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Proof step 20 from proof cast-mod-neg-high (previous step)

j < j % 2, ~1 ≤ j % 2, j < 0, j < ~1, 1 ≤ # int2bits((j - 1) / 2) + # int2bits(j % 2) ⊦ bits2int((int2bits((j - 1) / 2) + int2bits(j % 2)).last ') = j % 2, j = ~1, # int2bits((j - 1) / 2) + # int2bits(j % 2) = 0

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 21:
⊦ bits ≠ [] → ((bits0 + bits).last ↔ bits.last)
Proof step 22:
int2bits(j % 2) ≠ [], j < j % 2, ~1 ≤ j % 2, j < 0, j < ~1, 1 ≤ # int2bits((j - 1) / 2) + # int2bits(j % 2) ⊦ bits2int(int2bits(j % 2).last ') = j % 2, j = ~1, # int2bits((j - 1) / 2) + # int2bits(j % 2) = 0

Rule argument

seq: ⊦ bits ≠ [] → ((bits0 + bits).last ↔ bits.last) subst: [bits, bits0] → [int2bits(j % 2), int2bits((j - 1) / 2)] rotate: F spec: list-last inst: bitlista name: lapp

Additional information

Used simplifier rules: ⊦ int2bits(j) ≠ []; Used terms: int2bits(j % 2), int2bits((j - 1) / 2)