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Proof step 38 from proof no-leading-zero (previous step)

int2bytes(band(b2i(by0), 255)) = i2b(0) ' + by ' + bytes1 + by0 ', bits2int(byte2bits(i2b(0)) + byte2bits(by) + bytes2bits(bytes1)) = 0, band(b2i(by0), 255) < 256, 0 ≤ b2i(by), 0 ≤ band(b2i(by0), 255), i2b(0) ∈ int2bytes(band(b2i(by0), 255)), by0 ∈ int2bytes(band(b2i(by0), 255)), ∀ by, bytes0. # bytes0 < #(bytes1 + by0 ') → int2bytes(bytes2int(i2b(0) ' + by ' + bytes0)) = i2b(0) ' + by ' + bytes0 ∧ 0 ≤ b2i(by) → false ⊦

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 39:
⊦ bits ≠ [] → (bits2int(bits) = 0 ↔ ¬ true ∈ bits)
Proof step 40:
byte2bits(i2b(0)) + byte2bits(by) + bytes2bits(bytes1) ≠ [], int2bytes(band(b2i(by0), 255)) = i2b(0) ' + by ' + bytes1 + by0 ', ¬ true ∈ byte2bits(i2b(0)) + byte2bits(by) + bytes2bits(bytes1), band(b2i(by0), 255) < 256, 0 ≤ b2i(by), 0 ≤ band(b2i(by0), 255), i2b(0) ∈ int2bytes(band(b2i(by0), 255)), by0 ∈ int2bytes(band(b2i(by0), 255)), ∀ by, bytes0. # bytes0 < #(bytes1 + by0 ') → int2bytes(bytes2int(i2b(0) ' + by ' + bytes0)) = i2b(0) ' + by ' + bytes0 ∧ 0 ≤ b2i(by) → false ⊦

Rule argument

seq: ⊦ bits ≠ [] → (bits2int(bits) = 0 ↔ ¬ true ∈ bits) subst: [bits] → [byte2bits(i2b(0)) + byte2bits(by) + bytes2bits(bytes1)] rotate: F spec: int2bits inst: name: bits2int-zero-02

Additional information

Used simplifier rules: byte2bits-empty: ⊦ byte2bits(by) ≠ [];% ⊦ ¬ bits + bits0 ≠ [] ↔ bits = [] ∧ bits0 = [];% ⊦ (bits + bits0) + bits1 = bits + bits0 + bits1; Used terms: byte2bits(i2b(0)) + byte2bits(by) + bytes2bits(bytes1)