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Proof step 7 from proof bytes2int-mklist-zeros-01 (previous step)

# bytes = 1, 0 ≤ b2i(bytes.first), ∀ n, bytes0. # bytes0 < 1 → 0 ≤ b2i(bytes0.first) → bytes2int(mklist(i2b(0), n) + bytes0) = bytes2int(bytes0) ∨ bytes0 = [] ⊦ bytes = [], bytes2int(mklist(i2b(0), n) + bytes) = bytes2int(bytes)

User applied rule insert elim lemma

And obtained the following new goals

Proof step 8:
bytes = by + bytes1, # bytes = 1, 0 ≤ b2i(by), ∀ n, bytes0. # bytes0 < 1 → 0 ≤ b2i(bytes0.first) → bytes2int(mklist(i2b(0), n) + bytes0) = bytes2int(bytes0) ∨ bytes0 = [] ⊦ bytes = [], bytes2int(mklist(i2b(0), n) + bytes) = bytes2int(bytes)

Rule argument

seq: ⊦ bytes ≠ [] → (by = bytes.first ∧ bytes0 = bytes.rest ↔ bytes = by + bytes0) subst: [bytes, by, bytes0] → [bytes, by, bytes1] rotate: T spec: list-data inst: bytelist name: elim-1

Additional information

Used simplifier rules: ⊦ bytes ≠ [] → (by = bytes.first ∧ bytes0 = bytes.rest ↔ bytes = by + bytes0); (elim) Used terms: bytes, by, bytes1