[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 9 from proof uint2bits-2potrec (previous step)

2 ^ i < j, 0 ≤ i, 2 ^ i ≤ j ⊦ uint2bits(j) = butlastn(i→n(i), uint2bits(j)) + fillsgn(i→n(i) + 1, sgn(false ' + lastn(i→n(i), uint2bits(j).rest))).rest

User applied rule insert lemma

And obtained the following new goals

Proof step 10:
0 ≤ i, 0 ≤ j, 2 ^ i ≤ j ⊦ i→n(i + 1) < # uint2bits(j)
Proof step 11:
i→n(i + 1) < # uint2bits(j), 2 ^ i < j, 0 ≤ i, 2 ^ i ≤ j ⊦ uint2bits(j) = butlastn(i→n(i), uint2bits(j)) + fillsgn(i→n(i) + 1, sgn(false ' + lastn(i→n(i), uint2bits(j).rest))).rest

Rule argument

name: uint2bits-len-min subst: [i, j] → [i, j]

Additional information

Used simplifier rules: ⊦ ¬ i ≤ j ↔ j < i;% ⊦ i < j ∧ j ≤ j0 → i < j0; (forward)% ⊦ i ≤ j ∧ j < j0 → i < j0; (forward)% ⊦ i < j ∧ j < i0 → i +1 < i0; (forward)% ⊦ ¬ 2 ^ i < 0; Used terms: i, j