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

0 ≤ n→i(# vals) + i, 0 ≤ j, 0 ≤ i, i ≤ j, j ≤ n→i(# vals) + i ⊦ (rk ∈ putArray(vals, r, i, addarray(r, ty, j, st)) ↔ rk = r -- _length ∨ rk ∈ addarray(r, ty, mklist(initial_value(ty), i→n(i)) + vals, st)) ∧ (putArray(vals, r, i, addarray(r, ty, j, st))[rk]) = (addarray(r, ty, mklist(initial_value(ty), i→n(i)) + vals, st)[r -- _length, intval(j)][rk])

Heuristic weak cut applied rule cut formula

And obtained the following new goals

Proof step 120:
⊦ r -- _length ∈ addarray(r, ty, i, st)
Proof step 121:
⊦ (addarray(r, ty, i, st)[r -- _length]) = intval(i)
Proof step 223:
0 ≤ n→i(# vals) + i, 0 ≤ j, 0 ≤ i, i ≤ j, j ≤ n→i(# vals) + i ⊦ rk = r -- _length, (rk ∈ putArray(vals, r, i, addarray(r, ty, j, st)) ↔ rk = r -- _length ∨ rk ∈ addarray(r, ty, mklist(initial_value(ty), i→n(i)) + vals, st)) ∧ (putArray(vals, r, i, addarray(r, ty, j, st))[rk]) = (addarray(r, ty, mklist(initial_value(ty), i→n(i)) + vals, st)[r -- _length, intval(j)][rk])

Rule argument

[fma-arg: rk = r -- _length]

Additional information

[[CONCRETESIMPRULES : ([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)], [CSIMPSEQ : ⊦ (putArray(vals, r, i, st) [r0 -- _length ] ) = st[r0 -- _length]], [CSIMPSEQ : ⊦ (st[rk, val][rk]) = val], [CSIMPSEQ : ⊦ intval(i) = intval(i0) ↔ i = i0])], [EXTRAFMAS : (rk = r -- _length)]]