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Proof step 778 from proof hasSharing-put-index-refval (previous step)

st[r -- sks1] = refval(r0), (st[r0 -- i ', refval(r2)][r -- (sks1 + i ' ' + sks2)]) = refval(r1), st[r0 -- _type] .type = mkarraytype(ty), st[r -- sks] = refval(r1), validref(str, r2, ty, st), disjoint(str, r ' + r2 ', st), fits(r, sks, st), fits(r, sks1, st), r0 ≠ jvmref ∧ is_referencevalue(st[r0 -- i ', refval(r2)][r0 -- i ']) ∧ (is_classtype((st[r0 -- i ', refval(r2)][r0 -- _type]) .type) → i ' ∈ instfields((st[r0 -- i ', refval(r2)][r0 -- _type]) .type .class)) ∧ ( is_arraytype((st[r0 -- i ', refval(r2)][r0 -- _type]) .type) → is_indexkey(i ') ∧ 0 ≤ i ' .index ∧ i ' .index < (st[r0 -- i ', refval(r2)][r0 -- _length]) .intval) ∧ fits((st[r0 -- i ', refval(r2)][r0 -- i ']) .refval, sks2, st[r0 -- i ', refval(r2)]), r2 = jvmref → is_reftype(ty) ⊦ sks1 + i ' ' + sks2 = sks, sks = [], r1 = jvmref, r = r2, r0 = jvmref, hasSharing(r, st), hasSharing(r2, st), junkref(str, r, st), ∃ sks0, sks3. sks = sks0 + i ' ' + sks3 ∧ st[r -- sks0] .refval = r0 ∧ (∀ sks2. sks2 + i ' ' ⊑ sks0 → st[r -- sks2] .refval ≠ st[r -- sks0] .refval), ∃ sks3. ¬ (sks3 + i ' ' ⊑ sks1 → st[r -- sks3] .refval ≠ r0), ∃ sks0, sks3. sks1 = sks0 + i ' ' + sks3 ∧ st[r -- sks0] .refval = r0 ∧ (∀ sks4. sks4 + i ' ' ⊑ sks0 → st[r -- sks4] .refval ≠ st[r -- sks0] .refval)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 777:
st[r -- sks] = refval(r1), st[r0 -- _type] .type = mkarraytype(ty), (st[r0 -- i ', refval(r2)][r -- (sks1 + i ' ' + sks2)]) = refval(r1), st[r -- sks1] = refval(r0), fits(r2, sks2, st[r0 -- i ', refval(r2)]), fits(r, sks1, st), fits(r, sks, st), disjoint(str, r ' + r2 ', st), validref(str, r2, ty, st), i < st[r0 -- _length] .intval, 0 ≤ i, 0 < st[r0 -- _length] .intval, r2 = jvmref → is_reftype(ty) ⊦ r0 = jvmref, r = r2, r1 = jvmref, sks = [], sks1 + i ' ' + sks2 = sks, junkref(str, r, st), hasSharing(r2, st), hasSharing(r, st), ∃ sks0, sks3. sks1 = sks0 + i ' ' + sks3 ∧ st[r -- sks0] .refval = r0 ∧ (∀ sks4. sks4 + i ' ' ⊑ sks0 → st[r -- sks4] .refval ≠ st[r -- sks0] .refval), ∃ sks3. ¬ (sks3 + i ' ' ⊑ sks1 → st[r -- sks3] .refval ≠ r0), ∃ sks0, sks3. sks = sks0 + i ' ' + sks3 ∧ st[r -- sks0] .refval = r0 ∧ (∀ sks2. sks2 + i ' ' ⊑ sks0 → st[r -- sks2] .refval ≠ st[r -- sks0] .refval)

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPNAMEDFORWARD : int-abs, , forward-le-01, ⊦ i ≤ j ∧ 0 ≤ i → 0 ≤ j], [CSIMPNAMEDFORWARD : int-abs, , forward-le-05, ⊦ i < j ∧ 0 ≤ i → 0 < j], [CSIMPNAMEDSEQ : javatype, , test-09, ⊦ is_arraytype(mkarraytype(ty))], [CSIMPNAMEDSEQ : javatype, , test-16, ⊦ ¬ is_classtype (mkarraytype(ty))], [CSIMPNAMEDSEQ : javastore, , length-at, ⊦ (st[r -- i ', val] [r0 -- _length ] ) = st[r0 -- _length]], [CSIMPNAMEDSEQ : storekey, , sel-06, ⊦ i ' .index = i], [CSIMPNAMEDSEQ : storekey, , test-08, ⊦ is_indexkey(i ')], [CSIMPNAMEDSEQ : addfuns, , instfields-index, ⊦ ¬ i ' ∈ instfields(class)], [CSIMPNAMEDSEQ : javastore, , type-at, ⊦ (st[r -- i ', val] [r0 -- _type ] ) = st[r0 -- _type]], [CSIMPNAMEDSEQ : javavalue, , sel-09, ⊦ refval(r) .refval = r], [CSIMPNAMEDSEQ : javavalue, , test-19, ⊦ is_referencevalue(refval(r))], [CSIMPNAMEDSEQ : store, javastore, At-same, ⊦ (st[rk, val][rk]) = val])]]