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Proof step 72 from proof pathex-put-pathex-array-refval (previous step)

¬ (validrefs(str, r3 ' + refs2, ty, st) ∧ (r3 ' + refs2) .last ∈ refs2), list2set(refs1) ∩ list2set(refs2) = ∅, refs1 + r0 ' = r1 ' + refs0, st[r0 -- _type] .type = mkarraytype(ty), st[r0 -- i0 '] = refval(r3), is_array(str, r0, st), validrefs(str, r3 ' + refs2, ty, st), i0 < st[r0 -- _length] .intval, validrefs(str, r ' + refs1 + r0 ' + r3 ' + refs2, st[r -- _type] .type, st[r0 -- i ', refval(r2)]), path∃(str, r, r0, st), i < st[r0 -- _length] .intval, validref(str, r2, ty, st), 0 < st[r0 -- _length] .intval, 0 ≤ i, validrefs(str, refs1 + r0 ' + r3 ' + refs2, st[r1 -- _type] .type, st[r0 -- i ', refval(r2)]), is_array(str, r0, st[r0 -- i ', refval(r2)]), 0 ≤ i0, is_valid_ref(str, r3, st), st[r3 -- _type] .type ≤ ty, r2 = jvmref → is_reftype(ty) ⊦ r = r3, r0 = r3, r = (r3 ' + refs2) .last, r0 = jvmref, r = r0, i0 = i, r0 = (r3 ' + refs2) .last, r3 = jvmref, path∃(str, r, (r3 ' + refs2) .last, st), path∃(str, r2, (r3 ' + refs2) .last, st), r ∈ refs1, r ∈ refs2, r0 ∈ refs2, r0 ∈ refs1, r3 ∈ refs2, dups(refs2), dups(refs1), r3 ∈ refs1, path∃(str, r3, (r3 ' + refs2) .last, st), ¬ r1 ∈ refs1 ∧ r1 ≠ r0, r0 ≠ r1 ∧ ¬ r0 ∈ refs0

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 71:
list2set(refs1) ∩ list2set(refs2) = ∅, refs1 + r0 ' = r1 ' + refs0, st[r0 -- _type] .type = mkarraytype(ty), st[r0 -- i0 '] = refval(r3), is_array(str, r0, st), validrefs(str, r3 ' + refs2, ty, st), i0 < st[r0 -- _length] .intval, validrefs(str, r ' + refs1 + r0 ' + r3 ' + refs2, st[r -- _type] .type, st[r0 -- i ', refval(r2)]), path∃(str, r, r0, st), i < st[r0 -- _length] .intval, validref(str, r2, ty, st), 0 < st[r0 -- _length] .intval, 0 ≤ i, validrefs(str, refs1 + r0 ' + r3 ' + refs2, st[r1 -- _type] .type, st[r0 -- i ', refval(r2)]), is_array(str, r0, st[r0 -- i ', refval(r2)]), 0 ≤ i0, is_valid_ref(str, r3, st), st[r3 -- _type] .type ≤ ty, r2 = jvmref → is_reftype(ty) ⊦ r = r3, r0 = r3, r = (r3 ' + refs2) .last, r0 = jvmref, r = r0, i0 = i, r0 = (r3 ' + refs2) .last, r3 = jvmref, path∃(str, r, (r3 ' + refs2) .last, st), path∃(str, r2, (r3 ' + refs2) .last, st), r ∈ refs1, r ∈ refs2, r0 ∈ refs2, r0 ∈ refs1, r3 ∈ refs2, dups(refs2), dups(refs1), r3 ∈ refs1, path∃(str, r3, (r3 ' + refs2) .last, st), (r3 ' + refs2) .last ∈ refs2, ¬ r1 ∈ refs1 ∧ r1 ≠ r0, r0 ≠ r1 ∧ ¬ r0 ∈ refs0

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ()]]