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Proof step 63 from proof reach-n-path-n (previous step)

x = r2 + x1 ∧ x ≠ [], r2 = H[r].nxt, x.last = x2.last, # x = 2 + n, # x2 = n + 1, reachable-1(H, r2, r0), reachable-n(H, n, r0, x2.last), path(x, H), path(r2 ' + x2, H), r ∈ H ⊦ r = null, x2 = [], ∃ r0. reachable-1(H, r, r0) ∧ (∃ r1. reachable-1(H, r0, r1) ∧ reachable-n(H, n, r1, x2.last))

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 64:
# x2 = n + 1, (H[r].nxt ' + x1).last = x2.last, # x1 = n + 1, path(H[r].nxt ' + x2, H), r ∈ H, reachable-1(H, H[r].nxt, r0), reachable-n(H, n, r0, x2.last), path(H[r].nxt ' + x1, H) ⊦ r = null, x2 = [], ∃ r0. reachable-1(H, r, r0) ∧ (∃ r1. reachable-1(H, r0, r1) ∧ reachable-n(H, n, r1, x2.last))

Rule argument

Additional information

Used simplifier rules: e-01: ⊦ r ' + x0 ≠ []; from specification list[reflist]%c: ⊦ m + n = n + m; from specification nat-basic2%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic2%add-num-01: n < n0 ⊦ m + (* n) = m0 + (* n0) ↔ m = m0 + (n0 - n); from specification nat%a: ⊦ (x0 + x1) + x2 = x0 + x1 + x2; from specification list[reflist]%len-02: ⊦ # r ' = 0 +1; from specification list[reflist]%len: ⊦ #(x0 + x1) = # x0 + # x1; from specification list[reflist]%c: ⊦ r + x0 = r ' + x0; from specification list[reflist]