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Proof step 76 from proof junkrefs-put-refval-01 (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 75:
0 < st[r1 -- _length] .intval, 0 ≤ i, junkrefs(str, st[r1 -- i '] .refval ' + refs, st[r1 -- _type] .type .type, st[r -- mkfs(class, ty0, fieldvar) ', refval(r0)]), is_referencevalue(st[r1 -- i ']), i < st[r1 -- _length] .intval, st[r0 -- _type] .type ≤ ty0, st[r1 -- _type] .type ≤ ty, is_array(str, r1, st), ∀ str0, ty1, st0, r3, fs, r4. ¬ junkrefs(str0, st[r1 -- i '] .refval ' + refs, ty1, st0) ∧ ¬ junkref(str0, r3, st0) ∧ st0[r3 -- _type] .type ≤ fs .type ∧ r3 ≠ jvmref ∧ fs .type ≠ void_type ∧ fs ' ≠ _length → ¬ junkrefs(str0, st[r1 -- i '] .refval ' + refs, ty1, st0[r4 -- fs ', refval(r3)]) ⊦ r0 = jvmref, ty0 = void_type, mkfs(class, ty0, fieldvar) ' = _length, r1 = jvmref, r = r1, junkref(str, r0, st), ∃ i0. ¬ i0 < 0 ∧ ¬ st[r1 -- _length] .intval ≤ i0 ∧ is_referencevalue(st[r1 -- i0 ']) ∧ st[r1 -- i '] .refval = st[r1 -- i0 '] .refval ∧ junkrefs(str, st[r1 -- i0 '] .refval ' + refs, st[r1 -- _type] .type .type, st), r ≠ st[r1 -- i '] .refval ∧ ¬ r ∈ refs

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPFORWARD : ⊦ i ≤ j ∧ 0 ≤ i → 0 ≤ j], [CSIMPFORWARD : ⊦ i < j ∧ 0 ≤ i → 0 < j], [CSIMPSEQ : ⊦ sk ≠ sk0 → (st[r -- sk, val][r0 -- sk0]) = st[r0 -- sk0]], [CSIMPSEQ : ⊦ ty ≠ void_type → (st[ r -- mkfs (class, ty, fieldvar) ', val] [r0 -- _type ] ) = st[r0 -- _type]], [CSIMPSEQ : ⊦ r ≠ r0 → ( is_array (str, r0, st[r -- sk, val]) ↔ is_array(str, r0, st))], [CSIMPSEQ : ⊦ r ' + refs ≠ []], [CSIMPSEQ : ⊦ (st[r0 -- fs ', val][r -- i ']) = st[r -- i ']], [CSIMPSEQ : ⊦ (refs + refs0) + refs1 = refs + refs0 + refs1], [CSIMPSEQ : ⊦ (r ' + refs) .first = r])]]