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Proof step 12 from proof size-rmdup-del (previous step)

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

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 13:
# rmdup(x0) = m0 + 1 ∧ # rmdup(x0) ≠ 0, # rmdup(a0 ' + x0) = m + 1, a ∈ x0, ∀ a. a ∈ x0 → # rmdup(x0 -l a) = m0 ⊦ a = a0, # rmdup(a0 ' + (x0 -l a)) = m

Rule argument

spec: nat inst: name: elim-pred-c seq: n ≠ 0 ⊦ m = n - 1 ↔ n = m + 1 subst: [n, m] → [# rmdup(x0), m0] flags:

Additional information

Used simplifier rules: del-e: ⊦ [] -l a = [];%l: ⊦ # x = 0 ↔ x = []; from specification list-data%rm-empty: ⊦ rmdup(x) = [] ↔ x = []; from specification list-dup%app: ⊦ x + [] = x; from specification list%a: ⊦ (x + y) + z = x + y + z; from specification list%rm-one: ⊦ rmdup(a ') = a '; from specification list-dup%len-02: ⊦ # a ' = 0 +1; from specification list%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%in-empty: ⊦ ¬ a ∈ []; from specification list%n ≠ 0 ⊦ m = n - 1 ↔ n = m + 1; (elim) Used terms: # rmdup(x0), m0