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

is_fskey(sk) ∧ sk ≠ _length ∧ sk ≠ _type, 0 ≤ n→i(# vals) + i, 0 ≤ j, 0 ≤ i, i ≤ j, j ≤ n→i(# vals) + i ⊦ sk = _length, (r -- sk ∈ putArray(vals, r, i, addarray(r, ty, j, st)) ↔ r -- sk ∈ st) ∧ (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])

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 203:
⊦ is_fskey(sk) ∧ sk ≠ _length ∧ sk ≠ _type → (r -- sk ∈ addarray(r, ty, i, st) ↔ r -- sk ∈ st)
Proof step 204:
⊦ is_fskey(sk) ∧ sk ≠ _type ∧ sk ≠ _length → (addarray(r, ty, i, st)[r0 -- sk]) = st[r0 -- sk]
Proof step 211:
is_fskey(sk), 0 ≤ n→i(# vals) + i, 0 ≤ j, 0 ≤ i, i ≤ j, j ≤ n→i(# vals) + i ⊦ sk = _type, sk = _length, (r -- sk ∈ putArray(vals, r, i, addarray(r, ty, j, st)) → r -- sk ∈ st) ∧ st[r -- sk] = (addarray(r, ty, mklist(initial_value(ty), i→n(i)) + vals, st)[r -- sk])

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ is_fskey(sk) → (putArray(vals, r, i, st) [r0 -- sk ] ) = st[r0 -- sk]], [CSIMPSEQ : ⊦ rk ∈ putArray(vals, r, i, st) ↔ rk ∈ st ∨ rk .ref = r ∧ is_indexkey(rk .key) ∧ i ≤ rk .key .index ∧ rk .key .index < i + n→i(# vals)])]]