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Proof step 18 from proof validrefs-primarray (previous step)

is_array(str, r, st) ∧ st[r -- _type] .type ≤ mkarraytype(ty), st[r -- _type] .type = mkarraytype(ty0), ty0 ≤ ty, is_primtype(ty), is_array(str, r, st) ⊦ r = jvmref, 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 ' + refs0 = jvmref ' ∨ okarray(r, ty, st) ∧ refs0 = []

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 17:
refs0 .first = st[r -- i '] .refval, st[r -- _type] .type = mkarraytype(ty0), is_array(str, r, st), is_primtype(ty), 0 < st[r -- _length] .intval, 0 ≤ i, r ∈ st, validrefs(str, refs0, ty0, st), is_referencevalue(st[r -- i ']), i < st[r -- _length] .intval, okarray(r, ty, st), ty0 ≤ ty ⊦ refs0 = [], r ' + refs0 = jvmref ', r = jvmref

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ is_arraytype(mkarraytype(ty))], [CSIMPSEQ : ⊦ mkarraytype(ty) .type = ty], [CSIMPFORWARD : ⊦ okarray(r, ty, st) → r ≠ jvmref ∧ r ∈ st], [CSIMPFORWARD : ⊦ i ≤ j ∧ 0 ≤ i → 0 ≤ j], [CSIMPFORWARD : ⊦ i < j ∧ 0 ≤ i → 0 < j], [CSIMPSEQ : ⊦ ¬ okarray(r, ty, st) ∧ st[r -- _type] .type = mkarraytype(ty0) ∧ ty0 ≤ ty → ¬ is_array(str, r, st)], [CSIMPSEQ : ⊦ ty0 ≤ mkarraytype(ty) ↔ is_arraytype(ty0) ∧ ty0 .type ≤ ty], [CSIMPSEQ : ⊦ (refs + refs0) + refs1 = refs + refs0 + refs1], [CSIMPSEQ : ⊦ r ' = r0 ' + refs ↔ r = r0 ∧ refs = []])]]