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Proof step 1 from proof ins (conclusion)

⊦ sort(ins≤(a, x)) = ins≤(a, sort(x))

User applied rule insert spec-lemma

And obtained the following new goals

Proof step 2:
perm(x, y), ordered≤(x), ordered≤(y) ⊦ x = y

Rule argument

spec: olist inst: name: eqdef seq: perm(x, y), ordered≤(x), ordered≤(y) ⊦ x = y subst: [x, y] → [sort(ins≤(a, x)), ins≤(a, sort(x))] flags:

Additional information

Used simplifier rules: perm: ⊦ perm(sort(x), y) ↔ perm(x, y);%Ordered: ⊦ ordered≤(sort(x));%insperm-03: ⊦ perm(ins≤(a, x), y) ↔ perm(a + x, y); from specification olist%c: ⊦ a + x = a ' + x; from specification list%ole-01: ⊦ ordered≤(ins≤(a, x)) ↔ ordered≤(x); from specification olist%sym-02: ⊦ ¬ perm(x, y) → ¬ perm(y, x); (forward) from specification list-perm%app: ⊦ perm(x + y, x + z) ↔ perm(y, z); from specification list-perm%ref: ⊦ perm(x, x); from specification list-perm%a: ⊦ (x + y) + z = x + y + z; from specification list Used terms: sort(ins≤(a, x)), ins≤(a, sort(x))