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Proof step 41 from proof pathex-array (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 40:
is_referencevalue(st[r -- i ']), is_array(str, r, st), i < st[r -- _length] .intval, 0 ≤ i, 0 < st[r -- _length] .intval, st[st[r -- i '] .refval -- _type] .type ≤ st[r -- _type] .type .type, validrefs(str, st[r -- i '] .refval ' + refs0, st[st[r -- i '] .refval -- _type] .type, st) ⊦ st[r -- i '] .refval = jvmref, r = (st[r -- i '] .refval ' + refs0) .last, ∃ i0. ¬ i0 < 0 ∧ ¬ st[r -- _length] .intval ≤ i0 ∧ is_referencevalue(st[r -- i0 ']) ∧ st[r -- i '] .refval = st[r -- i0 '] .refval ∧ validrefs(str, st[r -- i '] .refval ' + refs0, st[r -- _type] .type .type, st)

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ (r ' + refs) .first = r], [CSIMPSEQ : ⊦ ¬ i < j ↔ j ≤ i], [CSIMPSEQ : ⊦ ¬ i ≤ j ↔ j < i], [CSIMPSEQ : ⊦ ty ≤ ty], [CSIMPSEQ : ⊦ (refs + refs0) + refs1 = refs + refs0 + refs1], [CSIMPSEQ : ⊦ r ' + refs ≠ []])]]