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Proof step 41 from proof pathex-put-pathex-array-refval (previous step)

is_array(str, r0, st[r0 -- i ', refval(r2)]) ∧ (st[r0 -- i ', refval(r2)][r0 -- _type]) .type ≤ mkarraytype(ty), st[r0 -- _type] .type = mkarraytype(ty), refs0 = [] ∨ (∃ i0. 0 ≤ i0 ∧ i0 < (st[r0 -- i ', refval(r2)][r0 -- _length]) .intval ∧ is_referencevalue(st[r0 -- i ', refval(r2)][r0 -- i0 ']) ∧ refs0 .first = (st[r0 -- i ', refval(r2)][r0 -- i0 ']) .refval ∧ validrefs(str, refs0, (st[r0 -- i ', refval(r2)][r0 -- _type]) .type .type, 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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 13:
⊦ ¬ r ∈ refs → (validrefs(str, refs, ty, st[r -- sk, val]) ↔ validrefs(str, refs, ty, st))
Proof step 40:
refs0 .first = (st[r0 -- i ', refval(r2)][r0 -- i0 ']) .refval, st[r0 -- _type] .type = mkarraytype(ty), is_referencevalue(st[r0 -- i ', refval(r2)][r0 -- i0 ']), 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, refs0, ty, st), r2 = jvmref → is_reftype(ty) ⊦ r0 = refs0 .last, r0 = jvmref, refs0 = [], path∃(str, r0, refs0 .last, st), path∃(str, r2, refs0 .last, st), r0 ∈ refs0, dups(refs0)

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], [CSIMPNAMEDFORWARD : int-abs, , forward-le-01, ⊦ i ≤ j ∧ 0 ≤ i → 0 ≤ j], [CSIMPNAMEDSEQ : list-last, references, l-02, ⊦ refs ≠ [] → (r ' + refs) .last = refs .last], [CSIMPNAMEDSEQ : list-last, references, l, ⊦ r ' .last = r], [CSIMPNAMEDSEQ : list, references, a, ⊦ (refs + refs0) + refs1 = refs + refs0 + refs1], [CSIMPNAMEDSEQ : list, references, app, ⊦ refs + [] = refs], [CSIMPNAMEDSEQ : javastore, , length-at, ⊦ (st[r -- i ', val] [r0 -- _length ] ) = st[r0 -- _length]], [CSIMPNAMEDSEQ : typefuns, , array, ⊦ ty0 ≤ mkarraytype(ty) ↔ is_arraytype(ty0) ∧ ty0 .type ≤ ty], [CSIMPNAMEDSEQ : javastore, , type-at, ⊦ (st[r -- i ', val] [r0 -- _type ] ) = st[r0 -- _type]])]]