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Proof step 30 from proof validrefs-levelsubset (previous step)

is_array(str, r, st), level⊆(str, str0), st[r -- _type] .type ≤ ty0, ∀ str, ty0, st, str0. validrefs(str, acc, ty0, st) ∧ level⊆(str, str0) → validrefs(str0, acc, ty0, st), acc = [] ∨ 0 ≤ i ∧ i < st[r -- _length] .intval ∧ is_referencevalue(st[r -- i ']) ∧ acc .first = st[r -- i '] .refval ∧ validrefs(str, acc, st[r -- _type] .type .type, st) ⊦ r = jvmref, validrefs(str0, r ' + acc, ty0, st)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 21:
⊦ is_array(str, r, st) ∧ st[r -- _type] .type ≤ ty → ( validrefs(str, r ' + refs, ty, st) ↔ refs = [] ∨ (∃ i. 0 ≤ i ∧ i < st[r -- _length] .intval ∧ is_referencevalue(st[r -- i ']) ∧ refs .first = st[r -- i '] .refval ∧ validrefs(str, refs, st[r -- _type] .type .type, st)))
Proof step 29:
is_array(str0, r, st) ∧ st[r -- _type] .type ≤ ty0, is_array(str, r, st), level⊆(str, str0), st[r -- _type] .type ≤ ty0, ∀ str, ty0, st, str0. validrefs(str, acc, ty0, st) ∧ level⊆(str, str0) → validrefs(str0, acc, ty0, st), acc = [] ∨ 0 ≤ i ∧ i < st[r -- _length] .intval ∧ is_referencevalue(st[r -- i ']) ∧ acc .first = st[r -- i '] .refval ∧ validrefs(str, acc, st[r -- _type] .type .type, st) ⊦ r = jvmref, acc = [] ∨ (∃ i. 0 ≤ i ∧ i < st[r -- _length] .intval ∧ is_referencevalue(st[r -- i ']) ∧ acc .first = st[r -- i '] .refval ∧ validrefs(str0, acc, st[r -- _type] .type .type, st))

Rule argument

[crewrite-arg: validrefs-array , F , [st, ty, refs, r, str] → [st, ty0, acc, r, str0] ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ is_array(str, r, st) ∧ level⊆(str, str0) → (¬ is_array(str0, r, st) ↔ false)])], [EXTRATERMS : (st, ty0, acc, r, str0)]]