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Proof step 31 from proof junkrefs-put-array-norefval (previous step)

(st[r1 -- i ', val][r -- i0 ']) = refval(r2), junkrefs(str, r2 ' + refs, st[r -- _type] .type .type, st[r1 -- i ', val]), i0 < st[r -- _length] .intval, okval(val, st[r1 -- _type] .type .type), is_array(str, r, st), st[r -- _type] .type ≤ ty, is_array(str, r, st[r1 -- i ', val]), 0 < st[r -- _length] .intval, 0 ≤ i0, ∀ val0, st0, r0, str0, ty0, i1. okval(val0, st0[r0 -- _type] .type .type) ∧ junkrefs(str0, r2 ' + refs, ty0, st0[r0 -- i1 ', val0]) → is_referencevalue(val0) ∨ junkrefs(str0, r2 ' + refs, ty0, st0) ⊦ r = jvmref, junkrefs(str, r ' + r2 ' + refs, ty, st), is_referencevalue(val)

Heuristic weak cut applied rule cut formula

And obtained the following new goals

Proof step 30:
(st[r1 -- i ', val][r -- i0 ']) = refval(r2), junkrefs(str, r2 ' + refs, st[r -- _type] .type .type, st[r1 -- i ', val]), i0 < st[r -- _length] .intval, okval(val, st[r1 -- _type] .type .type), is_array(str, r, st), st[r -- _type] .type ≤ ty, is_array(str, r, st[r1 -- i ', val]), 0 < st[r -- _length] .intval, 0 ≤ i0, ∀ val0, st0, r0, str0, ty0, i1. okval(val0, st0[r0 -- _type] .type .type) ∧ junkrefs(str0, r2 ' + refs, ty0, st0[r0 -- i1 ', val0]) → is_referencevalue(val0) ∨ junkrefs(str0, r2 ' + refs, ty0, st0) ⊦ r -- i0 ' = r1 -- i ', r = jvmref, junkrefs(str, r ' + r2 ' + refs, ty, st), is_referencevalue(val)

Rule argument

[fma-arg: r -- i0 ' = r1 -- 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 : ⊦ is_array(str, r, st) ∧ okval (val, st[r -- _type] .type .type) → is_array (str, r, st[r -- i ', val])], [CSIMPFORWARD : ⊦ i < j ∧ 0 ≤ i → 0 < j], [CSIMPFORWARD : ⊦ i ≤ j ∧ 0 ≤ i → 0 ≤ j], [CSIMPSEQ : ⊦ is_referencevalue(refval(r))])], [EXTRAFMAS : (r -- i0 ' = r1 -- i ')]]