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Proof step 59 from proof intshiftrsign-rec-pos (previous step)

# int2bits(i / 2) = 1, i0 < 31, 0 ≤ i, 0 ≤ i0, 1 < i, 0 < i, (mklist(false, i→n(i0)) + int2bits(i / 2))[0] ⊦

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 60:
⊦ bits ≠ [] → (bits[0] ↔ bits.first)
Proof step 61:
mklist(false, i→n(i0)) + int2bits(i / 2) ≠ [], # int2bits(i / 2) = 1, i0 < 31, 0 ≤ i, 0 ≤ i0, 1 < i, 0 < i, (mklist(false, i→n(i0)) + int2bits(i / 2)).first ⊦

Rule argument

seq: ⊦ bits ≠ [] → (bits[0] ↔ bits.first) subst: [bits] → [mklist(false, i→n(i0)) + int2bits(i / 2)] rotate: F spec: list-del inst: bitlista name: get-zero

Additional information

Used simplifier rules: ⊦ ¬ bits + bits0 ≠ [] ↔ bits = [] ∧ bits0 = [];% ⊦ mklist(boolvar, m) = [] ↔ m = 0;% ⊦ i→n(i) = 0 ↔ i = 0;% ⊦ int2bits(j) ≠ [];% ⊦ (bits + bits0) + bits1 = bits + bits0 + bits1; Used terms: mklist(false, i→n(i0)) + int2bits(i / 2)