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Proof step 8 from proof ls-push (conclusion)

⊦ (o[ls(r, x)] * true)[rs, cf, af(r ; o)] ∧ (o0[r => a × r0] * true)[rs, cf, af] ∧ o ≠ o0 ∧ (o[ls(r0, x0)] * true)[rs, cf, af] → (x ≠ a ' + x0 ↔ false)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 7:
(o[ls(r, x)] * true)[rs, cf, af(r ; o)], (o[ls(r0, x0)] * o0[r => a × r0] * true)[rs, cf, af] ⊦ o = o0, x = a ' + x0

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ (R0 * R)[rs, cf, af] → (true * R)[rs, cf, af]], [CSIMPSEQ : ⊦ (o[P] * true)[rs, cf, af] ∧ o0 ≠ o → ( (o0[P0] * true)[rs, cf, af] ↔ (o[P] * o0[P0] * true)[rs, cf, af])], [CSIMPSEQ : ⊦ R0 * R1 = R1 * R0], [CSIMPSEQ : ⊦ (R0 * R1) * R2 = R0 * R1 * R2])]]