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Proof step 69 from proof validref-refs-last-valid-subset (previous step)

acc + r1 ' = r2 ' + refs, st0[r0 -- i '] = refval(r2), st[r0 -- _type] = st0[r0 -- _type], st0[r0 -- _type] .type ≤ ty, validref(str, r0, st0[r0 -- _type] .type, st), st ⊆ st0, r0 ≠ jvmref ∧ r0 -- _type ∈ st0 ∧ is_typevalue(st0[r0 -- _type]) ∧ is_arraytype(st0[r0 -- _type] .type) ∧ okarray(r0, st0[r0 -- _type] .type .type, st0), type∃(str, st0[r0 -- _type] .type), 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) ⊦ st0[r0 -- _type] .type .jtelemtype = void_type, st0[r0 -- _type] .type .jtelemtype = abstract_type, r0 = jvmref, validref(str, r1, st[r1 -- _type] .type, st), r1 ≠ r2 ∧ ¬ r1 ∈ refs, ¬ r2 ∈ acc ∧ r2 ≠ r1

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 68:
acc + r1 ' = r2 ' + refs, st0[r0 -- i '] = refval(r2), st[r0 -- _type] = st0[r0 -- _type], st0[r0 -- _type] .type ≤ ty, validref(str, r0, st0[r0 -- _type] .type, st), st ⊆ st0, r0 -- _type ∈ st0, is_typevalue(st0[r0 -- _type]), is_arraytype(st0[r0 -- _type] .type), okarray(r0, st0[r0 -- _type] .type .type, st0), type∃(str, st0[r0 -- _type] .type), i < st0[r0 -- _length] .intval, validrefs(str, r2 ' + refs, st0[r0 -- _type] .type .type, st0), 0 ≤ i, 0 < st0[r0 -- _length] .intval, r0 ∈ st0, ∀ 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, st0[r0 -- _type] .type .type .jtelemtype = void_type, st0[r0 -- _type] .type .type .jtelemtype = abstract_type, validref(str, r1, st[r1 -- _type] .type, st), r1 ≠ r2 ∧ ¬ r1 ∈ refs, ¬ r2 ∈ acc ∧ r2 ≠ r1

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPFORWARD : ⊦ r -- sk ∈ st → r ∈ st], [CSIMPFORWARD : ⊦ okarray(r, ty, st) → r ≠ jvmref ∧ r ∈ st], [CSIMPSEQ : ⊦ is_arraytype(ty) → ty .jtelemtype = ty .type .jtelemtype])]]