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Proof step 81 from proof hasSharing-put-index-refval (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 80:
st[r0 -- _type] .type = mkarraytype(ty), (st[r0 -- i ', refval(r1)][r0 -- (sks + i ' ' + sks1)]) = refval(r1), st[r0 -- sks] = refval(r0), (st[r0 -- i ', refval(r1)][r0 -- sks]) = refval(r), i < st[r0 -- _length] .intval, 0 ≤ i, 0 < st[r0 -- _length] .intval, disjoint(str, r0 ' + r1 ', st), validref(str, r1, ty, st), fits(r0, sks, st[r0 -- i ', refval(r1)]), is_referencevalue(st[r0 -- i ', refval(r1)][r -- i ']), fits((st[r0 -- i ', refval(r1)][r -- i ']) .refval, sks1, st[r0 -- i ', refval(r1)]), is_arraytype(st[r -- _type] .type) → i < st[r -- _length] .intval ⊦ sks + i ' ' + sks1 = i ' ', r0 = jvmref, r0 = r1, r1 = jvmref, r = jvmref, junkref(str, r0, st), hasSharing(r1, st), hasSharing(r0, st), is_classtype(st[r -- _type] .type), ∃ sks2. ¬ (sks2 + i ' ' ⊑ sks → st[r0 -- sks2] .refval ≠ r0)

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPNAMEDSEQ : javastore, , length-at, ⊦ (st[r -- i ', val] [r0 -- _length ] ) = st[r0 -- _length]], [CSIMPNAMEDSEQ : int-abs, , zero-gels-04, ⊦ i ≤ 0 ∧ 0 ≤ j → i ≤ j], [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 : list, storekeys, c-07, ⊦ (sk ' + sks) .rest = sks], [CSIMPNAMEDSEQ : list, storekeys, c-08, ⊦ (sk ' + sks) .first = sk], [CSIMPNAMEDSEQ : list, storekeys, a, ⊦ (sks + sks0) + sks1 = sks + sks0 + sks1], [CSIMPNAMEDSEQ : list, storekeys, e-01, ⊦ sk ' + sks ≠ []])]]