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Proof step 4 from proof postfix-length (previous step)

a ' + x0 ⊒ y, # y ≤ # x0, (∃ y. # y < # x0 ∧ x0 ⊒ y) → x0 = [] ⊦

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: list-last inst: name: postfix seq: ⊦ x ⊒ y ↔ (∃ z. z + x = y) subst: [y, x] → [y, a ' + x0] flags: rewrite, current

Additional information

Used simplifier rules: len: ⊦ #(x + y) = # x + # y; from specification list%len-05: ⊦ #(a ' + x) = (# x)+1; from specification list%succ: ⊦ m +1 = m + 1; from specification nat-basic2%a: ⊦ (x + y) + z = x + y + z; from specification list%succ-01: ⊦ m + 1 ≤ n ↔ m < n; from specification nat%l-02: ⊦ ¬ m + n < m; from specification nat-basic2%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic2%c: ⊦ m + n = n + m; from specification nat-basic2 Used terms: y, a ' + x0