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Proof step 668 from proof hasSharing-put-index-refval (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 667:
(st[st[r2 -- sks2] .refval -- i ', refval(r2)][r2 -- (sks1 + i ' ' + sks0)]) = refval(r1), st[st[r2 -- sks2] .refval -- _type] .type = mkarraytype(ty), st[st[r2 -- sks2] .refval -- sks] = refval(r1), st[r2 -- sks1] = refval(st[r2 -- sks2] .refval), sks2 + i ' ' ⊑ sks1, fits(r2, sks1 + i ' ' + sks0, st), 0 ≤ i, i < st[st[r2 -- sks2] .refval -- _length] .intval, validref(str, r2, ty, st), disjoint(str, st[r2 -- sks2] .refval ' + r2 ', st), fits(st[r2 -- sks2] .refval, sks, st), 0 < st[st[r2 -- sks2] .refval -- _length] .intval, ∀ sks. sks + i ' ' ⊑ sks1 → st[r2 -- sks] .refval ≠ st[r2 -- sks2] .refval ⊦ i ' ' + sks1 + i ' ' + sks0 = sks, r2 = jvmref, sks = [], r1 = jvmref, st[r2 -- sks2] .refval = r2, st[r2 -- sks2] .refval = jvmref, hasSharing(st[r2 -- sks2] .refval, st), hasSharing(r2, st), junkref(str, st[r2 -- sks2] .refval, st), ∃ sks0, sks3. sks = sks0 + i ' ' + sks3 ∧ st[st[r2 -- sks2] .refval -- sks0] .refval = st[r2 -- sks2] .refval ∧ (∀ sks1. sks1 + i ' ' ⊑ sks0 → st[st[r2 -- sks2] .refval -- sks1] .refval ≠ st[st[r2 -- sks2] .refval -- sks0] .refval)

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPNAMEDFORWARD : int-abs, , forward-le-05, ⊦ i < j ∧ 0 ≤ i → 0 < j], [CSIMPNAMEDSEQ : javavalue, , sel-09, ⊦ refval(r) .refval = r], [CSIMPNAMEDSEQ : list, storekeys, a, ⊦ (sks + sks0) + sks1 = sks + sks0 + sks1])]]