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Proof step 46 from proof validrefs-put-notin (previous step)

is_array(str, r0, st), st[r0 -- _type] .type ≤ ty, ∀ str, ty, st, r, sk, val. (validrefs(str, acc, ty, st[r -- sk, val]) ↔ validrefs(str, acc, ty, st)) ∨ r ∈ acc ⊦ r0 = jvmref, r = r0, (∃ i. 0 ≤ i ∧ i < st[r0 -- _length] .intval ∧ is_referencevalue(st[r0 -- i ']) ∧ acc .first = st[r0 -- i '] .refval ∧ validrefs(str, acc, st[r0 -- _type] .type .type, st[r -- sk, val])) ↔ (∃ i. ¬ i < 0 ∧ ¬ st[r0 -- _length] .intval ≤ i ∧ is_referencevalue(st[r0 -- i ']) ∧ acc .first = st[r0 -- i '] .refval ∧ validrefs(str, acc, st[r0 -- _type] .type .type, st)), acc = [], r ∈ acc

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 45:
acc = r1 + refs, is_array(str, r0, st), st[r0 -- _type] .type ≤ ty, ∀ str, ty, st, r, sk, val. (validrefs(str, acc, ty, st[r -- sk, val]) ↔ validrefs(str, acc, ty, st)) ∨ r ∈ acc ⊦ r0 = jvmref, r = r0, (∃ i. 0 ≤ i ∧ i < st[r0 -- _length] .intval ∧ is_referencevalue(st[r0 -- i ']) ∧ r1 = st[r0 -- i '] .refval ∧ validrefs(str, acc, st[r0 -- _type] .type .type, st[r -- sk, val])) ↔ (∃ i. ¬ i < 0 ∧ ¬ st[r0 -- _length] .intval ≤ i ∧ is_referencevalue(st[r0 -- i ']) ∧ r1 = st[r0 -- i '] .refval ∧ validrefs(str, acc, st[r0 -- _type] .type .type, st)), acc = [], r ∈ acc

Rule argument

[speclemmaarg: refs ≠ [] ,r = refs .first ∧ refs0 = refs .rest ↔ refs = r + refs0 ,[refs, r, refs0] → [acc, r1, refs] ,T ,list-data ,references-olista ,elim-list-c ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPELIM : refs ≠ [] ⊦ r = refs .first ∧ refs0 = refs .rest ↔ refs = r + refs0])], [EXTRATERMS : (acc, r1, refs)]]