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Proof step 49 from proof maxpath-array (previous step)

validrefset(str, r, st) ≠ ∅ → (∃ refs. refs ∈ validrefset(str, r, st) ∧ maxpath(str, r, st) = # refs), st[r -- i '] = refval(r0), 0 < st[r -- _length] .intval, 0 ≤ i, i < st[r -- _length] .intval, is_array(str, r, st), maxpath(str, r, st) ≤ maxpath(str, r0, st) ⊦ # validrefset(str, r, st) = 0, validrefset(str, r, st) = ∅, junkref(str, r, st), cyclic(str, r, st)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 48:
st[r -- i '] = refval(r0), maxpath(str, r, st) = # refs, 0 < st[r -- _length] .intval, 0 ≤ i, i < st[r -- _length] .intval, is_array(str, r, st), maxpath(str, r, st) ≤ maxpath(str, r0, st), refs ∈ validrefset(str, r, st) ⊦ # validrefset(str, r, st) = 0, validrefset(str, r, st) = ∅, junkref(str, r, st), cyclic(str, r, st)

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ()]]