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Proof step 6 from proof ladr-split (previous step)

@(n, m, m0) ' + lax0.to-adr(n) = ax0 + ax1, ∀ n, ax0, ax1. lax0.to-adr(n) = ax0 + ax1 → (∃ lax2, lax1. lax0 = lax2 + lax1 ∧ ax0 = lax2.to-adr(n) ∧ ax1 = lax1.to-adr(n)), @(n, m, m0) ∈ ax0 ∨ @(n, m, m0) ∈ ax1 ⊦ ∃ lax, lax1. @(m, m0) ' + lax0 = lax + lax1 ∧ ax0 = lax.to-adr(n) ∧ ax1 = lax1.to-adr(n)

User applied rule constructor cut

And obtained the following new goals

Proof step 7:
@(n, m, m0) ' + lax0.to-adr(n) = ax0 + ax1, ax0 = adr + ax, ∀ n, ax0, ax1. lax0.to-adr(n) = ax0 + ax1 → (∃ lax2, lax1. lax0 = lax2 + lax1 ∧ ax0 = lax2.to-adr(n) ∧ ax1 = lax1.to-adr(n)), @(n, m, m0) ∈ ax0 ∨ @(n, m, m0) ∈ ax1 ⊦ ∃ lax, lax1. @(m, m0) ' + lax0 = lax + lax1 ∧ ax0 = lax.to-adr(n) ∧ ax1 = lax1.to-adr(n)

Rule argument

var: ax0

Additional information

Used simplifier rules: address-list freely generated by [], +;;% ⊦ [] + ax = ax; (s)%a: ⊦ (ax + ax0) + ax1 = ax + ax0 + ax1; from specification list[address-list-set]% ⊦ ¬ adr ∈ []; (s)% ⊦ lax.to-adr(n) = [] ↔ lax = []; (s)% ⊦ [] + lax = lax; (s)%a: ⊦ (lax + lax0) + lax1 = lax + lax0 + lax1; from specification list[laddress-list]%⊦ (ladr ' + lax).to-adr(n) = @(n, ladr.off, ladr.size) + lax.to-adr(n); (s)% ⊦ @(m, m0).off = m; (s)% ⊦ @(m, m0).size = m0; (s)% ⊦ adr + ax = adr ' + ax; (s)