[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 26 from proof getintarray-in (previous step)

0 < st[r -- _length] .intval, 0 ≤ j, j < st[r -- _length] .intval ⊦ (intvalues(getarray(r, 0, st[r -- _length] .intval, st))[i→n(j)]) = st[r -- j '] .intval

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 20:
⊦ m < # vals → (intvalues(vals)[m]) = vals[m] .intval
Proof step 21:
⊦ 0 < j → # getarray(r, i, j, st) = i→n(j)
Proof step 25:
i→n(j) < # getarray(r, 0, st[r -- _length] .intval, st), 0 < st[r -- _length] .intval, 0 ≤ j, j < st[r -- _length] .intval ⊦ (getarray(r, 0, st[r -- _length] .intval, st)[i→n(j)]) .intval = st[r -- j '] .intval

Rule argument

[speclemmaarg: ,m < # vals → (intvalues(vals)[m]) = vals[m] .intval ,[m, vals] → [i→n(j), getarray(r, 0, st[r -- _length] .intval, st)] ,F ,valuesfuns , ,intvalues-at ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ i→n(i) < i→n(j) ↔ abs(i) < abs(j)], [CSIMPSEQ : ⊦ 0 ≤ i → abs(i) = i], [CSIMPSEQ : ⊦ 0 < j → abs(j) = j], [CSIMPSEQ : ⊦ ¬ i < j ↔ j ≤ i], [CSIMPSEQ : ⊦ i < j → (¬ ¬ j ≤ i ↔ false)])], [EXTRATERMS : (i→n(j), getarray(r, 0, st[r -- _length] .intval, st))]]