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Proof step 8 from proof inv-flashsize-append (previous step)

⊦ #(x + a ') = #(lax + @(m, m0) ') ∧ (∀ n. n < #(x + a ') → (lax + @(m, m0) ')[n].size = (x + a ')[n].flashsize) ↔ # x = # lax ∧ (∀ n. n < # x → lax[n].size = x[n].flashsize) ∧ m0 = a.flashsize

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 9:
# x = # lax ⊦ (∀ n. ¬ # lax < n → (lax + @(m, m0) ')[n].size = (x + a ')[n].flashsize) ↔ (∀ n. n < # lax → lax[n].size = x[n].flashsize) ∧ m0 = a.flashsize

Rule argument

Additional information

Used simplifier rules: ⊦ m < n + 1 ↔ ¬ n < m; (s)%c: ⊦ m + n = n + m; from specification nat-basic%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic% ⊦ m + n = m + n0 ↔ n = n0; (s)%a: ⊦ (lax + lax0) + lax1 = lax + lax0 + lax1; from specification list[laddress-list]% ⊦ # ladr ' = 0 +1; (s)% ⊦ #(lax + lax0) = # lax + # lax0; (s)%a: ⊦ (x + y) + z = x + y + z; from specification list% ⊦ # a ' = 0 +1; (s)% ⊦ #(x + y) = # x + # y; (s)