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Proof step 27 from proof pathex-array (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 25:
⊦ validrefs(str, jvmref ', ty, st)
Proof step 26:
st[r -- i '] .refval = jvmref, is_referencevalue(st[r -- i ']), is_array(str, r, st), i < st[r -- _length] .intval, 0 ≤ i, 0 < st[r -- _length] .intval ⊦ r = jvmref, ∃ i0. ¬ i0 < 0 ∧ ¬ st[r -- _length] .intval ≤ i0 ∧ is_referencevalue(st[r -- i0 ']) ∧ jvmref = st[r -- i0 '] .refval

Rule argument

[emptyarg]

Additional information

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