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Proof step 3 from proof ocs-mklist (previous step)

∀ a. x0 = mklist(a, #oc(a, x0)) ↔ x0 -l a = [] ⊦ a0 ' + x0 = mklist(a, #oc(a, a0 ') + #oc(a, x0)) ↔ (a0 ' + x0) -l a = []

Heuristic weak cut applied rule cut formula

And obtained the following new goals

Proof step 4:
a = a0, ∀ a. x0 = mklist(a, #oc(a, x0)) ↔ x0 -l a = [] ⊦ a0 ' + x0 = mklist(a, #oc(a, a0 ') + #oc(a, x0)) ↔ (a0 ' + x0) -l a = []

Rule argument

fma: a = a0

Additional information

Used simplifier rules: one-01: ⊦ a ≠ b → #oc(a, b ') = 0;%add-base: ⊦ n + 0 = n; 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-n: ⊦ a ≠ b → (b ' + x) -l a = b ' + (x -l a); from specification list-del%a: ⊦ (x + y) + z = x + y + z; from specification list%e-01: ⊦ a ' + x ≠ []; from specification list%in-14: ⊦ a ' + x = y → a ∈ y; (forward) from specification list%mk-elem: ⊦ a ∈ mklist(b, n) → a = b; (forward) from specification list-last Used formulas: a = a0