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Proof step 146 from proof hasSharing-put-index-refval (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 145:
(st[r -- i ', refval(r2)][r2 -- sks3]) = refval(r1), st[r -- _type] .type = mkarraytype(ty), (st[r -- i ', refval(r2)][r2 -- (sks + i ' ' + sks0)]) = refval(r1), st[r2 -- sks] = refval(r), (st[r -- i ', refval(r2)][r2 -- sks]) = refval(r0), i < st[r -- _length] .intval, 0 ≤ i, fits(r2, sks3, st[r -- i ', refval(r2)]), disjoint(str, r ' + r2 ', st), validref(str, r2, ty, st), 0 < st[r -- _length] .intval, is_referencevalue(st[r -- i ', refval(r2)][r -- (i ' ' + sks + i ' ' + sks0)]), fits(r2, sks, st), is_referencevalue(st[r -- i ', refval(r2)][r0 -- i ']), fits((st[r -- i ', refval(r2)][r0 -- i ']) .refval, sks0, st[r -- i ', refval(r2)]), is_arraytype(st[r0 -- _type] .type) → i < st[r0 -- _length] .intval ⊦ r = jvmref, r = r2, r1 = jvmref, r2 = jvmref, sks3 = [], sks + i ' ' + sks0 = sks3, r0 = jvmref, junkref(str, r, st), hasSharing(r2, st), hasSharing(r, st), is_classtype(st[r0 -- _type] .type), ∃ sks2. ¬ (sks2 + i ' ' ⊑ sks → st[r2 -- sks2] .refval ≠ r), ∃ sks1, sks4. sks = sks1 + i ' ' + sks4 ∧ st[r2 -- sks1] .refval = r ∧ (∀ sks2. sks2 + i ' ' ⊑ sks1 → st[r2 -- sks2] .refval ≠ st[r2 -- sks1] .refval)

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 ≠ []])]]