### Nuprl Lemma : sq_stable__cancel

`∀[T,S:Type]. ∀[op:S ⟶ T ⟶ T].  SqStable(Cancel(T;S;op))`

Proof

Definitions occuring in Statement :  cancel: `Cancel(T;S;op)` sq_stable: `SqStable(P)` uall: `∀[x:A]. B[x]` function: `x:A ⟶ B[x]` universe: `Type`
Definitions unfolded in proof :  cancel: `Cancel(T;S;op)` uall: `∀[x:A]. B[x]` member: `t ∈ T` so_lambda: `λ2x.t[x]` uimplies: `b supposing a` infix_ap: `x f y` prop: `ℙ` so_apply: `x[s]` implies: `P `` Q` sq_stable: `SqStable(P)`
Lemmas referenced :  sq_stable__uall uall_wf isect_wf equal_wf infix_ap_wf sq_stable__equal squash_wf
Rules used in proof :  sqequalSubstitution sqequalRule sqequalReflexivity sqequalTransitivity computationStep isect_memberFormation introduction cut extract_by_obid sqequalHypSubstitution isectElimination thin hypothesisEquality lambdaEquality cumulativity because_Cache functionExtensionality applyEquality hypothesis independent_functionElimination dependent_functionElimination axiomEquality isect_memberEquality equalityTransitivity equalitySymmetry functionEquality universeEquality

Latex:
\mforall{}[T,S:Type].  \mforall{}[op:S  {}\mrightarrow{}  T  {}\mrightarrow{}  T].    SqStable(Cancel(T;S;op))

Date html generated: 2017_10_01-AM-08_12_59
Last ObjectModification: 2017_02_28-PM-01_57_30

Theory : gen_algebra_1

Home Index