[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 54 from proof div-inshort (previous step)

s2i(sho1) = ~1, s2i(sho0) < ~32767, s2i(sho0) < 0 ⊦ s2i(sho0) = ~32768

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 55:
⊦ i < j ↔ i + 1 ≤ j

Rule argument

spec: int-abs inst: name: ls-rew-succ seq: ⊦ i < j ↔ i + 1 ≤ j subst: [j, i] → [~32767, s2i(sho0)] flags: rewrite

Additional information

Used simplifier rules: short-min-03: ⊦ s2i(sho) ≤ ~32768 ↔ s2i(sho) = ~32768;%numle-03: ⊦ i + (* j) ≤ (* j0) ↔ i ≤ j0 - j; from specification int-abs%add-a: ⊦ i + j + i0 = (i + j) + i0; from specification int-basic2%add-c: ⊦ i + j = j + i; from specification int-basic2 Used terms: ~32767, s2i(sho0)