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Proof step 43 from proof pathex-put-pathex-array-refval (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 5:
⊦ path∃(str, r, r, st) ↔ r = jvmref ∨ r ≠ jvmref ∧ is_valid_ref(str, r, st)
Proof step 42:
st[r0 -- _type] .type = mkarraytype(ty), validrefs(str, r0 ' + refs0, mkarraytype(ty), st[r0 -- i ', refval(r2)]), 0 ≤ i, 0 < st[r0 -- _length] .intval, validref(str, r2, ty, st), i < st[r0 -- _length] .intval, is_array(str, r0, st), r2 = jvmref → is_reftype(ty) ⊦ r0 = jvmref, r0 = (r0 ' + refs0) .last, path∃(str, r2, (r0 ' + refs0) .last, st), path∃(str, r0, (r0 ' + refs0) .last, st), dups(refs0), r0 ∈ refs0

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPNAMEDSEQ : addfuns, , is_valid_ref-array, ⊦ st[r -- _type] .type = mkarraytype(ty) ∧ r ≠ jvmref → ( is_valid_ref(str, r, st) ↔ is_array(str, r, st))])]]