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Proof step 41 from proof junkrefs-put-null (previous step)

st[r0 -- i '] = refval(r2), mkfs(class, ty0, fieldvar) ' ∈ instfields(st[r -- _type] .type .class), is_reftype(ty0), is_obj(r, st), st[r0 -- _type] .type ≤ ty, is_array(str, r0, st[r -- mkfs(class, ty0, fieldvar) ', refval(jvmref)]), (st[r -- mkfs(class, ty0, fieldvar) ', refval(jvmref)][r0 -- _type]) .type ≤ ty, is_array(str, r0, st), i < (st[r -- mkfs(class, ty0, fieldvar) ', refval(jvmref)][r0 -- _length]) .intval, 0 ≤ i, 0 < (st[r -- mkfs(class, ty0, fieldvar) ', refval(jvmref)][r0 -- _length]) .intval, junkrefs (str, r2 ' + refs, (st[r -- mkfs(class, ty0, fieldvar) ', refval(jvmref)][r0 -- _type]) .type .type, st[r -- mkfs(class, ty0, fieldvar) ', refval(jvmref)]), ¬ junkrefs(str, r2 ' + refs, st[r0 -- _type] .type .type, st) ∧ is_obj(r, st) ∧ is_reftype(mkfs(class, ty0, fieldvar) .type) ∧ mkfs(class, ty0, fieldvar) ' ∈ instfields(st[r -- _type] .type .class) → ¬ junkrefs(str, r2 ' + refs, st[r0 -- _type] .type .type, st[r -- mkfs(class, ty0, fieldvar) ', refval(jvmref)]), ∀ str0, ty1, st0, r1, fs. ¬ junkrefs(str0, r2 ' + refs, ty1, st0) ∧ is_obj(r1, st0) ∧ is_reftype(fs .type) ∧ fs ' ∈ instfields(st0[r1 -- _type] .type .class) → ¬ junkrefs(str0, r2 ' + refs, ty1, st0[r1 -- fs ', refval(jvmref)]) ⊦ r0 = jvmref, ¬ st[r0 -- _length] .intval ≤ i ∧ junkrefs(str, r2 ' + refs, st[r0 -- _type] .type .type, st)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 40:
st[r0 -- i '] = refval(r2), mkfs(class, ty0, fieldvar) ' ∈ instfields(st[r -- _type] .type .class), is_reftype(ty0), is_obj(r, st), st[r0 -- _type] .type ≤ ty, is_array(str, r0, st[r -- mkfs(class, ty0, fieldvar) ', refval(jvmref)]), (st[r -- mkfs(class, ty0, fieldvar) ', refval(jvmref)][r0 -- _type]) .type ≤ ty, is_array(str, r0, st), i < (st[r -- mkfs(class, ty0, fieldvar) ', refval(jvmref)][r0 -- _length]) .intval, 0 ≤ i, 0 < (st[r -- mkfs(class, ty0, fieldvar) ', refval(jvmref)][r0 -- _length]) .intval, junkrefs (str, r2 ' + refs, (st[r -- mkfs(class, ty0, fieldvar) ', refval(jvmref)][r0 -- _type]) .type .type, st[r -- mkfs(class, ty0, fieldvar) ', refval(jvmref)]), ∀ str0, ty1, st0, r1, fs. ¬ junkrefs(str0, r2 ' + refs, ty1, st0) ∧ is_obj(r1, st0) ∧ is_reftype(fs .type) ∧ fs ' ∈ instfields(st0[r1 -- _type] .type .class) → ¬ junkrefs(str0, r2 ' + refs, ty1, st0[r1 -- fs ', refval(jvmref)]), ¬ junkrefs(str, r2 ' + refs, st[r0 -- _type] .type .type, st) → ¬ junkrefs(str, r2 ' + refs, st[r0 -- _type] .type .type, st[r -- mkfs(class, ty0, fieldvar) ', refval(jvmref)]) ⊦ r0 = jvmref, ¬ st[r0 -- _length] .intval ≤ i ∧ junkrefs(str, r2 ' + refs, st[r0 -- _type] .type .type, st)

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ mkfs(class, ty, fieldvar) .type = ty], [CSIMPSEQ : ⊦ (refs + refs0) + refs1 = refs + refs0 + refs1])]]