have := localRuleAppDecreasesLengthSide R Rcond res.2 hyp.1 precondProofR
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
this : Lcond ∩ res.1 = ∅ ∧ Rcond ∩ res.2 = ∅
hyp : lengthOf res.2 < lengthOf Rcond ∧ res.1 = ∅
⊢ lengthOfSet L + lengthOfSet (R \ Rcond ∪ res.2) < lengthOfSet L + lengthOfSet R
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
this✝ : Lcond ∩ res.1 = ∅ ∧ Rcond ∩ res.2 = ∅
hyp : lengthOf res.2 < lengthOf Rcond ∧ res.1 = ∅
this : lengthOf (R \ Rcond ∪ res.2) < lengthOf R
⊢ lengthOfSet L + lengthOfSet (R \ Rcond ∪ res.2) < lengthOfSet L + lengthOfSet R