[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 21 from proof bytes2bytes-fix (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 22:
⊦ 0 ≤ b2i(bytes.first) ∧ # bytes < n ∧ bytes ≠ [] → fix(n, bytes) = i2b(0) ' + fix(n -1, bytes)
Proof step 23:
¬ ( 0 ≤ b2i(int2bytes(bytes2int(by0 ' + bytes)).first) ∧ # int2bytes(bytes2int(by0 ' + bytes)) < 2 + # bytes ∧ int2bytes(bytes2int(by0 ' + bytes)) ≠ []), 0 ≤ b2i(by0), 0 ≤ b2i(by0), ∀ bytes0. # bytes0 < #(i2b(0) + by0 + bytes) → true → bytes0 = [] ∨ fix(# bytes0, int2bytes(bytes2int(bytes0))) = bytes0 ⊦ fix(2 + # bytes, int2bytes(bytes2int(by0 ' + bytes))) = i2b(0) ' + by0 ' + bytes
Proof step 29:
0 ≤ b2i(int2bytes(bytes2int(by0 ' + bytes)).first) ∧ # int2bytes(bytes2int(by0 ' + bytes)) < 2 + # bytes ∧ int2bytes(bytes2int(by0 ' + bytes)) ≠ [], 0 ≤ b2i(by0), 0 ≤ b2i(by0), ∀ bytes0. # bytes0 < #(i2b(0) + by0 + bytes) → true → bytes0 = [] ∨ fix(# bytes0, int2bytes(bytes2int(bytes0))) = bytes0 ⊦ i2b(0) ' + fix((2 + # bytes)-1, int2bytes(bytes2int(by0 ' + bytes))) = i2b(0) ' + by0 ' + bytes

Rule argument

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

Additional information

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