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Proof step 312 from proof hasSharing-put-index-refval (previous step)

¬ (sks1 ≠ [] ∧ i ' ' + sks3 ≠ []), (st[r0 -- i ', refval(r2)][r -- sks1]) = refval(r3), st[r -- sks1] = refval(r0), (st[r0 -- i ', refval(r2)][r -- (sks1 + i ' ' + sks3)]) = refval(r1), st[r0 -- _type] .type = mkarraytype(ty), (st[r0 -- i ', refval(r2)][r -- sks0]) = refval(r1), (st[r0 -- i ', refval(r2)][r3 -- i ']) = refval(r4), fits(r4, sks3, st[r0 -- i ', refval(r2)]), fits(r, sks1, st), disjoint(str, r ' + r2 ', st), validref(str, r2, ty, st), fits(r, sks0, st[r0 -- i ', refval(r2)]), is_arraytype(st[r3 -- _type] .type) → 0 ≤ i ∧ i < st[r3 -- _length] .intval, r2 = jvmref → is_reftype(ty) ⊦ r3 = jvmref, r0 = jvmref, r = r2, r1 = jvmref, sks0 = [], sks0 = sks1 + i ' ' + sks3, is_classtype(st[r3 -- _type] .type), junkref(str, r, st), hasSharing(r2, st), hasSharing(r, st), ∃ sks, sks2. sks1 = sks + i ' ' + sks2 ∧ st[r -- sks] .refval = r0 ∧ (∀ sks4. sks4 + i ' ' ⊑ sks → st[r -- sks4] .refval ≠ st[r -- sks] .refval), ∃ sks2. ¬ (sks2 + i ' ' ⊑ sks1 → st[r -- sks2] .refval ≠ r0)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 12:
⊦ fits(r, [], st)
Proof step 311:
(st[r0 -- i ', refval(r4)][r0 -- sks0]) = refval(r1), st[r0 -- _type] .type = mkarraytype(ty), (st[r0 -- i ', refval(r4)][r0 -- (i ' ' + sks3)]) = refval(r1), 0 < st[r0 -- _length] .intval, 0 ≤ i, i < st[r0 -- _length] .intval, fits(r0, sks0, st[r0 -- i ', refval(r4)]), validref(str, r4, ty, st), disjoint(str, r0 ' + r4 ', st), fits(r4, sks3, st[r0 -- i ', refval(r4)]), r4 = jvmref → is_reftype(ty) ⊦ sks0 = [], r1 = jvmref, r0 = r4, r0 = jvmref, sks0 = i ' ' + sks3, hasSharing(r0, st), hasSharing(r4, st), junkref(str, r0, st)

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPNAMEDSEQ : javatype, , test-09, ⊦ is_arraytype(mkarraytype(ty))], [CSIMPNAMEDFORWARD : int-abs, , forward-le-01, ⊦ i ≤ j ∧ 0 ≤ i → 0 ≤ j], [CSIMPNAMEDFORWARD : int-abs, , forward-le-05, ⊦ i < j ∧ 0 ≤ i → 0 < j], [CSIMPNAMEDSEQ : javatype, , diff-01, ⊦ is_arraytype(ty) → ¬ is_classtype(ty)], [CSIMPNAMEDSEQ : junkrefs, , junkref-bad-type, ⊦ ¬ is_classtype (st[r -- _type] .type) ∧ ¬ is_arraytype (st[r -- _type] .type) → ( junkref(str, r, st) ↔ r ≠ jvmref)], [CSIMPNAMEDSEQ : store, javastore, At-same, ⊦ (st[rk, val][rk]) = val], [CSIMPNAMEDSEQ : list, storekeys, e-03, ⊦ sks + sk ' + sks0 ≠ []], [CSIMPNAMEDSEQ : list, storekeys, e-02, ⊦ sks + sk ' ≠ []], [CSIMPNAMEDSEQ : list-last, storekeys, eq-01-01, ⊦ sks ⊑ [] ↔ sks = []], [CSIMPNAMEDSEQ : javavalue, , inj-03, ⊦ refval(r) = refval(r0) ↔ r = r0], [CSIMPNAMEDSEQ : storefuns, , lookup-empty, ⊦ st[r -- []] = refval(r)], [CSIMPNAMEDSEQ : list, storekeys, Nil, ⊦ [] + sks = sks], [CSIMPNAMEDSEQ : list, storekeys, a, ⊦ (sks + sks0) + sks1 = sks + sks0 + sks1], [CSIMPNAMEDSEQ : list, storekeys, e, ⊦ sk ' ≠ []], [CSIMPNAMEDSEQ : list, storekeys, app-02-ant, ⊦ ¬ sks + sks0 ≠ [] ↔ sks = [] ∧ sks0 = []])]]