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Proof step 42 from proof junkrefs-put-refval-02 (previous step)

r1 -- i0 ' = r -- i ', (st[r -- i ', refval(r0)][r1 -- i0 ']) = refval(r4), junkrefs(str, r4 ' + refs, st[r1 -- _type] .type .type, st[r -- i ', refval(r0)]), i0 < st[r1 -- _length] .intval, is_array(str, r1, st), st[r1 -- _type] .type ≤ ty, is_array(str, r1, st[r -- i ', refval(r0)]), mkarraytype(st[r0 -- _type] .type) ≤ st[r -- _type] .type, 0 < st[r1 -- _length] .intval, 0 ≤ i0, ∀ st0, r2, r3, str0, ty0, i1. mkarraytype(st0[r2 -- _type] .type) ≤ st0[r3 -- _type] .type ∧ junkrefs(str0, r4 ' + refs, ty0, st0[r3 -- i1 ', refval(r2)]) → r3 = jvmref ∨ r2 = jvmref ∨ junkrefs(str0, r4 ' + refs, ty0, st0) ∨ junkref(str0, r2, st0) ⊦ r = jvmref, r0 = jvmref, r1 = jvmref, junkref(str, r0, st), ∃ i1. ¬ i1 < 0 ∧ ¬ st[r1 -- _length] .intval ≤ i1 ∧ is_referencevalue(st[r1 -- i1 ']) ∧ r4 = st[r1 -- i1 '] .refval ∧ junkrefs(str, st[r1 -- i1 '] .refval ' + refs, st[r1 -- _type] .type .type, st)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 41:
0 < st[r -- _length] .intval, 0 ≤ i, junkrefs(str, r4 ' + refs, st[r -- _type] .type .type, st[r -- i ', refval(r4)]), is_array(str, r, st), st[r -- _type] .type ≤ ty, is_array(str, r, st[r -- i ', refval(r4)]), mkarraytype(st[r4 -- _type] .type) ≤ st[r -- _type] .type, i < st[r -- _length] .intval, mkarraytype(st[r4 -- _type] .type) ≤ ty, ∀ st0, r2, r3, str0, ty0, i1. mkarraytype(st0[r2 -- _type] .type) ≤ st0[r3 -- _type] .type ∧ junkrefs(str0, r4 ' + refs, ty0, st0[r3 -- i1 ', refval(r2)]) → r3 = jvmref ∨ r2 = jvmref ∨ junkrefs(str0, r4 ' + refs, ty0, st0) ∨ junkref(str0, r2, st0) ⊦ r = jvmref, r4 = jvmref, junkref(str, r4, st), ∃ i1. ¬ i1 < 0 ∧ ¬ st[r -- _length] .intval ≤ i1 ∧ is_referencevalue(st[r -- i1 ']) ∧ r4 = st[r -- i1 '] .refval ∧ junkrefs(str, st[r -- i1 '] .refval ' + refs, st[r -- _type] .type .type, st)

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPFORWARD : ⊦ i ≤ j ∧ 0 ≤ i → 0 ≤ j], [CSIMPFORWARD : ⊦ ty ≤ ty0 ∧ ty0 ≤ ty1 → ty ≤ ty1], [CSIMPFORWARD : ⊦ i < j ∧ 0 ≤ i → 0 < j], [CSIMPSEQ : ⊦ refval(r) = refval(r0) ↔ r = r0], [CSIMPSEQ : ⊦ (st[rk, val][rk]) = val], [CSIMPFORWARD : ⊦ i < i0 ∧ i = i1 → i1 < i0], [CSIMPSEQ : ⊦ (refs + refs0) + refs1 = refs + refs0 + refs1], [CSIMPSEQ : ⊦ i ' = i0 ' ↔ i = i0], [CSIMPSEQ : ⊦ r -- sk = r0 -- sk0 ↔ r = r0 ∧ sk = sk0])]]