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Proof step 74 from proof shiftright-rec-neg (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 75:
⊦ n ≠ 0 ∧ bits ≠ [] → (firstn(n, bits).first ↔ bits.first)
Proof step 76:
# int2bits((i - 1) / 2) ≠ 0 ∧ mklist(true, i→n(j) - 1) + int2bits((i - 1) / 2) ≠ [], int2bits(i % 2).butlast = [], i < ~1, i < 0 ⊦ abs(j) = 1, i→n(j) + # int2bits(i % 2) = 0, int2bits((i - 1) / 2) + int2bits(i % 2) = [], j = 0, bits2int(true ' + firstn(# int2bits((i - 1) / 2), mklist(true, i→n(j) - 1) + int2bits((i - 1) / 2))) = bits2int(firstn(# int2bits((i - 1) / 2), mklist(true, i→n(j) - 1) + int2bits((i - 1) / 2))), (mklist(true, i→n(j) - 1) + int2bits((i - 1) / 2)).first

Rule argument

seq: ⊦ n ≠ 0 ∧ bits ≠ [] → (firstn(n, bits).first ↔ bits.first) subst: [bits, n] → [mklist(true, i→n(j) - 1) + int2bits((i - 1) / 2), # int2bits((i - 1) / 2)] rotate: F spec: list-del inst: bitlista name: firstn-first

Additional information

Used simplifier rules: ⊦ # bits = 0 ↔ bits = [];% ⊦ int2bits(j) ≠ [];% ⊦ ¬ bits + bits0 ≠ [] ↔ bits = [] ∧ bits0 = [];% ⊦ mklist(boolvar, m) = [] ↔ m = 0;% ⊦ (bits + bits0) + bits1 = bits + bits0 + bits1; Used terms: mklist(true, i→n(j) - 1) + int2bits((i - 1) / 2), # int2bits((i - 1) / 2)