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Proof step 3 from proof ocs-del-del1 (previous step)

#oc(a, a0 ') + #oc(a, x0) = 1, ∀ a. #oc(a, x0) = 1 → x0 -l a = x0 -1l a ⊦ (a0 ' + x0) -l a = (a0 ' + x0) -1l a

Heuristic weak cut applied rule cut formula

And obtained the following new goals

Proof step 4:
#oc(a, a0 ') + #oc(a, x0) = 1, ∀ a. #oc(a, x0) = 1 → x0 -l a = x0 -1l a ⊦ a = a0, (a0 ' + x0) -l a = (a0 ' + x0) -1l a

Rule argument

fma: a = a0

Additional information

Used simplifier rules: one: ⊦ #oc(a, a ') = 1;%oc-zero: ⊦ #oc(a, x) = 0 ↔ ¬ a ∈ x;%one-03: ⊦ 1 = m + 1 ↔ m = 0; from specification nat-basic2%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic2%c: ⊦ m + n = n + m; from specification nat-basic2%del-y: ⊦ (a ' + x) -l a = x -l a; from specification list-del%in-03: ⊦ ¬ a ∈ x → x -l a = x; from specification list-del%a: ⊦ (x + y) + z = x + y + z; from specification list%del1-y: ⊦ (a ' + x) -1l a = x; from specification list-del Used formulas: a = a0