[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 42 from proof sis-neg-low (previous step)

16 = # int2bits(j0).rest, # int2bits(j0) = 17, i0 < 0, i0 * 65536 + j0 < 0, i0 * 65536 + j0 < ~32768, j0 < ~32768, j0 < 0, j0 < ~1, ~32769 < j0, ~98304 ≤ j0 ⊦ j0 = 0, int2bits(j0).rest = [], s2i(i2s(j0 + 65536)) = j0 + 65536

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: int-basic1 inst: name: lsrec seq: ⊦ i < j ↔ i +1 = j ∨ i +1 < j subst: [j, i] → [j0, ~32769] flags: rewrite

Additional information

Used simplifier rules: sis-pos-high: ⊦ 0 ≤ i ∧ 32767 < i % 65536 → s2i(i2s(i)) = i % 65536 - 65536;%commutativity: ⊦ i * j = j * i; from specification int-mult%add-a: ⊦ i + j + i0 = (i + j) + i0; from specification int-basic2%add-c: ⊦ i + j = j + i; from specification int-basic2%ls-01: ⊦ i < j → ¬ j < i; from specification int-basic1 Used terms: j0, ~32769