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Proof step 10 from proof validrefs-levelsubset-01 (previous step)

¬ (is_obj(str, r, st) ∧ st[r -- _type] .type ≤ ty0), is_obj(str0, r, st), level⊆(str, str0), validref(str, r, ty, st), st[r -- _type] .type ≤ ty0, is_valid_ref(str, r, st), st[r -- _type] .type ≤ ty, ∀ str, str0, ty0, st, ty. level⊆(str, str0) ∧ validrefs(str0, refs0, ty0, st) ∧ validref(str, refs0 .first, ty, st) → validrefs(str, refs0, ty0, st), refs0 = [] ∨ mkfs(class, ty1, fieldvar) ' ∈ instfields(st[r -- _type] .type .class) ∧ is_referencevalue(st[r -- mkfs(class, ty1, fieldvar) ']) ∧ refs0 .first = st[r -- mkfs(class, ty1, fieldvar) '] .refval ∧ validrefs(str0, refs0, ty1, st) ⊦ r = jvmref, validrefs(str, r ' + refs0, ty0, st)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 9:
st[r -- _type] .type ≤ ty, is_obj(str0, r, st), level⊆(str, str0), validref(str, r, ty, st), st[r -- _type] .type ≤ ty0, is_array(str, r, st), ∀ str, str0, ty0, st, ty. level⊆(str, str0) ∧ validrefs(str0, refs0, ty0, st) ∧ validref(str, refs0 .first, ty, st) → validrefs(str, refs0, ty0, st), refs0 = [] ∨ mkfs(class, ty1, fieldvar) ' ∈ instfields(st[r -- _type] .type .class) ∧ is_referencevalue(st[r -- mkfs(class, ty1, fieldvar) ']) ∧ refs0 .first = st[r -- mkfs(class, ty1, fieldvar) '] .refval ∧ validrefs(str0, refs0, ty1, st) ⊦ r = jvmref, validrefs(str, r ' + refs0, ty0, st)

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPNAMEDSEQ : addfuns, , isarray-isobj-01, ⊦ is_array(str, r, st) → ¬ is_obj(str, r, st)], [CSIMPNAMEDSEQ : addfuns, , is_valid_ref, ⊦ ¬ is_obj(str, r, st) → ( is_valid_ref(str, r, st) ↔ is_array(str, r, st))])]]