[Imprint][Data Privacy Statement][E-Mail]

View long theorem info. View the proof. Back to main index. View the specification. View theorem base summary, View theorem base listing, the used properties by spec, the dependency list, the symbol table,

Proof step 531 from proof hasSharing-put-index-refval (previous step)

(st[r0 -- i ', refval(r4)][r4 -- (sks2 + i ' ' + sks)]) = refval(r1), st[r0 -- _type] .type = mkarraytype(ty), st[r -- sks0] = refval(r1), st[r -- sks1] = refval(r0), st[r4 -- sks2] = refval(r0), 0 < st[r0 -- _length] .intval, fits(r4, sks2 + i ' ' + sks, st), fits(r, sks1, st), disjoint(str, r ' + r4 ', st), validref(str, r4, ty, st), fits(r, sks0, st), is_referencevalue(st[r0 -- i ', refval(r4)][r0 -- (i ' ' + sks2 + i ' ' + sks)]), 0 ≤ i, i < st[r0 -- _length] .intval, ∀ sks3. sks3 + i ' ' ⊑ sks2 → st[r4 -- sks3] .refval ≠ r0 ⊦ r4 = jvmref, sks0 = sks1 + i ' ' + sks2 + i ' ' + sks, sks1 = [], r0 = jvmref, r = r4, r1 = jvmref, sks0 = [], junkref(str, r, st), hasSharing(r4, st), hasSharing(r, st), ∃ sks3, sks4. sks2 + i ' ' + sks = sks3 + i ' ' + sks4 ∧ st[r4 -- sks3] .refval = r0 ∧ (∀ sks2. sks2 + i ' ' ⊑ sks3 → st[r4 -- sks2] .refval ≠ st[r4 -- sks3] .refval), ∃ sks, sks1. sks0 = sks + i ' ' + sks1 ∧ st[r -- sks] .refval = r0 ∧ (∀ sks4. sks4 + i ' ' ⊑ sks → st[r -- sks4] .refval ≠ st[r -- sks] .refval), ∃ sks, sks0. sks1 = sks + i ' ' + sks0 ∧ st[r -- sks] .refval = r0 ∧ (∀ sks4. sks4 + i ' ' ⊑ sks → st[r -- sks4] .refval ≠ st[r -- sks] .refval), ∃ sks. ¬ (sks + i ' ' ⊑ sks1 → st[r -- sks] .refval ≠ r0)

User applied rule exists right

And obtained the following new goals

Proof step 530:
(st[r0 -- i ', refval(r4)][r4 -- (sks2 + i ' ' + sks)]) = refval(r1), st[r0 -- _type] .type = mkarraytype(ty), st[r -- sks0] = refval(r1), st[r -- sks1] = refval(r0), st[r4 -- sks2] = refval(r0), 0 < st[r0 -- _length] .intval, fits(r4, sks2 + i ' ' + sks, st), fits(r, sks1, st), disjoint(str, r ' + r4 ', st), validref(str, r4, ty, st), fits(r, sks0, st), is_referencevalue(st[r0 -- i ', refval(r4)][r0 -- (i ' ' + sks2 + i ' ' + sks)]), 0 ≤ i, i < st[r0 -- _length] .intval, ∀ sks3. sks3 + i ' ' ⊑ sks2 → st[r4 -- sks3] .refval ≠ r0 ⊦ r4 = jvmref, sks0 = sks1 + i ' ' + sks2 + i ' ' + sks, sks1 = [], r0 = jvmref, r = r4, r1 = jvmref, sks0 = [], junkref(str, r, st), hasSharing(r4, st), hasSharing(r, st), sks2 + i ' ' + sks = sks2 + i ' ' + sks ∧ st[r4 -- sks2] .refval = r0 ∧ (∀ sks. sks + i ' ' ⊑ sks2 → st[r4 -- sks] .refval ≠ st[r4 -- sks2] .refval), ∃ sks, sks1. sks0 = sks + i ' ' + sks1 ∧ st[r -- sks] .refval = r0 ∧ (∀ sks4. sks4 + i ' ' ⊑ sks → st[r -- sks4] .refval ≠ st[r -- sks] .refval), ∃ sks, sks0. sks1 = sks + i ' ' + sks0 ∧ st[r -- sks] .refval = r0 ∧ (∀ sks4. sks4 + i ' ' ⊑ sks → st[r -- sks4] .refval ≠ st[r -- sks] .refval), ∃ sks. ¬ (sks + i ' ' ⊑ sks1 → st[r -- sks] .refval ≠ r0)

Rule argument

[EXRARG : pos: right 11, [extquanttermlist: (sks2, sks) abort:F , discard:T , computed:T ]]

Additional information

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