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Proof step 11 from proof getarray-addarray-06 (previous step)

0 ≤ i ⊦ # getarray(r, addarray(r, ty, i, st)) = i→n(i) ∧ (n < # getarray(r, addarray(r, ty, i, st)) → (addarray(r, ty, i, st)[r -- n→i(n) ']) = (mklist(initial_value(ty), i→n(i))[n]))

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 2:
⊦ 0 ≤ st[r -- _length] .intval → # getarray(r, st) = i→n(st[r -- _length] .intval)
Proof step 3:
⊦ (addarray(r, ty, i, st)[r -- _length]) = intval(i)
Proof step 10:
0 ≤ (addarray(r, ty, i, st)[r -- _length]) .intval, 0 ≤ i ⊦ i→n((addarray(r, ty, i, st)[r -- _length]) .intval) = i→n(i) ∧ (n < i→n((addarray(r, ty, i, st)[r -- _length]) .intval) → (addarray(r, ty, i, st)[r -- n→i(n) ']) = (mklist(initial_value(ty), i→n(i))[n]))

Rule argument

[speclemmaarg: , 0 ≤ st[r -- _length] .intval → # getarray(r, st) = i→n(st[r -- _length] .intval) ,[st, r] → [addarray(r, ty, i, st), r] ,F ,storearrays , ,getarray-length ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ intval(i) .intval = i], [CSIMPSEQ : ⊦ ¬ i ≤ j ↔ j < i], [CSIMPSEQ : ⊦ i ≤ j → (¬ ¬ j < i ↔ false)])], [EXTRATERMS : (addarray(r, ty, i, st), r)]]