[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-second (previous step)

0 < i, ∀ i0. i→n(i0) < i→n(i) → 0 < i0 → uint2bits(i0).rest.first ⊦ i = 1, (uint2bits(i / 2).rest + (i % 2 = 1)').first

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 10:
⊦ bits ≠ [] → ((bits + bits0).first ↔ bits.first)
Proof step 11:
¬ uint2bits(i / 2).rest ≠ [], 0 < i, ∀ i0. i→n(i0) < i→n(i) → 0 < i0 → uint2bits(i0).rest.first ⊦ i = 1, (uint2bits(i / 2).rest + (i % 2 = 1)').first
Proof step 15:
uint2bits(i / 2).rest ≠ [], 0 < i, ∀ i0. i→n(i0) < i→n(i) → 0 < i0 → uint2bits(i0).rest.first ⊦ i = 1, uint2bits(i / 2).rest.first

Rule argument

seq: ⊦ bits ≠ [] → ((bits + bits0).first ↔ bits.first) subst: [bits0, bits] → [(i % 2 = 1)', uint2bits(i / 2).rest] rotate: F spec: list inst: bitlista name: first-01

Additional information

Used terms: (i % 2 = 1)', uint2bits(i / 2).rest