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Proof step 17 from proof pathex-array (previous step)

is_array(str, r, st) ∧ st[r -- _type] .type ≤ st[r -- _type] .type, is_array(str, r, st), refs0 = [] ∨ (∃ i. 0 ≤ i ∧ i < st[r -- _length] .intval ∧ is_referencevalue(st[r -- i ']) ∧ refs0 .first = st[r -- i '] .refval ∧ validrefs(str, refs0, st[r -- _type] .type .type, st)) ⊦ r = (r ' + refs0) .last, ∃ i. ¬ i < 0 ∧ ¬ st[r -- _length] .intval ≤ i ∧ is_referencevalue(st[r -- i ']) ∧ ( st[r -- i '] .refval ≠ jvmref ∧ st[st[r -- i '] .refval -- _type] .type ≤ st[r -- _type] .type .type ∧ path∃(str, st[r -- i '] .refval, (r ' + refs0) .last, st) ∨ st[r -- i '] .refval = jvmref ∧ (r ' + refs0) .last = jvmref)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 16:
refs0 .first = st[r -- i '] .refval, is_array(str, r, st), i < st[r -- _length] .intval, is_referencevalue(st[r -- i ']), validrefs(str, refs0, st[r -- _type] .type .type, st), 0 ≤ i, 0 < st[r -- _length] .intval ⊦ refs0 = [], r = refs0 .last, ∃ i0. ¬ i0 < 0 ∧ ¬ st[r -- _length] .intval ≤ i0 ∧ is_referencevalue(st[r -- i0 ']) ∧ ( st[r -- i0 '] .refval ≠ jvmref ∧ st[st[r -- i0 '] .refval -- _type] .type ≤ st[r -- _type] .type .type ∧ path∃(str, st[r -- i0 '] .refval, refs0 .last, st) ∨ st[r -- i0 '] .refval = jvmref ∧ refs0 .last = jvmref)

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPFORWARD : ⊦ i ≤ j ∧ 0 ≤ i → 0 ≤ j], [CSIMPFORWARD : ⊦ i < j ∧ 0 ≤ i → 0 < j], [CSIMPSEQ : ⊦ refs ≠ [] → (r ' + refs) .last = refs .last], [CSIMPSEQ : ⊦ r ' .last = r], [CSIMPSEQ : ⊦ (refs + refs0) + refs1 = refs + refs0 + refs1], [CSIMPSEQ : ⊦ refs + [] = refs], [CSIMPSEQ : ⊦ ty ≤ ty])]]