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Proof step 81 from proof shiftright-rec-neg (previous step)

i < 0, i < ~1 ⊦ # int2bits(i % 2).butlast = # [] ∧ (∀ n. n < # int2bits(i % 2).butlast → (int2bits(i % 2).butlast[n] ↔ ([])[n])), int2bits((i - 1) / 2) + int2bits(i % 2) = [], i→n(j) + # int2bits(i % 2) = 0, bits2int(firstn(# int2bits((i - 1) / 2) + 1, mklist(true, i→n(j)) + int2bits((i - 1) / 2) + int2bits(i % 2).butlast)) = bits2int(firstn(# int2bits((i - 1) / 2), mklist(true, i→n(abs(j) - 1)) + int2bits((i - 1) / 2))), j = 0

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 82:
⊦ bits ≠ [] → # bits.butlast = # bits - 1
Proof step 83:
int2bits(i % 2) ≠ [], i < 0, i < ~1 ⊦ # int2bits(i % 2) - 1 = # [] ∧ (∀ n. n < # int2bits(i % 2) - 1 → (int2bits(i % 2).butlast[n] ↔ ([])[n])), int2bits((i - 1) / 2) + int2bits(i % 2) = [], i→n(j) + # int2bits(i % 2) = 0, bits2int(firstn(# int2bits((i - 1) / 2) + 1, mklist(true, i→n(j)) + int2bits((i - 1) / 2) + int2bits(i % 2).butlast)) = bits2int(firstn(# int2bits((i - 1) / 2), mklist(true, i→n(abs(j) - 1)) + int2bits((i - 1) / 2))), j = 0

Rule argument

seq: ⊦ bits ≠ [] → # bits.butlast = # bits - 1 subst: [bits] → [int2bits(i % 2)] rotate: F spec: list-last inst: bitlista name: lb

Additional information

Used simplifier rules: ⊦ int2bits(j) ≠ []; Used terms: int2bits(i % 2)