Nuprl Lemma : sym_cl_wf
∀[T:Type]. ∀[E:T ⟶ T ⟶ ℙ]. (E↔ ∈ T ⟶ T ⟶ ℙ)
Proof
Definitions occuring in Statement :
sym_cl: E↔,
uall: ∀[x:A]. B[x],
prop: ℙ,
member: t ∈ T,
function: x:A ⟶ B[x],
universe: Type
Definitions unfolded in proof :
sym_cl: E↔,
uall: ∀[x:A]. B[x],
member: t ∈ T,
prop: ℙ
Lemmas referenced :
and_wf
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
isect_memberFormation,
introduction,
cut,
lambdaEquality,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
applyEquality,
hypothesisEquality,
hypothesis,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
functionEquality,
cumulativity,
universeEquality,
isect_memberEquality,
because_Cache
Latex:
\mforall{}[T:Type]. \mforall{}[E:T {}\mrightarrow{} T {}\mrightarrow{} \mBbbP{}]. (E\mrightleftharpoons{} \mmember{} T {}\mrightarrow{} T {}\mrightarrow{} \mBbbP{})
Date html generated:
2016_05_15-PM-00_01_31
Last ObjectModification:
2015_12_26-PM-11_26_17
Theory : gen_algebra_1
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