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Proof step 28 from proof reach-n-path-n (previous step)

reachable-1(H, r, r1), reachable-1(H, r1, r2), reachable-1(H, r2, r3), reachable-n(H, n0, r3, r0), ∀ H0, r4, r5. (∃ r6. reachable-1(H0, r4, r6) ∧ (∃ r1. reachable-1(H0, r6, r1) ∧ reachable-n(H0, n0, r1, r5))) ↔ (∃ x. path(x, H0) ∧ hd x = r4 ∧ x.last = r5 ∧ # x = 3 + n0) ⊦ ∃ x. path(x, H) ∧ hd x = r ∧ x.last = r0 ∧ # x = 4 + n0

User applied rule all left

And obtained the following new goals

Proof step 29:
reachable-1(H, r, r1), reachable-1(H, r1, r2), reachable-1(H, r2, r3), reachable-n(H, n0, r3, r0), (∃ r6. reachable-1(H, r1, r6) ∧ (∃ r1. reachable-1(H, r6, r1) ∧ reachable-n(H, n0, r1, r0))) ↔ (∃ x. path(x, H) ∧ hd x = r1 ∧ x.last = r0 ∧ # x = 3 + n0) ⊦ ∃ x. path(x, H) ∧ hd x = r ∧ x.last = r0 ∧ # x = 4 + n0

Rule argument

pos: left 5 terms: H, r1, r0 abort: F discard: T computed: F

Additional information

Used terms: H, r1, r0