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Proof step 30 from proof maxpath-array (previous step)

is_array(str, r, st) ∧ st[r -- _type] .type ≤ st[r -- _type] .type, st[r -- i '] = refval(r0), maxpath(str, r, st) = 1 + # refs0, maxpath(str, r0, st) = 1 + # refs1, is_valid_ref(str, r0, st), maxpath(str, r, st) ≤ maxpath(str, r0, st), 0 ≤ i, i < st[r -- _length] .intval, is_array(str, r, st), # refs0 ≤ # refs1, validrefs(str, r ' + refs0, st[r -- _type] .type, st), 0 < st[r -- _length] .intval, validrefs(str, r0 ' + refs1, st[r0 -- _type] .type, st) ⊦ # validrefset(str, r0, st) = 0, validrefset(str, r0, st) = ∅, # validrefset(str, r, st) = 0, validrefset(str, r, st) = ∅, r0 ' + refs1 = [] ∨ (∃ i. 0 ≤ i ∧ i < st[r -- _length] .intval ∧ is_referencevalue(st[r -- i ']) ∧ (r0 ' + refs1) .first = st[r -- i '] .refval ∧ validrefs(str, r0 ' + refs1, st[r -- _type] .type .type, st)), junkref(str, r, st), cyclic(str, r, st), dups(refs0), r ∈ refs0, has_reffield((r ' + refs0) .last, st), has_reffield((r0 ' + refs1) .last, st), dups(refs1), r0 ∈ refs1

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 29:
st[r -- i '] = refval(r0), maxpath(str, r, st) = 1 + # refs0, maxpath(str, r0, st) = 1 + # refs1, is_valid_ref(str, r0, st), maxpath(str, r, st) ≤ maxpath(str, r0, st), 0 ≤ i, i < st[r -- _length] .intval, is_array(str, r, st), # refs0 ≤ # refs1, validrefs(str, r ' + refs0, st[r -- _type] .type, st), 0 < st[r -- _length] .intval, validrefs(str, r0 ' + refs1, st[r0 -- _type] .type, st) ⊦ # validrefset(str, r0, st) = 0, validrefset(str, r0, st) = ∅, # validrefset(str, r, st) = 0, validrefset(str, r, st) = ∅, junkref(str, r, st), cyclic(str, r, st), dups(refs0), r ∈ refs0, has_reffield((r ' + refs0) .last, st), has_reffield((r0 ' + refs1) .last, st), dups(refs1), r0 ∈ refs1, ∃ i0. ¬ i0 < 0 ∧ ¬ st[r -- _length] .intval ≤ i0 ∧ is_referencevalue(st[r -- i0 ']) ∧ r0 = st[r -- i0 '] .refval ∧ validrefs(str, st[r -- i0 '] .refval ' + refs1, st[r -- _type] .type .type, st)

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ (r ' + refs) .first = r], [CSIMPSEQ : ⊦ ¬ i < j ↔ j ≤ i], [CSIMPSEQ : ⊦ ¬ i ≤ j ↔ j < i], [CSIMPSEQ : ⊦ ty ≤ ty], [CSIMPSEQ : ⊦ (refs + refs0) + refs1 = refs + refs0 + refs1], [CSIMPSEQ : ⊦ r ' + refs ≠ []])]]