rcases c_child with ⟨res, res_in_ress, def_c⟩
L R : Finset Formula
c : TNode
ress : List SubPair
Lcond Rcond : Finset Formula
rule : LocalRule (Lcond, Rcond) ress
precondProofL : Lcond ⊆ L
precondProofR : Rcond ⊆ R
lrApp : LocalRuleApp (L, R) (applyLocalRule rule (L, R))
c_child : ∃ a ∈ ress, (L \ Lcond ∪ a.1, R \ Rcond ∪ a.2) = c
⊢ lengthOfTNode c < lengthOfTNode (L, R)
case intro.intro
L R : Finset Formula
c : TNode
ress : List SubPair
Lcond Rcond : Finset Formula
rule : LocalRule (Lcond, Rcond) ress
precondProofL : Lcond ⊆ L
precondProofR : Rcond ⊆ R
lrApp : LocalRuleApp (L, R) (applyLocalRule rule (L, R))
res : SubPair
res_in_ress : res ∈ ress
def_c : (L \ Lcond ∪ res.1, R \ Rcond ∪ res.2) = c
⊢ lengthOfTNode c < lengthOfTNode (L, R)