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Proof step 19 from proof validrefs-newref (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 18:
0 ≤ i, 0 < st[r0 -- _length] .intval, is_array(str, r0, st), newref(r, st), st[r0 -- _type] .type ≤ ty, i < st[r0 -- _length] .intval, is_referencevalue(st[r0 -- i ']), validrefs(str, st[r0 -- i '] .refval ' + refs, st[r0 -- _type] .type .type, st), ∀ str0, ty0, st0, r1. validrefs(str0, st[r0 -- i '] .refval ' + refs, ty0, st0) ∧ (r1 = st[r0 -- i '] .refval ∨ r1 ∈ refs) ∧ newref(r1, st0) → r1 = jvmref ⊦ r0 = jvmref, r = jvmref, r = r0, r ≠ st[r0 -- i '] .refval ∧ ¬ r ∈ refs

Rule argument

[emptyarg]

Additional information

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