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Proof step 578 from proof hasSharing-put-index-refval (previous step)

(st[r0 -- i ', refval(r2)][r -- (sks2 + i ' ' + sks1)]) = refval(r1), st[r0 -- _type] .type = mkarraytype(ty), (st[r0 -- i ', refval(r2)][r -- sks0]) = refval(r1), st[r -- sks2] = refval(r0), fits(r, sks2 + i ' ' + sks1, st), disjoint(str, r ' + r2 ', st), validref(str, r2, ty, st), fits(r, sks0, st[r0 -- i ', refval(r2)]), ∀ sks. sks + i ' ' ⊑ sks2 → st[r -- sks] .refval ≠ r0, r2 = jvmref → is_reftype(ty) ⊦ sks0 = sks2 + i ' ' + sks1, r0 = jvmref, r = r2, r1 = jvmref, sks0 = [], junkref(str, r, st), hasSharing(r2, st), hasSharing(r, st), ∃ sks, sks3. sks2 + i ' ' + sks1 = sks + i ' ' + sks3 ∧ st[r -- sks] .refval = r0 ∧ (∀ sks2. sks2 + i ' ' ⊑ sks → st[r -- sks2] .refval ≠ st[r -- sks] .refval)

User applied rule exists right

And obtained the following new goals

Proof step 577:
(st[r0 -- i ', refval(r2)][r -- (sks2 + i ' ' + sks1)]) = refval(r1), st[r0 -- _type] .type = mkarraytype(ty), (st[r0 -- i ', refval(r2)][r -- sks0]) = refval(r1), st[r -- sks2] = refval(r0), fits(r, sks2 + i ' ' + sks1, st), disjoint(str, r ' + r2 ', st), validref(str, r2, ty, st), fits(r, sks0, st[r0 -- i ', refval(r2)]), ∀ sks. sks + i ' ' ⊑ sks2 → st[r -- sks] .refval ≠ r0, r2 = jvmref → is_reftype(ty) ⊦ sks0 = sks2 + i ' ' + sks1, r0 = jvmref, r = r2, r1 = jvmref, sks0 = [], junkref(str, r, st), hasSharing(r2, st), hasSharing(r, st), sks2 + i ' ' + sks1 = sks2 + i ' ' + sks1 ∧ st[r -- sks2] .refval = r0 ∧ (∀ sks0. sks0 + i ' ' ⊑ sks2 → st[r -- sks0] .refval ≠ st[r -- sks2] .refval)

Rule argument

[EXRARG : pos: right 9, [extquanttermlist: (sks2, sks1) abort:F , discard:T , computed:T ]]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (sks2, sks1)]]