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Proof step 50 from proof shiftright-rec-pos (previous step)

0 ≤ i0 ⊦ bits2int(firstn(1, mklist(false, i→n(i0)) + false ' + false ')) = bits2int(firstn(1, mklist(false, i→n(i0)) + false '))

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 51:
⊦ ¬ true ∈ bits ∧ bits ≠ [] → bits2int(bits) = 0
Proof step 52:
¬(¬ true ∈ firstn(1, mklist(false, i→n(i0)) + false ') ∧ firstn(1, mklist(false, i→n(i0)) + false ') ≠ []), 0 ≤ i0 ⊦ bits2int(firstn(1, mklist(false, i→n(i0)) + false ' + false ')) = bits2int(firstn(1, mklist(false, i→n(i0)) + false '))
Proof step 55:
¬ true ∈ firstn(1, mklist(false, i→n(i0)) + false ') ∧ firstn(1, mklist(false, i→n(i0)) + false ') ≠ [], 0 ≤ i0 ⊦ bits2int(firstn(1, mklist(false, i→n(i0)) + false ' + false ')) = 0

Rule argument

seq: ⊦ ¬ true ∈ bits ∧ bits ≠ [] → bits2int(bits) = 0 subst: [bits] → [firstn(1, mklist(false, i→n(i0)) + false ')] rotate: F spec: int2bits inst: name: bits2int-zero-01

Additional information

Used terms: firstn(1, mklist(false, i→n(i0)) + false ')