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Proof step 67 from proof validrefs-put-notin-03 (previous step)

is_array(str, r, st) ∧ st[r -- _type] .type ≤ ty, is_array(str, r, st), is_valid_ref(str, r, st[r -- sk, val]), st[r -- _type] .type ≤ ty, is_valid_ref(r, st) ⊦ r = jvmref, validrefs(str, r ' + r0 ' + refs1, ty, st[r -- sk, val]) ↔ r0 ' + refs1 = [] ∨ (∃ i. 0 ≤ i ∧ i < st[r -- _length] .intval ∧ is_referencevalue(st[r -- i ']) ∧ (r0 ' + refs1) .first = st[r -- i '] .refval ∧ validrefs(str, r0 ' + refs1, st[r -- _type] .type .type, st)), sk = _length, sk = _type, r0 = st[r -- sk] .refval, val .refval = r0, r = r0, r0 ∈ refs1, dups(refs1), r ∈ refs1

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 66:
is_array(str, r, st), is_valid_ref(str, r, st[r -- sk, val]), st[r -- _type] .type ≤ ty, is_valid_ref(r, st) ⊦ sk = _length, sk = _type, r0 = st[r -- sk] .refval, val .refval = r0, r = r0, r = jvmref, validrefs(str, r ' + r0 ' + refs1, ty, st[r -- sk, val]) ↔ (∃ i. ¬ i < 0 ∧ ¬ st[r -- _length] .intval ≤ i ∧ is_referencevalue(st[r -- i ']) ∧ r0 = st[r -- i '] .refval ∧ validrefs(str, st[r -- i '] .refval ' + refs1, st[r -- _type] .type .type, st)), r0 ∈ refs1, dups(refs1), r ∈ refs1

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPNAMEDSEQ : list, references, c-08, ⊦ (r ' + refs) .first = r], [CSIMPNAMEDSEQ : int-abs, , lels, ⊦ ¬ i < j ↔ j ≤ i], [CSIMPNAMEDSEQ : int-abs, , lels-01, ⊦ ¬ i ≤ j ↔ j < i], [CSIMPNAMEDSEQ : list, references, a, ⊦ (refs + refs0) + refs1 = refs + refs0 + refs1], [CSIMPNAMEDSEQ : list, references, e-01, ⊦ r ' + refs ≠ []])]]