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Proof step 79 from proof validref-refs-last-valid-subset (previous step)

st0[r0 -- i '] = refval(r2), acc + r1 ' = r2 ' + refs, 0 < st0[r0 -- _length] .intval, 0 ≤ i, validrefs(str, acc + r1 ', st0[r0 -- _type] .type .type, st0), is_referencevalue(st0[r0 -- i ']), i < st0[r0 -- _length] .intval, is_array(str, r0, st0), st ⊆ st0, validref(str, r, st[r -- _type] .type, st), st0[r0 -- _type] .type ≤ ty, ∀ str, r, st, st0, r1, ty. validref(str, r, st[r -- _type] .type, st) ∧ st ⊆ st0 ∧ r ∈ acc ∧ validrefs(str, acc + r1 ', ty, st0) → validref(str, r1, st[r1 -- _type] .type, st) ⊦ r0 = jvmref, validref(str, r1, st[r1 -- _type] .type, st), r ≠ r0 ∧ ¬ r ∈ acc, r1 ≠ r2 ∧ ¬ r1 ∈ refs, ¬ r2 ∈ acc ∧ r2 ≠ r1

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 78:
acc + r1 ' = r2 ' + refs, st0[r0 -- i '] = refval(r2), st0[r0 -- _type] .type ≤ ty, validref(str, r, st[r -- _type] .type, st), st ⊆ st0, is_array(str, r0, st0), i < st0[r0 -- _length] .intval, validrefs(str, r2 ' + refs, st0[r0 -- _type] .type .type, st0), 0 ≤ i, 0 < st0[r0 -- _length] .intval, ∀ str, r, st, st0, r1, ty. validref(str, r, st[r -- _type] .type, st) ∧ st ⊆ st0 ∧ r ∈ acc ∧ validrefs(str, acc + r1 ', ty, st0) → validref(str, r1, st[r1 -- _type] .type, st) ⊦ r0 = jvmref, validref(str, r1, st[r1 -- _type] .type, st), r ≠ r0 ∧ ¬ r ∈ acc, r1 ≠ r2 ∧ ¬ r1 ∈ refs, ¬ r2 ∈ acc ∧ r2 ≠ r1

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ is_referencevalue(refval(r))], [CSIMPSEQ : ⊦ r ∈ r0 ' ↔ r = r0], [CSIMPSEQ : ⊦ r ∈ refs + refs0 ↔ ¬ ¬ (r ∈ refs ∨ r ∈ refs0)], [CSIMPFORWARD : ⊦ r ' + refs = refs0 → r ∈ refs0], [CSIMPSEQ : ⊦ (refs + refs0) + refs1 = refs + refs0 + refs1], [CSIMPFORWARD : ⊦ refs + r ' = refs0 → r ∈ refs0])]]