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Proof step 29 from proof pathex-put-pathex-array-refval (previous step)

is_array(str, r0, st) ∧ st[r0 -- _type] .type ≤ mkarraytype(ty), st[r0 -- _type] .type = mkarraytype(ty), st[r0 -- i0 '] = refval(r), validrefs(str, r ' + refs, ty, st), 0 ≤ i0, 0 ≤ i, 0 < st[r0 -- _length] .intval, validref(str, r2, ty, st), i < st[r0 -- _length] .intval, is_array(str, r0, st), is_array(str, r0, st[r0 -- i ', refval(r2)]), i0 < st[r0 -- _length] .intval, r2 = jvmref → is_reftype(ty) ⊦ r0 = r, r0 = (r ' + refs) .last, r0 = jvmref, i0 = i, r ∈ refs, dups(refs), r0 ∈ refs, path∃(str, r2, (r ' + refs) .last, st), r ' + refs = [] ∨ (∃ i. 0 ≤ i ∧ i < st[r0 -- _length] .intval ∧ is_referencevalue(st[r0 -- i ']) ∧ (r ' + refs) .first = st[r0 -- i '] .refval ∧ validrefs(str, r ' + refs, st[r0 -- _type] .type .type, st))

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 28:
st[r0 -- i0 '] = refval(r), st[r0 -- _type] .type = mkarraytype(ty), i0 < st[r0 -- _length] .intval, is_array(str, r0, st[r0 -- i ', refval(r2)]), is_array(str, r0, st), i < st[r0 -- _length] .intval, validref(str, r2, ty, st), 0 < st[r0 -- _length] .intval, 0 ≤ i, 0 ≤ i0, validrefs(str, r ' + refs, ty, st), r2 = jvmref → is_reftype(ty) ⊦ i0 = i, r0 = jvmref, r0 = (r ' + refs) .last, r0 = r, path∃(str, r2, (r ' + refs) .last, st), r0 ∈ refs, dups(refs), r ∈ refs, ∃ i1. ¬ i1 < 0 ∧ ¬ st[r0 -- _length] .intval ≤ i1 ∧ is_referencevalue(st[r0 -- i1 ']) ∧ r = st[r0 -- i1 '] .refval

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPNAMEDSEQ : javatype, , test-09, ⊦ is_arraytype(mkarraytype(ty))], [CSIMPNAMEDSEQ : typefuns, , ref, ⊦ ty ≤ ty], [CSIMPNAMEDSEQ : javatype, , sel-01, ⊦ mkarraytype(ty) .type = ty], [CSIMPNAMEDSEQ : list, references, c-08, ⊦ (r ' + refs) .first = r], [CSIMPNAMEDSEQ : int-abs, , lels, ⊦ ¬ i < j ↔ j ≤ i], [CSIMPNAMEDSEQ : int-abs, , lels-01, ⊦ ¬ i ≤ j ↔ j < i], [CSIMPNAMEDSEQ : typefuns, , array, ⊦ ty0 ≤ mkarraytype(ty) ↔ is_arraytype(ty0) ∧ ty0 .type ≤ ty], [CSIMPNAMEDSEQ : list, references, a, ⊦ (refs + refs0) + refs1 = refs + refs0 + refs1], [CSIMPNAMEDSEQ : list, references, e-01, ⊦ r ' + refs ≠ []])]]