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Proof step 34 from proof validrefs-levelsubset-01 (previous step)

¬ (is_array(str, r, st) ∧ st[r -- _type] .type ≤ ty0), is_array(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 = [] ∨ 0 ≤ i ∧ i < st[r -- _length] .intval ∧ is_referencevalue(st[r -- i ']) ∧ refs0 .first = st[r -- i '] .refval ∧ validrefs(str0, refs0, st[r -- _type] .type .type, st) ⊦ r = jvmref, validrefs(str, r ' + refs0, ty0, st)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 33:
st[r -- _type] .type ≤ ty, is_array(str0, r, st), level⊆(str, str0), validref(str, r, ty, st), st[r -- _type] .type ≤ ty0, is_obj(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 = [] ∨ 0 ≤ i ∧ i < st[r -- _length] .intval ∧ is_referencevalue(st[r -- i ']) ∧ refs0 .first = st[r -- i '] .refval ∧ validrefs(str0, refs0, st[r -- _type] .type .type, st) ⊦ r = jvmref, validrefs(str, r ' + refs0, ty0, st)

Rule argument

[emptyarg]

Additional information

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