[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 13 from proof copy-same-01-01 (previous step)

r2 ∈ st0, 0 < i3, 0 ≤ i, 0 ≤ i2, exactarray(r2, int_type, st0), i < i3, i2 + i3 ≤ st0[r2 -- _length] .intval ⊦ r2 = jvmref, r1 = r2, (r2 -- sk ∈ arraycopy(r1, i1, r2, i2, i3, st0[r2 -- (i2 + i) ', val]) ↔ r2 -- sk ∈ arraycopy(r1, i1, r2, i2, i3, st0)) ∧ (arraycopy(r1, i1, r2, i2, i3, st0[r2 -- (i2 + i) ', val])[r2 -- sk]) = (arraycopy(r1, i1, r2, i2, i3, st0)[r2 -- sk])

User applied rule structural induction

And obtained the following new goals

Proof step 12:
r2 ∈ st0, 0 < i3, 0 ≤ i, 0 ≤ i2, exactarray(r2, int_type, st0), i < i3, i2 + i3 ≤ st0[r2 -- _length] .intval ⊦ r2 = jvmref, r1 = r2, (r2 -- i0 ' ∈ arraycopy(r1, i1, r2, i2, i3, st0[r2 -- (i2 + i) ', val]) ↔ r2 -- i0 ' ∈ arraycopy(r1, i1, r2, i2, i3, st0)) ∧ (arraycopy(r1, i1, r2, i2, i3, st0[r2 -- (i2 + i) ', val])[r2 -- i0 ']) = (arraycopy(r1, i1, r2, i2, i3, st0)[r2 -- i0 '])

Rule argument

[VARWITHVARSEQSARG : sk, ()]

Additional information

[[CONCRETESIMPRULES : ([CSIMPGEN : storekey generated by ', ';], [CSIMPSEQ : ⊦ r -- fs ' ∈ arraycopy (r1, i1, r2, i2, j, st) ↔ r -- fs ' ∈ st], [CSIMPSEQ : ⊦ r -- fs ' ∈ st[r0 -- i ', val0] ↔ r -- fs ' ∈ st], [CSIMPSEQ : ⊦ (arraycopy(r1, i1, r2, i2, j, st) [r -- fs ' ] ) = st[r -- fs ']], [CSIMPSEQ : ⊦ (st[rk0, val][rk]) = ((rk = rk0 ⊃ val; st[rk]))], [CSIMPSEQ : ⊦ r -- sk = r0 -- sk0 ↔ ¬ ¬ (r = r0 ∧ sk = sk0)], [CSIMPSEQ : ⊦ fs ' ≠ i '])]]