2bytes(i / 256), ∀ bytes, by, i0. i→n(i0) < i→n(i) → int2bytes(i0) = i2b(0) ' + by ' + bytes ∧ 0 ≤ b2i(by) ∧ i2b(0) ∈ int2bytes(i0) → false ⊦ bytes = [], (by ' + bytes).last ≠ i2b(0) ∧ (by ' + bytes).last ≠ by ∧ ¬ (by ' + bytes).last ∈ bytes

Rule argument

fma: bytes = []

Additional information

Used formulas: bytes = []