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Proof step 185 from proof hasSharing-put-index-refval (previous step)

is_referencevalue(st[r -- i ', refval(r2)][r0 -- (i ' ' + sks0)]) ∧ i ' ' + sks0 ≠ [], st[r -- _type] .type = mkarraytype(ty), st[r2 -- sks1] = refval(r1), st[r2 -- sks] = refval(r), (st[r -- i ', refval(r2)][r2 -- sks]) = refval(r0), (st[r -- i ', refval(r2)][r0 -- i ']) = refval(r3), (st[r -- i ', refval(r2)][(st[r -- i ', refval(r2)][r0 -- (i ' ' + sks0) .first]) .refval -- (i ' ' + sks0) .rest]) = refval(r1), disjoint(str, r ' + r2 ', st), validref(str, r2, ty, st), 0 < st[r -- _length] .intval, is_referencevalue(st[r -- i ', refval(r2)][r -- (i ' ' + sks1)]), fits(r2, sks1, st), i < st[r -- _length] .intval, 0 ≤ i, fits(r2, sks, st), fits(r3, sks0, st[r -- i ', refval(r2)]), is_arraytype(st[r0 -- _type] .type) → i < st[r0 -- _length] .intval ⊦ sks = [], r = jvmref, r = r2, r1 = jvmref, r2 = jvmref, sks1 = sks + i ' ' + sks0, r0 = jvmref, junkref(str, r, st), hasSharing(r2, st), hasSharing(r, st), is_classtype(st[r0 -- _type] .type), ∃ sks2, sks0. sks1 = sks2 + i ' ' + sks0 ∧ st[r2 -- sks2] .refval = r ∧ (∀ sks3. sks3 + i ' ' ⊑ sks2 → st[r2 -- sks3] .refval ≠ st[r2 -- sks2] .refval), ∃ sks2. ¬ (sks2 + i ' ' ⊑ sks → st[r2 -- sks2] .refval ≠ r), ∃ sks3, sks4. sks = sks3 + i ' ' + sks4 ∧ st[r2 -- sks3] .refval = r ∧ (∀ sks2. sks2 + i ' ' ⊑ sks3 → st[r2 -- sks2] .refval ≠ st[r2 -- sks3] .refval)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 184:
(st[r -- i ', refval(r2)][r0 -- i ']) = refval(r3), (st[r -- i ', refval(r2)][r2 -- sks]) = refval(r0), st[r2 -- sks] = refval(r), st[r2 -- sks1] = refval(r1), st[r -- _type] .type = mkarraytype(ty), (st[r -- i ', refval(r2)][r3 -- sks0]) = refval(r1), fits(r3, sks0, st[r -- i ', refval(r2)]), fits(r2, sks, st), 0 ≤ i, i < st[r -- _length] .intval, fits(r2, sks1, st), is_referencevalue(st[r -- i ', refval(r2)][r -- (i ' ' + sks1)]), 0 < st[r -- _length] .intval, validref(str, r2, ty, st), disjoint(str, r ' + r2 ', st), is_referencevalue(st[r -- i ', refval(r2)][r0 -- (i ' ' + sks0)]), is_arraytype(st[r0 -- _type] .type) → i < st[r0 -- _length] .intval ⊦ r0 = jvmref, sks1 = sks + i ' ' + sks0, r2 = jvmref, r1 = jvmref, r = r2, r = jvmref, sks = [], is_classtype(st[r0 -- _type] .type), hasSharing(r, st), hasSharing(r2, st), junkref(str, r, st), ∃ sks3, sks4. sks = sks3 + i ' ' + sks4 ∧ st[r2 -- sks3] .refval = r ∧ (∀ sks2. sks2 + i ' ' ⊑ sks3 → st[r2 -- sks2] .refval ≠ st[r2 -- sks3] .refval), ∃ sks2. ¬ (sks2 + i ' ' ⊑ sks → st[r2 -- sks2] .refval ≠ r), ∃ sks2, sks0. sks1 = sks2 + i ' ' + sks0 ∧ st[r2 -- sks2] .refval = r ∧ (∀ sks3. sks3 + i ' ' ⊑ sks2 → st[r2 -- sks3] .refval ≠ st[r2 -- sks2] .refval)

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPNAMEDSEQ : javavalue, , sel-09, ⊦ refval(r) .refval = r], [CSIMPNAMEDSEQ : list, storekeys, e-01, ⊦ sk ' + sks ≠ []], [CSIMPNAMEDSEQ : list, storekeys, c-07, ⊦ (sk ' + sks) .rest = sks], [CSIMPNAMEDSEQ : list, storekeys, a, ⊦ (sks + sks0) + sks1 = sks + sks0 + sks1], [CSIMPNAMEDSEQ : list, storekeys, c-08, ⊦ (sk ' + sks) .first = sk])]]