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Proof step 87 from proof junkrefs-put-refval (previous step)

st[r1 -- i '] = refval(r2), 0 < st[r1 -- _length] .intval, 0 ≤ i, junkrefs(str, r2 ' + refs, st[r1 -- _type] .type .type, st[r -- mkfs(class, ty0, fieldvar) ', refval(r0)]), is_referencevalue(st[r1 -- i ']), i < st[r1 -- _length] .intval, mkfs(class, ty0, fieldvar) ' ∈ instfields(st[r -- _type] .type .class), st[r0 -- _type] .type ≤ ty0, is_obj(r, st), st[r1 -- _type] .type ≤ ty, is_array(str, r1, st), ∀ str0, ty1, st0, r3, r4, fs. ¬ junkrefs(str0, r2 ' + refs, ty1, st0) ∧ ¬ junkref(str0, r3, st0) ∧ is_obj(r4, st0) ∧ st0[r3 -- _type] .type ≤ fs .type ∧ r3 ≠ jvmref ∧ fs ' ∈ instfields(st0[r4 -- _type] .type .class) → ¬ junkrefs(str0, r2 ' + refs, ty1, st0[r4 -- fs ', refval(r3)]) ⊦ r0 = jvmref, r1 = jvmref, r = r1, junkref(str, r0, st), ∃ i0. ¬ i0 < 0 ∧ ¬ st[r1 -- _length] .intval ≤ i0 ∧ is_referencevalue(st[r1 -- i0 ']) ∧ r2 = st[r1 -- i0 '] .refval ∧ junkrefs(str, st[r1 -- i0 '] .refval ' + refs, st[r1 -- _type] .type .type, st), r ≠ r2 ∧ ¬ r ∈ refs

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 86:
st[r1 -- i '] = refval(r2), is_array(str, r1, st), st[r1 -- _type] .type ≤ ty, is_obj(r, st), st[r0 -- _type] .type ≤ ty0, mkfs(class, ty0, fieldvar) ' ∈ instfields(st[r -- _type] .type .class), i < st[r1 -- _length] .intval, junkrefs(str, r2 ' + refs, st[r1 -- _type] .type .type, st[r -- mkfs(class, ty0, fieldvar) ', refval(r0)]), 0 ≤ i, 0 < st[r1 -- _length] .intval, ∀ str0, ty1, st0, r3, r4, fs. ¬ junkrefs(str0, r2 ' + refs, ty1, st0) ∧ ¬ junkref(str0, r3, st0) ∧ is_obj(r4, st0) ∧ st0[r3 -- _type] .type ≤ fs .type ∧ r3 ≠ jvmref ∧ fs ' ∈ instfields(st0[r4 -- _type] .type .class) → ¬ junkrefs(str0, r2 ' + refs, ty1, st0[r4 -- fs ', refval(r3)]) ⊦ r = r1, r1 = jvmref, r0 = jvmref, junkref(str, r0, st), r ≠ r2 ∧ ¬ r ∈ refs, ∃ i0. ¬ i0 < 0 ∧ ¬ st[r1 -- _length] .intval ≤ i0 ∧ is_referencevalue(st[r1 -- i0 ']) ∧ r2 = st[r1 -- i0 '] .refval ∧ junkrefs(str, st[r1 -- i0 '] .refval ' + refs, st[r1 -- _type] .type .type, st)

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ is_referencevalue(refval(r))], [CSIMPSEQ : ⊦ (refs + refs0) + refs1 = refs + refs0 + refs1])]]