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Proof step 35 from proof junkrefs-put-null-02 (previous step)

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

Heuristic weak cut applied rule cut formula

And obtained the following new goals

Proof step 27:
⊦ ¬ junkrefs(str, jvmref ' + refs, ty, st)
Proof step 34:
(st[r -- i ', refval(jvmref)][r0 -- i0 ']) = refval(r2), junkrefs(str, r2 ' + refs, st[r0 -- _type] .type .type, st[r -- i ', refval(jvmref)]), i0 < st[r0 -- _length] .intval, is_array(str, r0, st), st[r0 -- _type] .type ≤ ty, is_array(str, r0, st[r -- i ', refval(jvmref)]), is_reftype(st[r -- _type] .type .type), 0 < st[r0 -- _length] .intval, 0 ≤ i0, ∀ st0, r1, str0, ty0, i1. is_reftype(st0[r1 -- _type] .type .type) ∧ junkrefs(str0, r2 ' + refs, ty0, st0[r1 -- i1 ', refval(jvmref)]) → r1 = jvmref ∨ junkrefs(str0, r2 ' + refs, ty0, st0) ⊦ r0 -- i0 ' = r -- i ', r = jvmref, r0 = jvmref, junkrefs(str, r0 ' + r2 ' + refs, ty, st)

Rule argument

[fma-arg: r0 -- i0 ' = r -- i ']

Additional information

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