Nuprl Lemma : cancel_wf
∀[T,S:Type]. ∀[op:S ⟶ T ⟶ T]. (Cancel(T;S;op) ∈ ℙ)
Proof
Definitions occuring in Statement :
cancel: Cancel(T;S;op),
uall: ∀[x:A]. B[x],
prop: ℙ,
member: t ∈ T,
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]
Lemmas referenced :
uall_wf,
isect_wf,
equal_wf,
infix_ap_wf
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
isect_memberFormation,
introduction,
cut,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
cumulativity,
hypothesisEquality,
lambdaEquality,
because_Cache,
functionExtensionality,
applyEquality,
hypothesis,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
functionEquality,
isect_memberEquality,
universeEquality
Latex:
\mforall{}[T,S:Type]. \mforall{}[op:S {}\mrightarrow{} T {}\mrightarrow{} T]. (Cancel(T;S;op) \mmember{} \mBbbP{})
Date html generated:
2017_10_01-AM-08_12_58
Last ObjectModification:
2017_02_28-PM-01_57_07
Theory : gen_algebra_1
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