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Proof step 114 from proof validrefs-lastelem (previous step)

is_array(str, r0, st) ∧ st[r0 -- _type] .type ≤ ty, is_array(str, r0, st), acc + r ' = [] ∨ (∃ i. 0 ≤ i ∧ i < st[r0 -- _length] .intval ∧ is_referencevalue(st[r0 -- i ']) ∧ (acc + r ') .first = st[r0 -- i '] .refval ∧ validrefs(str, acc + r ', st[r0 -- _type] .type .type, st)), validrefs(str, r0 ' + acc, ty, st), st[r0 -- _type] .type ≤ ty, ∀ str, ty, st, r. validrefs(str, acc, ty, st) ∧ validrefs(str, acc + r ', ty, st) → acc = [] ∨ has_reffield(acc .last, st) ⊦ r0 = jvmref, has_reffield((r0 ' + acc) .last, st)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 113:
(acc + r ') .first = st[r0 -- i '] .refval, is_array(str, r0, st), validrefs(str, r0 ' + acc, ty, st), st[r0 -- _type] .type ≤ ty, i < st[r0 -- _length] .intval, is_referencevalue(st[r0 -- i ']), validrefs(str, acc + r ', st[r0 -- _type] .type .type, st), 0 ≤ i, 0 < st[r0 -- _length] .intval, ∀ str, ty, st, r. validrefs(str, acc, ty, st) ∧ validrefs(str, acc + r ', ty, st) → acc = [] ∨ has_reffield(acc .last, st) ⊦ r0 = jvmref, has_reffield((r0 ' + acc) .last, st)

Rule argument

[emptyarg]

Additional information

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