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Proof step 19 from proof firstn-append-01 (previous step)

# x0 = n1 + # z, x0 = firstn(n1 - 1, x0) + a ' + z, x0 = firstn(# x0 - # z, x0) + z, # z ≤ # x0, ∀ z, a. x0 = firstn(# x0 - 1 + # z, x0) + a ' + z → x0 = firstn(# x0 - # z, x0) + z ⊦ n1 = 0, x0 = firstn(n1, x0) + z

User applied rule insert equation

And closed the goal!

Rule argument

pos: left 1 flags: discard

Additional information

Used simplifier rules: ⊦ m + n - m = n; (s)%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic%c: ⊦ m + n = n + m; from specification nat-basic