:: deftheorem defines is_a_proof_wrt CQC_THE1:def 5 :
for Al being QC-alphabet
for X being Subset of (CQC-WFF Al)
for f being FinSequence of [:(CQC-WFF Al),Proof_Step_Kinds:] holds
( f is_a_proof_wrt X iff ( f <> {} & ( for n being Nat st 1 <= n & n <= len f holds
f,n is_a_correct_step_wrt X ) ) );