Nuprl Lemma : sym_wf
∀[T:Type]. ∀[E:T ⟶ T ⟶ ℙ]. (Sym(T;x,y.E[x;y]) ∈ ℙ)
Proof
Definitions occuring in Statement :
sym: Sym(T;x,y.E[x; y]),
uall: ∀[x:A]. B[x],
prop: ℙ,
so_apply: x[s1;s2],
member: t ∈ T,
function: x:A ⟶ B[x],
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
sym: Sym(T;x,y.E[x; y]),
so_lambda: λ2x.t[x],
implies: P ⇒ Q,
prop: ℙ,
so_apply: x[s1;s2],
so_apply: x[s]
Lemmas referenced :
all_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
Error :isect_memberFormation_alt,
introduction,
cut,
sqequalRule,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
lambdaEquality,
functionEquality,
applyEquality,
hypothesis,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
Error :functionIsType,
Error :universeIsType,
Error :inhabitedIsType,
universeEquality,
isect_memberEquality,
cumulativity
Latex:
\mforall{}[T:Type]. \mforall{}[E:T {}\mrightarrow{} T {}\mrightarrow{} \mBbbP{}]. (Sym(T;x,y.E[x;y]) \mmember{} \mBbbP{})
Date html generated:
2019_06_20-PM-00_28_45
Last ObjectModification:
2018_09_26-AM-11_46_34
Theory : rel_1
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