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Proof step 93 from proof validrefs-subset-equiv (previous step)

is_array(str, r, st0), validrefs(str, r ' + refs, ty, st0), st ⊆ st0, is_valid_ref(str, r, st), st0[r -- _type] .type ≤ ty, ∀ st, st0, ty, r, str, refs0. # refs0 < # refs → (validrefs(str, r ' + refs0, ty, st0) ∧ st ⊆ st0 ∧ validref(str, r, st[r -- _type] .type, st) → validrefs(str, r ' + refs0, ty, st)) ⊦ r = jvmref, junkref(str, r, st), validrefs(str, r ' + refs, ty, st)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 45:
⊦ 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 92:
is_array(str, r, st0) ∧ st0[r -- _type] .type ≤ ty, is_array(str, r, st0), refs = [] ∨ (∃ i. 0 ≤ i ∧ i < st0[r -- _length] .intval ∧ is_referencevalue(st0[r -- i ']) ∧ refs .first = st0[r -- i '] .refval ∧ validrefs(str, refs, st0[r -- _type] .type .type, st0)), st ⊆ st0, is_valid_ref(str, r, st), st0[r -- _type] .type ≤ ty, ∀ st, st0, ty, r, str, refs0. # refs0 < # refs → (validrefs(str, r ' + refs0, ty, st0) ∧ st ⊆ st0 ∧ validref(str, r, st[r -- _type] .type, st) → validrefs(str, r ' + refs0, ty, st)) ⊦ r = jvmref, junkref(str, r, st), validrefs(str, r ' + refs, ty, st)

Rule argument

[crewrite-arg: validrefs-array , F , [st, ty, refs, r, str] → [st0, ty, refs, r, str] ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ (refs + refs0) + refs1 = refs + refs0 + refs1])], [EXTRATERMS : (st0, ty, refs, r, str)]]