Nuprl Lemma : equalf_from_lef_wf
∀[y:Type]. ∀[lef:y ⟶ y ⟶ 𝔹]. ∀[x,y:y]. (equalf_from_lef(lef;x;y) ∈ 𝔹)
Proof
Definitions occuring in Statement :
equalf_from_lef: equalf_from_lef(lef;x;y),
bool: 𝔹,
uall: ∀[x:A]. B[x],
member: t ∈ T,
function: x:A ⟶ B[x],
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
equalf_from_lef: equalf_from_lef(lef;x;y),
all: ∀x:A. B[x],
implies: P ⇒ Q,
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
uiff: uiff(P;Q),
and: P ∧ Q,
uimplies: b supposing a,
ifthenelse: if b then t else f fi ,
bfalse: ff
Lemmas referenced :
bool_wf,
eqtt_to_assert,
uiff_transitivity,
equal_wf,
bfalse_wf,
assert_wf,
bnot_wf,
not_wf,
eqff_to_assert,
assert_of_bnot
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
applyEquality,
hypothesisEquality,
thin,
lemma_by_obid,
hypothesis,
lambdaFormation,
sqequalHypSubstitution,
unionElimination,
equalityElimination,
isectElimination,
because_Cache,
productElimination,
independent_isectElimination,
independent_functionElimination,
equalityEquality,
equalityTransitivity,
equalitySymmetry,
dependent_functionElimination,
axiomEquality,
isect_memberEquality,
functionEquality,
universeEquality
Latex:
\mforall{}[y:Type]. \mforall{}[lef:y {}\mrightarrow{} y {}\mrightarrow{} \mBbbB{}]. \mforall{}[x,y:y]. (equalf\_from\_lef(lef;x;y) \mmember{} \mBbbB{})
Date html generated:
2016_05_16-AM-08_42_52
Last ObjectModification:
2015_12_28-PM-06_41_39
Theory : labeled!trees
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