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Proof step 38 from proof validrefs-delcycle (previous step)

acc + r ' = r1 + refs ∧ acc + r ' ≠ [], refs1 .last = jvmref, r1 = st[r0 -- i '] .refval, is_array(str, r0, st), st[r0 -- _type] .type ≤ ty, i < st[r0 -- _length] .intval, is_referencevalue(st[r0 -- i ']), validrefs(str, acc + r ' + refs0 + r ' + refs1, st[r0 -- _type] .type .type, st), 0 ≤ i, 0 < st[r0 -- _length] .intval, ∀ str, r, refs0, refs1, ty, st. validrefs(str, acc + r ' + refs0 + r ' + refs1, ty, st) ∧ refs1 ≠ [] ∧ refs1 .last = jvmref → validrefs(str, acc + r ' + refs1, ty, st) ⊦ r0 = jvmref, refs1 = [], validrefs(str, (r0 ' + acc) + r ' + refs1, ty, st)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 37:
acc + r ' = st[r0 -- i '] .refval ' + refs, refs1 .last = jvmref, 0 < st[r0 -- _length] .intval, 0 ≤ i, validrefs(str, acc + r ' + refs0 + r ' + refs1, st[r0 -- _type] .type .type, st), is_referencevalue(st[r0 -- i ']), i < st[r0 -- _length] .intval, st[r0 -- _type] .type ≤ ty, is_array(str, r0, st), ∀ str, r, refs0, refs1, ty, st. validrefs(str, acc + r ' + refs0 + r ' + refs1, ty, st) ∧ refs1 ≠ [] ∧ refs1 .last = jvmref → validrefs(str, acc + r ' + refs1, ty, st) ⊦ refs1 = [], r0 = jvmref, validrefs(str, (r0 ' + acc) + r ' + refs1, ty, st), r ≠ st[r0 -- i '] .refval ∧ ¬ r ∈ refs, ¬ st[r0 -- i '] .refval ∈ acc ∧ st[r0 -- i '] .refval ≠ r

Rule argument

[emptyarg]

Additional information

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