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Proof step 28 from proof pathexplus-pathex (previous step)

is_array(str, (r ' + refs) .last, st) ∧ st[(r ' + refs) .last -- _type] .type ≤ st[(r ' + refs) .last -- _type] .type, is_array(str, (r ' + refs) .last, st), r0 ' = [] ∨ (∃ i. 0 ≤ i ∧ i < st[(r ' + refs) .last -- _length] .intval ∧ is_referencevalue(st[(r ' + refs) .last -- i ']) ∧ r0 ' .first = st[(r ' + refs) .last -- i '] .refval ∧ validrefs(str, r0 ', st[(r ' + refs) .last -- _type] .type .type, st)), is_valid_ref(str, r, st), validrefs(str, r ' + refs + r0 ', mkclasstype(`java.lang.Object' .class), st), validrefs(str, r ' + refs, mkclasstype(`java.lang.Object' .class), st), is_arraytype(st[(r ' + refs) .last -- _type] .type) ⊦ (r ' + refs) .last = jvmref, r = jvmref, r = r0, ∃ i. ¬ i < 0 ∧ ¬ st[(r ' + refs) .last -- _length] .intval ≤ i ∧ is_referencevalue(st[(r ' + refs) .last -- i ']) ∧ st[(r ' + refs) .last -- i '] .refval = r0

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 27:
0 < st[(r ' + refs) .last -- _length] .intval, 0 ≤ i, validrefs(str, st[(r ' + refs) .last -- i '] .refval ', st[(r ' + refs) .last -- _type] .type .type, st), is_referencevalue(st[(r ' + refs) .last -- i ']), i < st[(r ' + refs) .last -- _length] .intval, is_arraytype(st[(r ' + refs) .last -- _type] .type), validrefs(str, r ' + refs, mkclasstype(`java.lang.Object' .class), st), validrefs(str, r ' + refs + st[(r ' + refs) .last -- i '] .refval ', mkclasstype(`java.lang.Object' .class), st), is_valid_ref(str, r, st), is_array(str, (r ' + refs) .last, st) ⊦ r = st[(r ' + refs) .last -- i '] .refval, r = jvmref, (r ' + refs) .last = jvmref, ∃ i0. ¬ i0 < 0 ∧ ¬ st[(r ' + refs) .last -- _length] .intval ≤ i0 ∧ is_referencevalue(st[(r ' + refs) .last -- i0 ']) ∧ st[(r ' + refs) .last -- i0 '] .refval = st[(r ' + refs) .last -- i '] .refval

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPFORWARD : ⊦ i ≤ j ∧ 0 ≤ i → 0 ≤ j], [CSIMPFORWARD : ⊦ i < j ∧ 0 ≤ i → 0 < j], [CSIMPSEQ : ⊦ r ' .first = r], [CSIMPSEQ : ⊦ r ' ≠ []], [CSIMPSEQ : ⊦ ty ≤ ty])]]