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Proof step 290 from proof hasSharing-put-index-refval (previous step)

(st[r -- i ', refval(r4)][r4 -- (sks1 + i ' ' + sks)]) = refval(r1), st[r -- _type] .type = mkarraytype(ty), st[r -- sks0] = refval(r1), st[r4 -- sks1] = refval(r), 0 < st[r -- _length] .intval, fits(r4, sks1 + i ' ' + sks, st), disjoint(str, r ' + r4 ', st), validref(str, r4, ty, st), fits(r, sks0, st), i < st[r -- _length] .intval, 0 ≤ i, ∀ sks2. sks2 + i ' ' ⊑ sks1 → st[r4 -- sks2] .refval ≠ r ⊦ sks0 = i ' ' + sks1 + i ' ' + sks, r = jvmref, r = r4, r1 = jvmref, sks0 = [], r4 = jvmref, junkref(str, r, st), hasSharing(r4, st), hasSharing(r, st), sks1 + i ' ' + sks = sks1 + i ' ' + sks ∧ st[r4 -- sks1] .refval = r ∧ (∀ sks. sks + i ' ' ⊑ sks1 → st[r4 -- sks] .refval ≠ st[r4 -- sks1] .refval), ∃ sks, sks2. sks0 = sks + i ' ' + sks2 ∧ st[r -- sks] .refval = r ∧ (∀ sks2. sks2 + i ' ' ⊑ sks → st[r -- sks2] .refval ≠ r)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 289:
(st[st[r4 -- sks2] .refval -- i ', refval(r4)][r4 -- (sks1 + i ' ' + sks)]) = refval(r1), st[st[r4 -- sks2] .refval -- _type] .type = mkarraytype(ty), st[st[r4 -- sks2] .refval -- sks0] = refval(r1), st[r4 -- sks1] = refval(st[r4 -- sks2] .refval), sks2 + i ' ' ⊑ sks1, fits(r4, sks1 + i ' ' + sks, st), disjoint(str, st[r4 -- sks2] .refval ' + r4 ', st), validref(str, r4, ty, st), fits(st[r4 -- sks2] .refval, sks0, st), i < st[st[r4 -- sks2] .refval -- _length] .intval, 0 ≤ i, 0 < st[st[r4 -- sks2] .refval -- _length] .intval, ∀ sks. sks + i ' ' ⊑ sks1 → st[r4 -- sks] .refval ≠ st[r4 -- sks2] .refval ⊦ sks0 = i ' ' + sks1 + i ' ' + sks, st[r4 -- sks2] .refval = jvmref, st[r4 -- sks2] .refval = r4, r1 = jvmref, sks0 = [], r4 = jvmref, junkref(str, st[r4 -- sks2] .refval, st), hasSharing(r4, st), hasSharing(st[r4 -- sks2] .refval, st), ∃ sks, sks1. sks0 = sks + i ' ' + sks1 ∧ st[st[r4 -- sks2] .refval -- sks] .refval = st[r4 -- sks2] .refval ∧ (∀ sks1. sks1 + i ' ' ⊑ sks → st[st[r4 -- sks2] .refval -- sks1] .refval ≠ st[r4 -- sks2] .refval)

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPNAMEDFORWARD : int-abs, , forward-lels, ⊦ i ≤ j ∧ j < j0 → i < j0], [CSIMPNAMEDSEQ : javavalue, , sel-09, ⊦ refval(r) .refval = r], [CSIMPNAMEDSEQ : list, storekeys, a, ⊦ (sks + sks0) + sks1 = sks + sks0 + sks1])]]