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Proof step 4 from proof ins-02 (previous step)

ordered≤(x + a ' + y) ⊦ sort(a ' + x + y) = x + a ' + y

User applied rule insert spec-lemma

And obtained the following new goals

Proof step 5:
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(a ' + x + y), x + a ' + y] flags:

Additional information

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