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Proof step 4 from proof hassharing-bytearray (previous step)

sk ' + sks1 ≠ [], st[r -- sks0] = refval(r0), st[r -- (sk ' + sks1)] = refval(r0), fits(r, sks0, st), okbytearray(r, st), r ≠ jvmref ∧ is_referencevalue(st[r -- (sk ' + sks1) .first]) ∧ (is_classtype(st[r -- _type] .type) → (sk ' + sks1) .first ∈ instfields(st[r -- _type] .type .class)) ∧ ( is_arraytype(st[r -- _type] .type) → is_indexkey((sk ' + sks1) .first) ∧ 0 ≤ (sk ' + sks1) .first .index ∧ (sk ' + sks1) .first .index < st[r -- _length] .intval) ∧ fits(st[r -- (sk ' + sks1) .first] .refval, (sk ' + sks1) .rest, st), ∀ st, r, sks0, r0. st[r -- sks0] = refval(r0) ∧ st[r -- sks1] = refval(r0) ∧ okbytearray(r, st) ∧ fits(r, sks1, st) ∧ fits(r, sks0, st) → sks0 = sks1 ∨ sks0 = [] ∨ sks1 = [] ∨ r0 = jvmref ⊦ sks0 = [], r0 = jvmref, sks0 = sk ' + sks1

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 3:
st[r -- sks0] = refval(r0), st[r -- (sk ' + sks1)] = refval(r0), fits(r, sks0, st), okbytearray(r, st), is_referencevalue(st[r -- sk]), fits(st[r -- sk] .refval, sks1, st), is_indexkey(sk), sk .index < st[r -- _length] .intval, 0 ≤ sk .index, 0 < st[r -- _length] .intval, ∀ st, r, sks0, r0. st[r -- sks0] = refval(r0) ∧ st[r -- sks1] = refval(r0) ∧ okbytearray(r, st) ∧ fits(r, sks1, st) ∧ fits(r, sks0, st) → sks0 = sks1 ∨ sks0 = [] ∨ sks1 = [] ∨ r0 = jvmref ⊦ sks0 = [], r0 = jvmref, sks0 = sk ' + sks1, r = jvmref

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([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, , test-09, ⊦ is_arraytype(mkarraytype(ty))], [CSIMPNAMEDSEQ : javatype, , test-16, ⊦ ¬ is_classtype (mkarraytype(ty))], [CSIMPNAMEDSEQ : javavalue, , sel-11, ⊦ typeval(ty) .type = ty], [CSIMPNAMEDSEQ : okfuns, , okbytearray-type, ⊦ okbytearray(r, st) → st[r -- _type] = typeval (mkarraytype(byte_type))], [CSIMPNAMEDSEQ : list, storekeys, c-07, ⊦ (sk ' + sks) .rest = sks], [CSIMPNAMEDSEQ : list, storekeys, c-08, ⊦ (sk ' + sks) .first = sk], [CSIMPNAMEDSEQ : list, storekeys, a, ⊦ (sks + sks0) + sks1 = sks + sks0 + sks1], [CSIMPNAMEDSEQ : list, storekeys, e-01, ⊦ sk ' + sks ≠ []])]]