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Proof step 50 from proof junkrefs-put-refval-02 (previous step)

acc = r2 + refs, r2 = (st[r -- i ', refval(r0)][r1 -- i0 ']) .refval, mkarraytype(st[r0 -- _type] .type) ≤ st[r -- _type] .type, is_array(str, r1, st[r -- i ', refval(r0)]), st[r1 -- _type] .type ≤ ty, is_array(str, r1, st), i0 < st[r1 -- _length] .intval, is_referencevalue(st[r -- i ', refval(r0)][r1 -- i0 ']), junkrefs(str, acc, st[r1 -- _type] .type .type, st[r -- i ', refval(r0)]), 0 ≤ i0, 0 < st[r1 -- _length] .intval, ∀ st, r0, r, str, ty, i. mkarraytype(st[r0 -- _type] .type) ≤ st[r -- _type] .type ∧ junkrefs(str, acc, ty, st[r -- i ', refval(r0)]) → r = jvmref ∨ r0 = jvmref ∨ junkrefs(str, acc, ty, st) ∨ junkref(str, r0, st) ⊦ r1 = jvmref, r0 = jvmref, r = jvmref, acc = [], junkref(str, r0, st), ∃ i0. ¬ i0 < 0 ∧ ¬ st[r1 -- _length] .intval ≤ i0 ∧ is_referencevalue(st[r1 -- i0 ']) ∧ r2 = st[r1 -- i0 '] .refval ∧ junkrefs(str, acc, st[r1 -- _type] .type .type, st)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 49:
0 ≤ i0, 0 < st[r1 -- _length] .intval, mkarraytype(st[r0 -- _type] .type) ≤ st[r -- _type] .type, is_array(str, r1, st[r -- i ', refval(r0)]), st[r1 -- _type] .type ≤ ty, is_array(str, r1, st), i0 < st[r1 -- _length] .intval, is_referencevalue(st[r -- i ', refval(r0)][r1 -- i0 ']), junkrefs(str, (st[r -- i ', refval(r0)][r1 -- i0 ']) .refval ' + refs, st[r1 -- _type] .type .type, st[r -- i ', refval(r0)]), ∀ st0, r2, r3, str0, ty0, i1. mkarraytype(st0[r2 -- _type] .type) ≤ st0[r3 -- _type] .type ∧ junkrefs(str0, (st[r -- i ', refval(r0)][r1 -- i0 ']) .refval ' + refs, ty0, st0[r3 -- i1 ', refval(r2)]) → r3 = jvmref ∨ r2 = jvmref ∨ junkrefs(str0, (st[r -- i ', refval(r0)][r1 -- i0 ']) .refval ' + refs, ty0, st0) ∨ junkref(str0, r2, st0) ⊦ r1 = jvmref, r0 = jvmref, r = jvmref, junkref(str, r0, st), ∃ i1. ¬ i1 < 0 ∧ ¬ st[r1 -- _length] .intval ≤ i1 ∧ is_referencevalue(st[r1 -- i1 ']) ∧ (st[r -- i ', refval(r0)][r1 -- i0 ']) .refval = st[r1 -- i1 '] .refval ∧ junkrefs(str, (st[r -- i ', refval(r0)][r1 -- i0 ']) .refval ' + refs, st[r1 -- _type] .type .type, st)

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ (refs + refs0) + refs1 = refs + refs0 + refs1], [CSIMPSEQ : ⊦ r ' + refs ≠ []], [CSIMPSEQ : ⊦ r + refs = r ' + refs])]]