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Proof step 36 from proof junkrefs-put-refval-02 (previous step)

0 < st[r -- _length] .intval, 0 ≤ i, junkrefs(str, r4 ' + refs, st[r -- _type] .type .type, st[r -- i ', refval(r4)]), is_array(str, r, st), st[r -- _type] .type ≤ ty, is_array(str, r, st[r -- i ', refval(r4)]), mkarraytype(st[r4 -- _type] .type) ≤ st[r -- _type] .type, i < st[r -- _length] .intval, mkarraytype(st[r4 -- _type] .type) ≤ ty, junkrefs(str, r4 ' + refs, st[r -- _type] .type .type, st), ∀ st0, r2, r3, str0, ty0, i1. mkarraytype(st0[r2 -- _type] .type) ≤ st0[r3 -- _type] .type ∧ junkrefs(str0, r4 ' + refs, ty0, st0[r3 -- i1 ', refval(r2)]) → r3 = jvmref ∨ r2 = jvmref ∨ junkrefs(str0, r4 ' + refs, ty0, st0) ∨ junkref(str0, r2, st0) ⊦ r = jvmref, r4 = jvmref, ∃ i0. ¬ i0 < 0 ∧ ¬ st[r -- _length] .intval ≤ i0 ∧ is_referencevalue(st[r -- i0 ']) ∧ r4 = st[r -- i0 '] .refval, r4 ' + refs ≠ [] ∧ (r4 ' + refs) .first = r4 ∧ junkrefs(str, r4 ' + refs, st[(r4 ' + refs) .first -- _type] .type, st), ∃ refs0. refs0 ≠ [] ∧ refs0 .first = r4 ∧ junkrefs(str, refs0, st[refs0 .first -- _type] .type, st)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 33:
⊦ ¬ junkrefs(str, r ' + refs, st[r -- _type] .type, st) ∧ r ≠ jvmref → (junkrefs(str, r ' + refs, ty, st) ↔ ¬ st[r -- _type] .type ≤ ty)
Proof step 35:
0 < st[r -- _length] .intval, 0 ≤ i, junkrefs(str, r4 ' + refs, st[r -- _type] .type .type, st[r -- i ', refval(r4)]), is_array(str, r, st), st[r -- _type] .type ≤ ty, is_array(str, r, st[r -- i ', refval(r4)]), mkarraytype(st[r4 -- _type] .type) ≤ st[r -- _type] .type, i < st[r -- _length] .intval, mkarraytype(st[r4 -- _type] .type) ≤ ty, ∀ st0, r2, r3, str0, ty0, i1. mkarraytype(st0[r2 -- _type] .type) ≤ st0[r3 -- _type] .type ∧ junkrefs(str0, r4 ' + refs, ty0, st0[r3 -- i1 ', refval(r2)]) → r3 = jvmref ∨ r2 = jvmref ∨ junkrefs(str0, r4 ' + refs, ty0, st0) ∨ junkref(str0, r2, st0) ⊦ r = jvmref, r4 = jvmref, junkrefs(str, r4 ' + refs, st[r4 -- _type] .type, st), st[r4 -- _type] .type ≤ st[r -- _type] .type .type, ∃ refs0. refs0 ≠ [] ∧ refs0 .first = r4 ∧ junkrefs(str, refs0, st[refs0 .first -- _type] .type, st), ∃ i0. ¬ i0 < 0 ∧ ¬ st[r -- _length] .intval ≤ i0 ∧ is_referencevalue(st[r -- i0 ']) ∧ r4 = st[r -- i0 '] .refval

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ (r ' + refs) .first = r], [CSIMPSEQ : ⊦ r ' ≠ []], [CSIMPSEQ : ⊦ ¬ refs + refs0 ≠ [] ↔ refs = [] ∧ refs0 = []], [CSIMPSEQ : ⊦ (refs + refs0) + refs1 = refs + refs0 + refs1])]]