Nuprl Lemma : assert_equal
∀[a,b:𝔹]. uiff((↑a) = (↑b) ∈ Type;↑a ⇐⇒ ↑b)
Proof
Definitions occuring in Statement :
assert: ↑b,
bool: 𝔹,
uiff: uiff(P;Q),
uall: ∀[x:A]. B[x],
iff: P ⇐⇒ Q,
universe: Type,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uiff: uiff(P;Q),
and: P ∧ Q,
uimplies: b supposing a,
iff: P ⇐⇒ Q,
implies: P ⇒ Q,
guard: {T},
rev_implies: P ⇐ Q,
prop: ℙ,
squash: ↓T,
true: True,
subtype_rel: A ⊆r B
Lemmas referenced :
bool_wf,
iff_wf,
iff_imp_equal_bool,
equal_wf,
assert_witness,
assert_wf,
iff_weakening_equal
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
independent_pairFormation,
lambdaFormation,
hypothesis,
equalitySymmetry,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
equalityTransitivity,
independent_isectElimination,
productElimination,
independent_functionElimination,
hypothesisEquality,
sqequalRule,
independent_pairEquality,
lambdaEquality,
dependent_functionElimination,
instantiate,
universeEquality,
applyEquality,
imageElimination,
because_Cache,
natural_numberEquality,
imageMemberEquality,
baseClosed,
isect_memberEquality,
axiomEquality
Latex:
\mforall{}[a,b:\mBbbB{}]. uiff((\muparrow{}a) = (\muparrow{}b);\muparrow{}a \mLeftarrow{}{}\mRightarrow{} \muparrow{}b)
Date html generated:
2016_05_13-PM-03_56_27
Last ObjectModification:
2016_01_14-PM-07_20_47
Theory : bool_1
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