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Proof step 5 from proof shiftright-not-pos-01 (previous step)

0 ≤ bits2int(sublist(0, # int2bits(i), mklist(true, i→n(j)) + int2bits(i))), i < 0 ⊦

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 6:
⊦ bits ≠ [] → (0 ≤ bits2int(bits) ↔ ¬ bits.first)
Proof step 7:
sublist(0, # int2bits(i), mklist(true, i→n(j)) + int2bits(i)) ≠ [], ¬ sublist(0, # int2bits(i), mklist(true, i→n(j)) + int2bits(i)).first, i < 0 ⊦

Rule argument

seq: ⊦ bits ≠ [] → (0 ≤ bits2int(bits) ↔ ¬ bits.first) subst: [bits] → [sublist (0, # int2bits(i), mklist(true, i→n(j)) + int2bits(i))] rotate: F spec: int2bits inst: name: bits2int-ge-zero

Additional information

Used simplifier rules: ⊦ sublist(0, n, bits) = [] ↔ n = 0;% ⊦ # bits = 0 ↔ bits = [];% ⊦ int2bits(j) ≠ []; Used terms: sublist(0, # int2bits(i), mklist(true, i→n(j)) + int2bits(i))