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Proof step 4 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 5:
#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, a = a0

Rule argument

fma: a = a0

Additional information

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