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Proof step 57 from proof validrefs-subset-equiv (previous step)

st0[r -- _type] .type ≤ ty, is_valid_ref(str, r, st), st ⊆ st0, is_array(str, r, st0), refs = [] ∨ 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, 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, validrefs(str, r ' + refs, ty, st), junkref(str, r, st), is_array(str, r, st) ∧ st[r -- _type] .type ≤ ty

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 47:
⊦ rk ∈ st ∧ st ⊆ st1 → st1[rk] = st[rk]
Proof step 56:
r -- _type ∈ st ∧ st ⊆ st0, st[r -- _type] .type ≤ ty, is_valid_ref(str, r, st), st ⊆ st0, is_array(str, r, st0), refs = [] ∨ 0 ≤ i ∧ i < st0[r -- _length] .intval ∧ is_referencevalue(st0[r -- i ']) ∧ refs .first = st0[r -- i '] .refval ∧ validrefs(str, refs, st[r -- _type] .type .type, st0), ∀ 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, validrefs(str, r ' + refs, ty, st), junkref(str, r, st), is_array(str, r, st) ∧ st[r -- _type] .type ≤ ty

Rule argument

[speclemmaarg: ,rk ∈ st ∧ st ⊆ st1 → st1[rk] = st[rk] ,[rk, st, st1] → [r -- _type, st, st0] ,F ,store ,javastore-ostorea ,superset-elem-eq ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ ¬ r -- _type ∈ st → ¬ is_valid_ref(str, r, st)])], [EXTRATERMS : (r -- _type, st, st0)]]