[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 199 from proof putarray-addarray-01 (previous step)

0 ≤ n→i(# vals) + i, 0 ≤ j, 0 ≤ i, i ≤ j, j ≤ n→i(# vals) + i, is_indexkey(sk) ⊦ (putArray(vals, r, i, addarray(r, ty, j, st))[r -- sk]) = (addarray(r, ty, mklist(initial_value(ty), i→n(i)) + vals, st)[r -- sk]), sk = _length, sk = _type

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 154:
⊦ is_fskey(sk) ∧ sk ≠ _length ∧ sk ≠ _type → (addarray(r, ty, vals, st)[r0 -- sk]) = st[r0 -- sk]
Proof step 197:
¬ (is_fskey(sk) ∧ sk ≠ _length ∧ sk ≠ _type), 0 ≤ n→i(# vals) + i, 0 ≤ j, 0 ≤ i, i ≤ j, j ≤ n→i(# vals) + i, is_indexkey(sk) ⊦ (putArray(vals, r, i, addarray(r, ty, j, st))[r -- sk]) = (addarray(r, ty, mklist(initial_value(ty), i→n(i)) + vals, st)[r -- sk]), sk = _length, sk = _type
Proof step 198:
⊦ is_fskey(sk) ∧ sk ≠ _type ∧ sk ≠ _length → (addarray(r, ty, i, st)[r0 -- sk]) = st[r0 -- sk]

Rule argument

[crewrite-arg: add-at-04 , F , [sk, r0, st, vals, ty, r] → [sk, r, st, mklist(initial_value(ty), i→n(i)) + vals, ty, r] ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ is_fskey(sk) → (putArray(vals, r, i, st) [r0 -- sk ] ) = st[r0 -- sk]])], [EXTRATERMS : (sk, r, st, mklist(initial_value(ty), i→n(i)) + vals, ty, r)]]