[Imprint][Data Privacy Statement][E-Mail]

View long theorem info. View the proof. Back to main index. View the specification. View theorem base summary, View theorem base listing, the used properties by spec, the dependency list, the symbol table,

Proof step 56 from proof intshiftrsign-rec-pos (previous step)

# int2bits(i / 2) = m + 1, 0 < i, 1 < i, 0 ≤ i0, 0 ≤ i, i0 < 31, (sublist(0, m, mklist(false, i→n(i0)) + int2bits(i / 2)) + (mklist(false, i→n(i0)) + int2bits(i / 2))[m] ').first ⊦ bits2uint(sublist(0, m, mklist(false, i→n(i0)) + int2bits(i / 2)) + (mklist(false, i→n(i0)) + int2bits(i / 2))[m] ') = bits2int(sublist(0, m, mklist(false, i→n(i0)) + int2bits(i / 2)) + (mklist(false, i→n(i0)) + int2bits(i / 2))[m] ')

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 57:
⊦ bits ≠ [] ∧ n ≠ 0 → sublist(0, n, bits) = bits.first ' + sublist(0, n -1, bits.rest)
Proof step 58:
¬(mklist(false, i→n(i0)) + int2bits(i / 2) ≠ [] ∧ m ≠ 0), # int2bits(i / 2) = m + 1, 0 < i, 1 < i, 0 ≤ i0, 0 ≤ i, i0 < 31, (sublist(0, m, mklist(false, i→n(i0)) + int2bits(i / 2)) + (mklist(false, i→n(i0)) + int2bits(i / 2))[m] ').first ⊦ bits2uint(sublist(0, m, mklist(false, i→n(i0)) + int2bits(i / 2)) + (mklist(false, i→n(i0)) + int2bits(i / 2))[m] ') = bits2int(sublist(0, m, mklist(false, i→n(i0)) + int2bits(i / 2)) + (mklist(false, i→n(i0)) + int2bits(i / 2))[m] ')
Proof step 70:
mklist(false, i→n(i0)) + int2bits(i / 2) ≠ [] ∧ m ≠ 0, # int2bits(i / 2) = m + 1, 0 < i, 1 < i, 0 ≤ i0, 0 ≤ i, i0 < 31, ( ((mklist(false, i→n(i0)) + int2bits(i / 2)).first ' + sublist(0, m -1, (mklist(false, i→n(i0)) + int2bits(i / 2)).rest)) + (mklist(false, i→n(i0)) + int2bits(i / 2))[m] ' ).first ⊦ bits2uint ( ((mklist(false, i→n(i0)) + int2bits(i / 2)).first ' + sublist(0, m -1, (mklist(false, i→n(i0)) + int2bits(i / 2)).rest)) + (mklist(false, i→n(i0)) + int2bits(i / 2))[m] ') = bits2int ( ((mklist(false, i→n(i0)) + int2bits(i / 2)).first ' + sublist(0, m -1, (mklist(false, i→n(i0)) + int2bits(i / 2)).rest)) + (mklist(false, i→n(i0)) + int2bits(i / 2))[m] ')

Rule argument

seq: ⊦ bits ≠ [] ∧ n ≠ 0 → sublist(0, n, bits) = bits.first ' + sublist(0, n -1, bits.rest) subst: [bits, n] → [mklist(false, i→n(i0)) + int2bits(i / 2), m] rotate: F spec: list-del inst: bitlista name: sublist-rec

Additional information

Used terms: mklist(false, i→n(i0)) + int2bits(i / 2), m